Example #1
0
bool LinearTermTests::testLinearTermEvaluation()
{
  bool success = true;
  double eps = .1;

  FunctionPtr one = Function::constant(1.0);
  vector<double> e1,e2;
  e1.push_back(1.0);
  e1.push_back(0.0);
  e2.push_back(0.0);
  e2.push_back(1.0);

  // define test variables
  VarFactoryPtr varFactory = VarFactory::varFactory();
  VarPtr tau = varFactory->testVar("\\tau", HDIV);
  VarPtr v = varFactory->testVar("v", HGRAD);

  // define a couple LinearTerms
  LinearTermPtr vVecLT = Teuchos::rcp(new LinearTerm);
  LinearTermPtr tauVecLT = Teuchos::rcp(new LinearTerm);
  vVecLT->addTerm(sqrt(eps)*v->grad());
  tauVecLT->addTerm((1/sqrt(eps))*tau);

  //////////////////// evaluate LinearTerms /////////////////

  map<int,FunctionPtr> errRepMap;
  errRepMap[v->ID()] = one;
  errRepMap[tau->ID()] = one*e1+one*e2; // vector valued fxn (1,1)
  FunctionPtr errTau = tauVecLT->evaluate(errRepMap,false);
  FunctionPtr errV = vVecLT->evaluate(errRepMap,false);
  try
  {
    bool xTauZero = errTau->x()->isZero();
    bool yTauZero = errTau->y()->isZero();
    bool xVZero = errV->dx()->isZero();
    bool yVZero = errV->dy()->isZero();

  }
  catch (...)
  {
    cout << "testLinearTermEvaluation: Caught exception.\n";
    success = false;
  }
  /*
  FunctionPtr xErr = (errTau->x())*(errTau->x()) + (errV->dx())*(errV->dx());
  FunctionPtr yErr = (errTau->y())*(errTau->y()) + (errV->dy())*(errV->dy());
  double xErrVal = xErr->integrate(mesh,15,true);
  */

  // if we don't crash, return success
  return success;

}
void PoissonExactSolution::setUseSinglePointBCForPHI(bool useSinglePointBCForPhi, IndexType vertexIndexForZeroValue)
{
  FunctionPtr phi_exact = phi();

  VarFactoryPtr vf = _bf->varFactory();
  VarPtr psi_hat_n = vf->fluxVar(PoissonBilinearForm::S_PSI_HAT_N);
  VarPtr q = vf->testVar(PoissonBilinearForm::S_Q, HGRAD);

  VarPtr phi = vf->fieldVar(PoissonBilinearForm::S_PHI);

  SpatialFilterPtr wholeBoundary = SpatialFilter::allSpace();

  FunctionPtr n = Function::normal();
  FunctionPtr psi_n_exact = phi_exact->grad() * n;

  _bc = BC::bc();
  _bc->addDirichlet(psi_hat_n, wholeBoundary, psi_n_exact);
  if (!useSinglePointBCForPhi)
  {
    _bc->addZeroMeanConstraint(phi);

  }
  else
  {
    std::vector<double> point = getPointForBCImposition();
    double value = Function::evaluate(phi_exact, point[0], point[1]);
//    cout << "PoissonExactSolution: imposing phi = " << value << " at (" << point[0] << ", " << point[1] << ")\n";
    _bc->addSpatialPointBC(phi->ID(), value, point);
  }
}
void writePatchValues(double xMin, double xMax, double yMin, double yMax,
                      SolutionPtr solution, VarPtr u1, string filename,
                      int numPoints=100)
{
  FieldContainer<double> points = pointGrid(xMin,xMax,yMin,yMax,numPoints);
  FieldContainer<double> values(numPoints*numPoints);
  solution->solutionValues(values, u1->ID(), points);
  ofstream fout(filename.c_str());
  fout << setprecision(15);

  fout << "X = zeros(" << numPoints << ",1);\n";
  //    fout << "Y = zeros(numPoints);\n";
  fout << "U = zeros(" << numPoints << "," << numPoints << ");\n";
  for (int i=0; i<numPoints; i++)
  {
    fout << "X(" << i+1 << ")=" << points(i,0) << ";\n";
  }
  for (int i=0; i<numPoints; i++)
  {
    fout << "Y(" << i+1 << ")=" << points(i,1) << ";\n";
  }

  for (int i=0; i<numPoints; i++)
  {
    for (int j=0; j<numPoints; j++)
    {
      int pointIndex = i*numPoints + j;
      fout << "U("<<i+1<<","<<j+1<<")=" << values(pointIndex) << ";" << endl;
    }
  }
  fout.close();
}
map<int, FunctionPtr > PreviousSolutionFunction::functionMap( vector< VarPtr > varPtrs, SolutionPtr soln) {
  map<int, FunctionPtr > functionMap;
  for (vector< VarPtr >::iterator varIt = varPtrs.begin(); varIt != varPtrs.end(); varIt++) {
    VarPtr var = *varIt;
    functionMap[var->ID()] = Teuchos::rcp( new PreviousSolutionFunction(soln, var));
  }
  return functionMap;
}
double integralOverMesh(LinearTermPtr testTerm, VarPtr testVar, FunctionPtr fxnToSubstitute) {
  map<int, FunctionPtr > varAsFunction;
  varAsFunction[testVar->ID()] = fxnToSubstitute;
  
  FunctionPtr substituteOnBoundary = testTerm->evaluate(varAsFunction, true);
  FunctionPtr substituteOnInterior = testTerm->evaluate(varAsFunction, false);
  double integral = substituteOnBoundary->integrate(mesh);
  integral += substituteOnInterior->integrate(mesh);
  return integral;
}
FieldContainer<double> solutionData(FieldContainer<double> &points, SolutionPtr solution, VarPtr u1) {
  int numPoints = points.dimension(0);
  FieldContainer<double> values(numPoints);
  solution->solutionValues(values, u1->ID(), points);
  
  FieldContainer<double> xyzData(numPoints, 3);
  for (int ptIndex=0; ptIndex<numPoints; ptIndex++) {
    xyzData(ptIndex,0) = points(ptIndex,0);
    xyzData(ptIndex,1) = points(ptIndex,1);
    xyzData(ptIndex,2) = values(ptIndex);
  }
  return xyzData;
}
int main(int argc, char *argv[]) {

#ifdef HAVE_MPI
  Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
  choice::MpiArgs args( argc, argv );
#else
  choice::Args args( argc, argv );
#endif
  int rank = Teuchos::GlobalMPISession::getRank();
  int numProcs = Teuchos::GlobalMPISession::getNProc();

  int nCells = args.Input<int>("--nCells", "num cells",2);
  int numSteps = args.Input<int>("--numSteps", "num NR steps",20);

  int polyOrder = 0;
  
  // define our manufactured solution or problem bilinear form:
  bool useTriangles = false;
  
  int pToAdd = 1;

  args.Process();

  int H1Order = polyOrder + 1;
  
  ////////////////////////////////////////////////////////////////////
  // DEFINE VARIABLES 
  ////////////////////////////////////////////////////////////////////
  
  // new-style bilinear form definition
  VarFactory varFactory;
  VarPtr fn = varFactory.fluxVar("\\widehat{\\beta_n_u}");
  VarPtr u = varFactory.fieldVar("u");
  
  VarPtr v = varFactory.testVar("v",HGRAD);
  BFPtr bf = Teuchos::rcp( new BF(varFactory) ); // initialize bilinear form
  
  ////////////////////////////////////////////////////////////////////
  // CREATE MESH 
  ////////////////////////////////////////////////////////////////////
  
  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells , bf, H1Order, H1Order+pToAdd);
  
  ////////////////////////////////////////////////////////////////////
  // INITIALIZE BACKGROUND FLOW FUNCTIONS
  ////////////////////////////////////////////////////////////////////
  BCPtr nullBC = Teuchos::rcp((BC*)NULL); RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL); IPPtr nullIP = Teuchos::rcp((IP*)NULL);
  SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
  SolutionPtr solnPerturbation = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
  
  vector<double> e1(2),e2(2);
  e1[0] = 1; e2[1] = 1;
  
  FunctionPtr u_prev = Teuchos::rcp( new PreviousSolutionFunction(backgroundFlow, u) );
  FunctionPtr beta = e1 * u_prev + Teuchos::rcp( new ConstantVectorFunction( e2 ) );
  
  ////////////////////////////////////////////////////////////////////
  // DEFINE BILINEAR FORM
  ////////////////////////////////////////////////////////////////////
  
  // v:
  bf->addTerm( -u, beta * v->grad());
  bf->addTerm( fn, v);

  ////////////////////////////////////////////////////////////////////
  // DEFINE RHS
  ////////////////////////////////////////////////////////////////////

  Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
  FunctionPtr u_prev_squared_div2 = 0.5 * u_prev * u_prev;  
  rhs->addTerm((e1 * u_prev_squared_div2 + e2 * u_prev) * v->grad());

  // ==================== SET INITIAL GUESS ==========================

  mesh->registerSolution(backgroundFlow);
  FunctionPtr zero = Function::constant(0.0);
  FunctionPtr u0 = Teuchos::rcp( new U0 );
  FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
  //  FunctionPtr parity = Teuchos::rcp(new SideParityFunction);

  FunctionPtr u0_squared_div_2 = 0.5 * u0 * u0;

  map<int, Teuchos::RCP<Function> > functionMap;
  functionMap[u->ID()] = u0;
  //  functionMap[fn->ID()] = -(e1 * u0_squared_div_2 + e2 * u0) * n * parity;
  backgroundFlow->projectOntoMesh(functionMap);

  // ==================== END SET INITIAL GUESS ==========================

  ////////////////////////////////////////////////////////////////////
  // DEFINE INNER PRODUCT
  ////////////////////////////////////////////////////////////////////

  IPPtr ip = Teuchos::rcp( new IP );
  ip->addTerm( v );
  ip->addTerm(v->grad());
  //  ip->addTerm( beta * v->grad() ); // omitting term to make IP non-dependent on u

  ////////////////////////////////////////////////////////////////////
  // DEFINE DIRICHLET BC
  ////////////////////////////////////////////////////////////////////

  SpatialFilterPtr outflowBoundary = Teuchos::rcp( new TopBoundary);
  SpatialFilterPtr inflowBoundary = Teuchos::rcp( new NegatedSpatialFilter(outflowBoundary) );
  Teuchos::RCP<BCEasy> inflowBC = Teuchos::rcp( new BCEasy );
  inflowBC->addDirichlet(fn,inflowBoundary, 
                         ( e1 * u0_squared_div_2 + e2 * u0) * n );
  
  ////////////////////////////////////////////////////////////////////
  // CREATE SOLUTION OBJECT
  ////////////////////////////////////////////////////////////////////

  Teuchos::RCP<Solution> solution = Teuchos::rcp(new Solution(mesh, inflowBC, rhs, ip));
  mesh->registerSolution(solution); solution->setCubatureEnrichmentDegree(10);

  ////////////////////////////////////////////////////////////////////
  // HESSIAN BIT + CHECKS ON GRADIENT + HESSIAN
  ////////////////////////////////////////////////////////////////////

  VarFactory hessianVars = varFactory.getBubnovFactory(VarFactory::BUBNOV_TRIAL);
  VarPtr du = hessianVars.test(u->ID());
  //  BFPtr hessianBF = Teuchos::rcp( new BF(hessianVars) ); // initialize bilinear form

  FunctionPtr du_current  = Teuchos::rcp( new PreviousSolutionFunction(solution, u) );

  FunctionPtr fnhat = Teuchos::rcp(new PreviousSolutionFunction(solution,fn));
  LinearTermPtr residual = Teuchos::rcp(new LinearTerm);// residual
  residual->addTerm(fnhat*v,true);
  residual->addTerm( - (e1 * (u_prev_squared_div2) + e2 * (u_prev)) * v->grad(),true);

  LinearTermPtr Bdu = Teuchos::rcp(new LinearTerm);// residual
  Bdu->addTerm( - du_current*(beta*v->grad()));

  Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(mesh, ip, residual));
  Teuchos::RCP<RieszRep> duRiesz = Teuchos::rcp(new RieszRep(mesh, ip, Bdu));
  riesz->computeRieszRep();
  FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,riesz));
  e_v->writeValuesToMATLABFile(mesh, "e_v.m");
  FunctionPtr posErrPart = Teuchos::rcp(new PositivePart(e_v->dx()));
  //  hessianBF->addTerm(e_v->dx()*u,du); 
  //  hessianBF->addTerm(posErrPart*u,du); 
  //  Teuchos::RCP<NullFilter> nullFilter = Teuchos::rcp(new NullFilter);
  //  Teuchos::RCP<HessianFilter> hessianFilter = Teuchos::rcp(new HessianFilter(hessianBF));

  Teuchos::RCP< LineSearchStep > LS_Step = Teuchos::rcp(new LineSearchStep(riesz));

  double NL_residual = 9e99;
  for (int i = 0;i<numSteps;i++){
    // write matrix to file and then resollve without hessian
    /*
    solution->setFilter(hessianFilter);           
    stringstream oss;
    oss << "hessianMatrix" << i << ".dat";
    solution->setWriteMatrixToFile(true,oss.str());      
    solution->solve(false);

    solution->setFilter(nullFilter);
    oss.str(""); // clear
    oss << "stiffnessMatrix" << i << ".dat";
    solution->setWriteMatrixToFile(false,oss.str());      
    */

    solution->solve(false); // do one solve to initialize things...   
    double stepLength = 1.0;
    stepLength = LS_Step->stepSize(backgroundFlow,solution, NL_residual);

    //      solution->setWriteMatrixToFile(true,"stiffness.dat");    

    backgroundFlow->addSolution(solution,stepLength);
    NL_residual = LS_Step->getNLResidual();
    if (rank==0){
      cout << "NL residual after adding = " << NL_residual << " with step size " << stepLength << endl;    
    }

    double fd_gradient;
    for (int dofIndex = 0;dofIndex<mesh->numGlobalDofs();dofIndex++){
      TestingUtilities::initializeSolnCoeffs(solnPerturbation);
      TestingUtilities::setSolnCoeffForGlobalDofIndex(solnPerturbation,1.0,dofIndex);
      fd_gradient = FiniteDifferenceUtilities::finiteDifferenceGradient(mesh, riesz, backgroundFlow, dofIndex);
      
      // CHECK GRADIENT
      LinearTermPtr b_u =  bf->testFunctional(solnPerturbation);
      map<int,FunctionPtr> NL_err_rep_map;

      NL_err_rep_map[v->ID()] = Teuchos::rcp(new RepFunction(v,riesz));
      FunctionPtr gradient = b_u->evaluate(NL_err_rep_map, TestingUtilities::isFluxOrTraceDof(mesh,dofIndex)); // use boundary part only if flux or trace
      double grad;
      if (TestingUtilities::isFluxOrTraceDof(mesh,dofIndex)){
	grad = gradient->integralOfJump(mesh,10);
      }else{
	grad = gradient->integrate(mesh,10);
      }
      double fdgrad = fd_gradient;
      double diff = grad-fdgrad;
      if (abs(diff)>1e-6 && i>0){
	cout << "Found difference of " << diff << ", " << " with fd val = " << fdgrad << " and gradient = " << grad << " in dof " << dofIndex << ", isTraceDof = " << TestingUtilities::isFluxOrTraceDof(mesh,dofIndex) << endl;
      }
    }
  }
  
  VTKExporter exporter(solution, mesh, varFactory);
  if (rank==0){
    exporter.exportSolution("qopt");
    cout << endl;
  }

  return 0;
}
int main(int argc, char *argv[])
{
  int rank = 0;
#ifdef HAVE_MPI
  // TODO: figure out the right thing to do here...
  // may want to modify argc and argv before we make the following call:
  Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
  rank=mpiSession.getRank();
#else
#endif
  bool useLineSearch = false;

  int pToAdd = 2; // for optimal test function approximation
  int pToAddForStreamFunction = 2;
  double nonlinearStepSize = 1.0;
  double dt = 0.5;
  double nonlinearRelativeEnergyTolerance = 0.015; // used to determine convergence of the nonlinear solution
  //  double nonlinearRelativeEnergyTolerance = 0.15; // used to determine convergence of the nonlinear solution
  double eps = 1.0/64.0; // width of ramp up to 1.0 for top BC;  eps == 0 ==> soln not in H1
  // epsilon above is chosen to match our initial 16x16 mesh, to avoid quadrature errors.
  //  double eps = 0.0; // John Evans's problem: not in H^1
  bool enforceLocalConservation = false;
  bool enforceOneIrregularity = true;
  bool reportPerCellErrors  = true;
  bool useMumps = true;

  int horizontalCells, verticalCells;

  int maxIters = 50; // for nonlinear steps

  vector<double> ReValues;

  // usage: polyOrder [numRefinements]
  // parse args:
  if (argc < 6)
  {
    cout << "Usage: NavierStokesCavityFlowContinuationFixedMesh fieldPolyOrder hCells vCells energyErrorGoal Re0 [Re1 ...]\n";
    return -1;
  }
  int polyOrder = atoi(argv[1]);
  horizontalCells = atoi(argv[2]);
  verticalCells = atoi(argv[3]);
  double energyErrorGoal = atof(argv[4]);
  for (int i=5; i<argc; i++)
  {
    ReValues.push_back(atof(argv[i]));
  }
  if (rank == 0)
  {
    cout << "L^2 order: " << polyOrder << endl;
    cout << "initial mesh size: " << horizontalCells << " x " << verticalCells << endl;
    cout << "energy error goal: " << energyErrorGoal << endl;
    cout << "Reynolds number values for continuation:\n";
    for (int i=0; i<ReValues.size(); i++)
    {
      cout << ReValues[i] << ", ";
    }
    cout << endl;
  }

  FieldContainer<double> quadPoints(4,2);

  quadPoints(0,0) = 0.0; // x1
  quadPoints(0,1) = 0.0; // y1
  quadPoints(1,0) = 1.0;
  quadPoints(1,1) = 0.0;
  quadPoints(2,0) = 1.0;
  quadPoints(2,1) = 1.0;
  quadPoints(3,0) = 0.0;
  quadPoints(3,1) = 1.0;

  // define meshes:
  int H1Order = polyOrder + 1;
  bool useTriangles = false;
  bool meshHasTriangles = useTriangles;

  double minL2Increment = 1e-8;

  // get variable definitions:
  VarFactory varFactory = VGPStokesFormulation::vgpVarFactory();
  u1 = varFactory.fieldVar(VGP_U1_S);
  u2 = varFactory.fieldVar(VGP_U2_S);
  sigma11 = varFactory.fieldVar(VGP_SIGMA11_S);
  sigma12 = varFactory.fieldVar(VGP_SIGMA12_S);
  sigma21 = varFactory.fieldVar(VGP_SIGMA21_S);
  sigma22 = varFactory.fieldVar(VGP_SIGMA22_S);
  p = varFactory.fieldVar(VGP_P_S);

  u1hat = varFactory.traceVar(VGP_U1HAT_S);
  u2hat = varFactory.traceVar(VGP_U2HAT_S);
  t1n = varFactory.fluxVar(VGP_T1HAT_S);
  t2n = varFactory.fluxVar(VGP_T2HAT_S);

  v1 = varFactory.testVar(VGP_V1_S, HGRAD);
  v2 = varFactory.testVar(VGP_V2_S, HGRAD);
  tau1 = varFactory.testVar(VGP_TAU1_S, HDIV);
  tau2 = varFactory.testVar(VGP_TAU2_S, HDIV);
  q = varFactory.testVar(VGP_Q_S, HGRAD);

  FunctionPtr u1_0 = Teuchos::rcp( new U1_0(eps) );
  FunctionPtr u2_0 = Teuchos::rcp( new U2_0 );
  FunctionPtr zero = Function::zero();
  ParameterFunctionPtr Re_param = ParameterFunction::parameterFunction(1);
  VGPNavierStokesProblem problem = VGPNavierStokesProblem(Re_param,quadPoints,
                                   horizontalCells,verticalCells,
                                   H1Order, pToAdd,
                                   u1_0, u2_0,  // BC for u
                                   zero, zero); // zero forcing function
  SolutionPtr solution = problem.backgroundFlow();
  SolutionPtr solnIncrement = problem.solutionIncrement();

  Teuchos::RCP<Mesh> mesh = problem.mesh();
  mesh->registerSolution(solution);
  mesh->registerSolution(solnIncrement);

  ///////////////////////////////////////////////////////////////////////////

  // define bilinear form for stream function:
  VarFactory streamVarFactory;
  VarPtr phi_hat = streamVarFactory.traceVar("\\widehat{\\phi}");
  VarPtr psin_hat = streamVarFactory.fluxVar("\\widehat{\\psi}_n");
  VarPtr psi_1 = streamVarFactory.fieldVar("\\psi_1");
  VarPtr psi_2 = streamVarFactory.fieldVar("\\psi_2");
  VarPtr phi = streamVarFactory.fieldVar("\\phi");
  VarPtr q_s = streamVarFactory.testVar("q_s", HGRAD);
  VarPtr v_s = streamVarFactory.testVar("v_s", HDIV);
  BFPtr streamBF = Teuchos::rcp( new BF(streamVarFactory) );
  streamBF->addTerm(psi_1, q_s->dx());
  streamBF->addTerm(psi_2, q_s->dy());
  streamBF->addTerm(-psin_hat, q_s);

  streamBF->addTerm(psi_1, v_s->x());
  streamBF->addTerm(psi_2, v_s->y());
  streamBF->addTerm(phi, v_s->div());
  streamBF->addTerm(-phi_hat, v_s->dot_normal());

  Teuchos::RCP<Mesh> streamMesh, overkillMesh;

  streamMesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
                                          streamBF, H1Order+pToAddForStreamFunction,
                                          H1Order+pToAdd+pToAddForStreamFunction, useTriangles);

  mesh->registerObserver(streamMesh); // will refine streamMesh in the same way as mesh.

  map<int, double> dofsToL2error; // key: numGlobalDofs, value: total L2error compared with overkill
  vector< VarPtr > fields;
  fields.push_back(u1);
  fields.push_back(u2);
  fields.push_back(sigma11);
  fields.push_back(sigma12);
  fields.push_back(sigma21);
  fields.push_back(sigma22);
  fields.push_back(p);

  if (rank == 0)
  {
    cout << "Starting mesh has " << horizontalCells << " x " << verticalCells << " elements and ";
    cout << mesh->numGlobalDofs() << " total dofs.\n";
    cout << "polyOrder = " << polyOrder << endl;
    cout << "pToAdd = " << pToAdd << endl;
    cout << "eps for top BC = " << eps << endl;

    if (useTriangles)
    {
      cout << "Using triangles.\n";
    }
    if (enforceLocalConservation)
    {
      cout << "Enforcing local conservation.\n";
    }
    else
    {
      cout << "NOT enforcing local conservation.\n";
    }
    if (enforceOneIrregularity)
    {
      cout << "Enforcing 1-irregularity.\n";
    }
    else
    {
      cout << "NOT enforcing 1-irregularity.\n";
    }
  }

  ////////////////////   CREATE BCs   ///////////////////////
  SpatialFilterPtr entireBoundary = Teuchos::rcp( new SpatialFilterUnfiltered );

  FunctionPtr u1_prev = Function::solution(u1,solution);
  FunctionPtr u2_prev = Function::solution(u2,solution);

  FunctionPtr u1hat_prev = Function::solution(u1hat,solution);
  FunctionPtr u2hat_prev = Function::solution(u2hat,solution);


  ////////////////////   SOLVE & REFINE   ///////////////////////

  FunctionPtr vorticity = Teuchos::rcp( new PreviousSolutionFunction(solution, - u1->dy() + u2->dx() ) );
  //  FunctionPtr vorticity = Teuchos::rcp( new PreviousSolutionFunction(solution,sigma12 - sigma21) );
  RHSPtr streamRHS = RHS::rhs();
  streamRHS->addTerm(vorticity * q_s);
  ((PreviousSolutionFunction*) vorticity.get())->setOverrideMeshCheck(true);
  ((PreviousSolutionFunction*) u1_prev.get())->setOverrideMeshCheck(true);
  ((PreviousSolutionFunction*) u2_prev.get())->setOverrideMeshCheck(true);

  BCPtr streamBC = BC::bc();
  //  streamBC->addDirichlet(psin_hat, entireBoundary, u0_cross_n);
  streamBC->addDirichlet(phi_hat, entireBoundary, zero);
  //  streamBC->addZeroMeanConstraint(phi);

  IPPtr streamIP = Teuchos::rcp( new IP );
  streamIP->addTerm(q_s);
  streamIP->addTerm(q_s->grad());
  streamIP->addTerm(v_s);
  streamIP->addTerm(v_s->div());
  SolutionPtr streamSolution = Teuchos::rcp( new Solution( streamMesh, streamBC, streamRHS, streamIP ) );

  if (enforceLocalConservation)
  {
    FunctionPtr zero = Function::zero();
    solution->lagrangeConstraints()->addConstraint(u1hat->times_normal_x() + u2hat->times_normal_y()==zero);
    solnIncrement->lagrangeConstraints()->addConstraint(u1hat->times_normal_x() + u2hat->times_normal_y()==zero);
  }

  if (true)
  {
    FunctionPtr u1_incr = Function::solution(u1, solnIncrement);
    FunctionPtr u2_incr = Function::solution(u2, solnIncrement);
    FunctionPtr sigma11_incr = Function::solution(sigma11, solnIncrement);
    FunctionPtr sigma12_incr = Function::solution(sigma12, solnIncrement);
    FunctionPtr sigma21_incr = Function::solution(sigma21, solnIncrement);
    FunctionPtr sigma22_incr = Function::solution(sigma22, solnIncrement);
    FunctionPtr p_incr = Function::solution(p, solnIncrement);

    FunctionPtr l2_incr = u1_incr * u1_incr + u2_incr * u2_incr + p_incr * p_incr
                          + sigma11_incr * sigma11_incr + sigma12_incr * sigma12_incr
                          + sigma21_incr * sigma21_incr + sigma22_incr * sigma22_incr;

    double energyThreshold = 0.20;
    Teuchos::RCP< RefinementStrategy > refinementStrategy = Teuchos::rcp( new RefinementStrategy( solnIncrement, energyThreshold ));

    for (int i=0; i<ReValues.size(); i++)
    {
      double Re = ReValues[i];
      Re_param->setValue(Re);
      if (rank==0) cout << "Solving with Re = " << Re << ":\n";
      double energyErrorTotal;
      do
      {
        double incr_norm;
        do
        {
          problem.iterate(useLineSearch);
          incr_norm = sqrt(l2_incr->integrate(problem.mesh()));
          if (rank==0)
          {
            cout << "\x1B[2K"; // Erase the entire current line.
            cout << "\x1B[0E"; // Move to the beginning of the current line.
            cout << "Iteration: " << problem.iterationCount() << "; L^2(incr) = " << incr_norm;
            flush(cout);
          }
        }
        while ((incr_norm > minL2Increment ) && (problem.iterationCount() < maxIters));
        if (rank==0) cout << endl;
        problem.setIterationCount(1); // 1 means reuse background flow (which we must, given that we want continuation in Re...)
        energyErrorTotal = solnIncrement->energyErrorTotal(); //solution->energyErrorTotal();
        if (energyErrorTotal > energyErrorGoal)
        {
          refinementStrategy->refine(false);
        }
        if (rank==0)
        {
          cout << "Energy error: " << energyErrorTotal << endl;
        }
      }
      while (energyErrorTotal > energyErrorGoal);
    }
  }

  double energyErrorTotal = solution->energyErrorTotal();
  double incrementalEnergyErrorTotal = solnIncrement->energyErrorTotal();
  if (rank == 0)
  {
    cout << "final mesh has " << mesh->numActiveElements() << " elements and " << mesh->numGlobalDofs() << " dofs.\n";
    cout << "energy error: " << energyErrorTotal << endl;
    cout << "  (Incremental solution's energy error is " << incrementalEnergyErrorTotal << ".)\n";
  }

  FunctionPtr u1_sq = u1_prev * u1_prev;
  FunctionPtr u_dot_u = u1_sq + (u2_prev * u2_prev);
  FunctionPtr u_mag = Teuchos::rcp( new SqrtFunction( u_dot_u ) );
  FunctionPtr u_div = Teuchos::rcp( new PreviousSolutionFunction(solution, u1->dx() + u2->dy() ) );
  FunctionPtr massFlux = Teuchos::rcp( new PreviousSolutionFunction(solution, u1hat->times_normal_x() + u2hat->times_normal_y()) );

  // check that the zero mean pressure is being correctly imposed:
  FunctionPtr p_prev = Teuchos::rcp( new PreviousSolutionFunction(solution,p) );
  double p_avg = p_prev->integrate(mesh);
  if (rank==0)
    cout << "Integral of pressure: " << p_avg << endl;

  // integrate massFlux over each element (a test):
  // fake a new bilinear form so we can integrate against 1
  VarPtr testOne = varFactory.testVar("1",CONSTANT_SCALAR);
  BFPtr fakeBF = Teuchos::rcp( new BF(varFactory) );
  LinearTermPtr massFluxTerm = massFlux * testOne;

  CellTopoPtrLegacy quadTopoPtr = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ));
  DofOrderingFactory dofOrderingFactory(fakeBF);
  int fakeTestOrder = H1Order;
  DofOrderingPtr testOrdering = dofOrderingFactory.testOrdering(fakeTestOrder, *quadTopoPtr);

  int testOneIndex = testOrdering->getDofIndex(testOne->ID(),0);
  vector< ElementTypePtr > elemTypes = mesh->elementTypes(); // global element types
  map<int, double> massFluxIntegral; // cellID -> integral
  double maxMassFluxIntegral = 0.0;
  double totalMassFlux = 0.0;
  double totalAbsMassFlux = 0.0;
  double maxCellMeasure = 0;
  double minCellMeasure = 1;
  for (vector< ElementTypePtr >::iterator elemTypeIt = elemTypes.begin(); elemTypeIt != elemTypes.end(); elemTypeIt++)
  {
    ElementTypePtr elemType = *elemTypeIt;
    vector< ElementPtr > elems = mesh->elementsOfTypeGlobal(elemType);
    vector<GlobalIndexType> cellIDs;
    for (int i=0; i<elems.size(); i++)
    {
      cellIDs.push_back(elems[i]->cellID());
    }
    FieldContainer<double> physicalCellNodes = mesh->physicalCellNodesGlobal(elemType);
    BasisCachePtr basisCache = Teuchos::rcp( new BasisCache(elemType,mesh,polyOrder) ); // enrich by trial space order
    basisCache->setPhysicalCellNodes(physicalCellNodes,cellIDs,true); // true: create side caches
    FieldContainer<double> cellMeasures = basisCache->getCellMeasures();
    FieldContainer<double> fakeRHSIntegrals(elems.size(),testOrdering->totalDofs());
    massFluxTerm->integrate(fakeRHSIntegrals,testOrdering,basisCache,true); // true: force side evaluation
    //      cout << "fakeRHSIntegrals:\n" << fakeRHSIntegrals;
    for (int i=0; i<elems.size(); i++)
    {
      int cellID = cellIDs[i];
      // pick out the ones for testOne:
      massFluxIntegral[cellID] = fakeRHSIntegrals(i,testOneIndex);
    }
    // find the largest:
    for (int i=0; i<elems.size(); i++)
    {
      int cellID = cellIDs[i];
      maxMassFluxIntegral = max(abs(massFluxIntegral[cellID]), maxMassFluxIntegral);
    }
    for (int i=0; i<elems.size(); i++)
    {
      int cellID = cellIDs[i];
      maxCellMeasure = max(maxCellMeasure,cellMeasures(i));
      minCellMeasure = min(minCellMeasure,cellMeasures(i));
      maxMassFluxIntegral = max(abs(massFluxIntegral[cellID]), maxMassFluxIntegral);
      totalMassFlux += massFluxIntegral[cellID];
      totalAbsMassFlux += abs( massFluxIntegral[cellID] );
    }
  }
  if (rank==0)
  {
    cout << "largest mass flux: " << maxMassFluxIntegral << endl;
    cout << "total mass flux: " << totalMassFlux << endl;
    cout << "sum of mass flux absolute value: " << totalAbsMassFlux << endl;
    cout << "largest h: " << sqrt(maxCellMeasure) << endl;
    cout << "smallest h: " << sqrt(minCellMeasure) << endl;
    cout << "ratio of largest / smallest h: " << sqrt(maxCellMeasure) / sqrt(minCellMeasure) << endl;
  }
  if (rank == 0)
  {
    cout << "phi ID: " << phi->ID() << endl;
    cout << "psi1 ID: " << psi_1->ID() << endl;
    cout << "psi2 ID: " << psi_2->ID() << endl;

    cout << "streamMesh has " << streamMesh->numActiveElements() << " elements.\n";
    cout << "solving for approximate stream function...\n";
  }

  streamSolution->solve(useMumps);
  energyErrorTotal = streamSolution->energyErrorTotal();
  if (rank == 0)
  {
    cout << "...solved.\n";
    cout << "Stream mesh has energy error: " << energyErrorTotal << endl;
  }

  if (rank==0)
  {
    solution->writeToVTK("nsCavitySoln.vtk");
    if (! meshHasTriangles )
    {
      massFlux->writeBoundaryValuesToMATLABFile(solution->mesh(), "massFlux.dat");
      u_mag->writeValuesToMATLABFile(solution->mesh(), "u_mag.m");
      u_div->writeValuesToMATLABFile(solution->mesh(), "u_div.m");
      solution->writeFieldsToFile(u1->ID(), "u1.m");
      solution->writeFluxesToFile(u1hat->ID(), "u1_hat.dat");
      solution->writeFieldsToFile(u2->ID(), "u2.m");
      solution->writeFluxesToFile(u2hat->ID(), "u2_hat.dat");
      solution->writeFieldsToFile(p->ID(), "p.m");
      streamSolution->writeFieldsToFile(phi->ID(), "phi.m");

      streamSolution->writeFluxesToFile(phi_hat->ID(), "phi_hat.dat");
      streamSolution->writeFieldsToFile(psi_1->ID(), "psi1.m");
      streamSolution->writeFieldsToFile(psi_2->ID(), "psi2.m");
      vorticity->writeValuesToMATLABFile(streamMesh, "vorticity.m");

      FunctionPtr ten = Teuchos::rcp( new ConstantScalarFunction(10) );
      ten->writeBoundaryValuesToMATLABFile(solution->mesh(), "skeleton.dat");
      cout << "wrote files: u_mag.m, u_div.m, u1.m, u1_hat.dat, u2.m, u2_hat.dat, p.m, phi.m, vorticity.m.\n";
    }
    else
    {
      solution->writeToFile(u1->ID(), "u1.dat");
      solution->writeToFile(u2->ID(), "u2.dat");
      solution->writeToFile(u2->ID(), "p.dat");
      cout << "wrote files: u1.dat, u2.dat, p.dat\n";
    }

    FieldContainer<double> points = pointGrid(0, 1, 0, 1, 100);
    FieldContainer<double> pointData = solutionData(points, streamSolution, phi);
    GnuPlotUtil::writeXYPoints("phi_patch_navierStokes_cavity.dat", pointData);
    set<double> patchContourLevels = diagonalContourLevels(pointData,1);
    vector<string> patchDataPath;
    patchDataPath.push_back("phi_patch_navierStokes_cavity.dat");
    GnuPlotUtil::writeContourPlotScript(patchContourLevels, patchDataPath, "lidCavityNavierStokes.p");

    GnuPlotUtil::writeExactMeshSkeleton("lid_navierStokes_continuation_adaptive", mesh, 2);

    writePatchValues(0, 1, 0, 1, streamSolution, phi, "phi_patch.m");
    writePatchValues(0, .1, 0, .1, streamSolution, phi, "phi_patch_detail.m");
    writePatchValues(0, .01, 0, .01, streamSolution, phi, "phi_patch_minute_detail.m");
    writePatchValues(0, .001, 0, .001, streamSolution, phi, "phi_patch_minute_minute_detail.m");
  }

  return 0;
}
Example #9
0
int main(int argc, char *argv[]) {
  // Process command line arguments
  if (argc > 1)
    numRefs = atof(argv[1]);
#ifdef HAVE_MPI
  Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
  int rank=mpiSession.getRank();
  int numProcs=mpiSession.getNProc();
#else
  int rank = 0;
  int numProcs = 1;
#endif

  FunctionPtr beta = Teuchos::rcp(new Beta());

  ////////////////////////////////////////////////////////////////////
  // DEFINE VARIABLES 
  ////////////////////////////////////////////////////////////////////
  // test variables
  VarFactory varFactory; 
  VarPtr tau = varFactory.testVar("\\tau", HDIV);
  VarPtr v = varFactory.testVar("v", HGRAD);

  // trial variables
  VarPtr uhat = varFactory.traceVar("\\widehat{u}");
  VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
  VarPtr u = varFactory.fieldVar("u");
  VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
  VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");

  ////////////////////////////////////////////////////////////////////
  // CREATE MESH 
  ////////////////////////////////////////////////////////////////////

  BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );

  FieldContainer<double> meshBoundary(4,2);

  meshBoundary(0,0) =  0.0; // x1
  meshBoundary(0,1) = -2.0; // y1
  meshBoundary(1,0) =  4.0;
  meshBoundary(1,1) = -2.0;
  meshBoundary(2,0) =  4.0;
  meshBoundary(2,1) =  2.0;
  meshBoundary(3,0) =  0.0;
  meshBoundary(3,1) =  2.0;

  int horizontalCells = 4, verticalCells = 4;

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
      confusionBF, H1Order, H1Order+pToAdd, false);

  ////////////////////////////////////////////////////////////////////
  // INITIALIZE BACKGROUND FLOW FUNCTIONS
  ////////////////////////////////////////////////////////////////////

  BCPtr nullBC = Teuchos::rcp((BC*)NULL);
  RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
  IPPtr nullIP = Teuchos::rcp((IP*)NULL);
  SolutionPtr prevTimeFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );  
  SolutionPtr flowResidual = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );  

  FunctionPtr u_prev_time = Teuchos::rcp( new PreviousSolutionFunction(prevTimeFlow, u) );

  // ==================== SET INITIAL GUESS ==========================
  double u_free = 0.0;
  double sigma1_free = 0.0;
  double sigma2_free = 0.0;
  map<int, Teuchos::RCP<Function> > functionMap;
  functionMap[u->ID()] = Teuchos::rcp( new ConstantScalarFunction(u_free) );
  functionMap[sigma1->ID()] = Teuchos::rcp( new ConstantScalarFunction(sigma1_free) );
  functionMap[sigma2->ID()] = Teuchos::rcp( new ConstantScalarFunction(sigma2_free) );

  prevTimeFlow->projectOntoMesh(functionMap);
  // ==================== END SET INITIAL GUESS ==========================

  ////////////////////////////////////////////////////////////////////
  // DEFINE BILINEAR FORM
  ////////////////////////////////////////////////////////////////////

  // tau terms:
  confusionBF->addTerm(sigma1 / epsilon, tau->x());
  confusionBF->addTerm(sigma2 / epsilon, tau->y());
  confusionBF->addTerm(u, tau->div());
  confusionBF->addTerm(-uhat, tau->dot_normal());

  // v terms:
  confusionBF->addTerm( sigma1, v->dx() );
  confusionBF->addTerm( sigma2, v->dy() );
  confusionBF->addTerm( beta * u, - v->grad() );
  confusionBF->addTerm( beta_n_u_minus_sigma_n, v);

  ////////////////////////////////////////////////////////////////////
  // TIMESTEPPING TERMS
  ////////////////////////////////////////////////////////////////////
  Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );

  double dt = 0.25;
  FunctionPtr invDt = Teuchos::rcp(new ScalarParamFunction(1.0/dt));    
  if (rank==0){
    cout << "Timestep dt = " << dt << endl;
  }
  if (transient)
  {
    confusionBF->addTerm( u, invDt*v );
    rhs->addTerm( u_prev_time * invDt * v );
  }

  ////////////////////////////////////////////////////////////////////
  // DEFINE INNER PRODUCT
  ////////////////////////////////////////////////////////////////////

  // mathematician's norm
  IPPtr mathIP = Teuchos::rcp(new IP());
  mathIP->addTerm(tau);
  mathIP->addTerm(tau->div());

  mathIP->addTerm(v);
  mathIP->addTerm(v->grad());

  // quasi-optimal norm
  IPPtr qoptIP = Teuchos::rcp(new IP);
  qoptIP->addTerm( v );
  qoptIP->addTerm( tau / epsilon + v->grad() );
  qoptIP->addTerm( beta * v->grad() - tau->div() );

  // robust test norm
  IPPtr robIP = Teuchos::rcp(new IP);
  FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) ); 
  if (!enforceLocalConservation)
  {
    robIP->addTerm( ip_scaling * v );
    if (transient)
      robIP->addTerm( invDt * v );
  }
  robIP->addTerm( sqrt(epsilon) * v->grad() );
  // Weight these two terms for inflow
  FunctionPtr ip_weight = Teuchos::rcp( new IPWeight() );
  robIP->addTerm( ip_weight * beta * v->grad() );
  robIP->addTerm( ip_weight * tau->div() );
  robIP->addTerm( ip_scaling/sqrt(epsilon) * tau );
  if (enforceLocalConservation)
    robIP->addZeroMeanTerm( v );

  ////////////////////////////////////////////////////////////////////
  // DEFINE RHS
  ////////////////////////////////////////////////////////////////////

  FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
  rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!

  ////////////////////////////////////////////////////////////////////
  // DEFINE BC
  ////////////////////////////////////////////////////////////////////

  Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
  // Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );
  SpatialFilterPtr lBoundary = Teuchos::rcp( new LeftBoundary );
  SpatialFilterPtr tbBoundary = Teuchos::rcp( new TopBottomBoundary );
  SpatialFilterPtr rBoundary = Teuchos::rcp( new RightBoundary );
  FunctionPtr u0 = Teuchos::rcp( new ZeroBC );
  FunctionPtr u_inlet = Teuchos::rcp( new InletBC );
  // FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
  bc->addDirichlet(beta_n_u_minus_sigma_n, lBoundary, u_inlet);
  bc->addDirichlet(beta_n_u_minus_sigma_n, tbBoundary, u0);
  bc->addDirichlet(uhat, rBoundary, u0);
  // pc->addConstraint(beta_n_u_minus_sigma_n - uhat == u0, rBoundary);

  ////////////////////////////////////////////////////////////////////
  // CREATE SOLUTION OBJECT
  ////////////////////////////////////////////////////////////////////
  Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) );
  // solution->setFilter(pc);

  // ==================== Enforce Local Conservation ==================
  if (enforceLocalConservation) {
    if (transient)
    {
      FunctionPtr conserved_rhs = u_prev_time * invDt;
      LinearTermPtr conserved_quantity = invDt * u;
      LinearTermPtr flux_part = Teuchos::rcp(new LinearTerm(-1.0, beta_n_u_minus_sigma_n));
      conserved_quantity->addTerm(flux_part, true);
      // conserved_quantity = conserved_quantity - beta_n_u_minus_sigma_n;
      solution->lagrangeConstraints()->addConstraint(conserved_quantity == conserved_rhs);
    }
    else
    {
      FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
      solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero);
    }
  }

  // ==================== Register Solutions ==========================
  mesh->registerSolution(solution);
  mesh->registerSolution(prevTimeFlow); // u_t(i-1)
  mesh->registerSolution(flowResidual); // u_t(i-1)

  double energyThreshold = 0.25; // for mesh refinements
  Teuchos::RCP<RefinementStrategy> refinementStrategy;
  refinementStrategy = Teuchos::rcp(new RefinementStrategy(solution,energyThreshold));

  ////////////////////////////////////////////////////////////////////
  // PSEUDO-TIME SOLVE STRATEGY 
  ////////////////////////////////////////////////////////////////////

  double time_tol = 1e-8;
  for (int refIndex=0; refIndex<=numRefs; refIndex++)
  {
    double L2_time_residual = 1e7;
    int timestepCount = 0;
    if (!transient)
      numTimeSteps = 1;
    while((L2_time_residual > time_tol) && (timestepCount < numTimeSteps))
    {
      solution->solve(false);
      // subtract solutions to get residual
      flowResidual->setSolution(solution); // reset previous time solution to current time sol
      flowResidual->addSolution(prevTimeFlow, -1.0);       
      double L2u = flowResidual->L2NormOfSolutionGlobal(u->ID());
      double L2sigma1 = flowResidual->L2NormOfSolutionGlobal(sigma1->ID());
      double L2sigma2 = flowResidual->L2NormOfSolutionGlobal(sigma2->ID());
      L2_time_residual = sqrt(L2u*L2u + L2sigma1*L2sigma1 + L2sigma2*L2sigma2);
      cout << endl << "Timestep: " << timestepCount << ", dt = " << dt << ", Time residual = " << L2_time_residual << endl;    	

      if (rank == 0)
      {
        stringstream outfile;
        if (transient)
          outfile << "TransientConfusion_" << refIndex << "_" << timestepCount;
        else
          outfile << "TransientConfusion_" << refIndex;
        solution->writeToVTK(outfile.str(), 5);
      }

      //////////////////////////////////////////////////////////////////////////
      // Check conservation by testing against one
      //////////////////////////////////////////////////////////////////////////
      VarPtr testOne = varFactory.testVar("1", CONSTANT_SCALAR);
      // Create a fake bilinear form for the testing
      BFPtr fakeBF = Teuchos::rcp( new BF(varFactory) );
      // Define our mass flux
      FunctionPtr flux_current_time = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_minus_sigma_n) );
      FunctionPtr delta_u = Teuchos::rcp( new PreviousSolutionFunction(flowResidual, u) );
      LinearTermPtr surfaceFlux = -1.0 * flux_current_time * testOne;
      LinearTermPtr volumeChange = invDt * delta_u * testOne;
      LinearTermPtr massFluxTerm;
      if (transient)
      {
        massFluxTerm = volumeChange;
        // massFluxTerm->addTerm(surfaceFlux);
      }
      else
      {
        massFluxTerm = surfaceFlux;
      }
      // cout << "surface case = " << surfaceFlux->summands()[0].first->boundaryValueOnly() << " volume case = " << volumeChange->summands()[0].first->boundaryValueOnly() << endl;

      // FunctionPtr massFlux= Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_minus_sigma_n) );
      // LinearTermPtr massFluxTerm = massFlux * testOne;

      Teuchos::RCP<shards::CellTopology> quadTopoPtr = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ));
      DofOrderingFactory dofOrderingFactory(fakeBF);
      int fakeTestOrder = H1Order;
      DofOrderingPtr testOrdering = dofOrderingFactory.testOrdering(fakeTestOrder, *quadTopoPtr);

      int testOneIndex = testOrdering->getDofIndex(testOne->ID(),0);
      vector< ElementTypePtr > elemTypes = mesh->elementTypes(); // global element types
      map<int, double> massFluxIntegral; // cellID -> integral
      double maxMassFluxIntegral = 0.0;
      double totalMassFlux = 0.0;
      double totalAbsMassFlux = 0.0;
      for (vector< ElementTypePtr >::iterator elemTypeIt = elemTypes.begin(); elemTypeIt != elemTypes.end(); elemTypeIt++) 
      {
        ElementTypePtr elemType = *elemTypeIt;
        vector< ElementPtr > elems = mesh->elementsOfTypeGlobal(elemType);
        vector<int> cellIDs;
        for (int i=0; i<elems.size(); i++) {
          cellIDs.push_back(elems[i]->cellID());
        }
        FieldContainer<double> physicalCellNodes = mesh->physicalCellNodesGlobal(elemType);
        BasisCachePtr basisCache = Teuchos::rcp( new BasisCache(elemType,mesh) );
        basisCache->setPhysicalCellNodes(physicalCellNodes,cellIDs,true); // true: create side caches
        FieldContainer<double> cellMeasures = basisCache->getCellMeasures();
        FieldContainer<double> fakeRHSIntegrals(elems.size(),testOrdering->totalDofs());
        massFluxTerm->integrate(fakeRHSIntegrals,testOrdering,basisCache,true); // true: force side evaluation
        for (int i=0; i<elems.size(); i++) {
          int cellID = cellIDs[i];
          // pick out the ones for testOne:
          massFluxIntegral[cellID] = fakeRHSIntegrals(i,testOneIndex);
        }
        // find the largest:
        for (int i=0; i<elems.size(); i++) {
          int cellID = cellIDs[i];
          maxMassFluxIntegral = max(abs(massFluxIntegral[cellID]), maxMassFluxIntegral);
        }
        for (int i=0; i<elems.size(); i++) {
          int cellID = cellIDs[i];
          maxMassFluxIntegral = max(abs(massFluxIntegral[cellID]), maxMassFluxIntegral);
          totalMassFlux += massFluxIntegral[cellID];
          totalAbsMassFlux += abs( massFluxIntegral[cellID] );
        }
      }

      // Print results from processor with rank 0
      if (rank == 0)
      {
        cout << "largest mass flux: " << maxMassFluxIntegral << endl;
        cout << "total mass flux: " << totalMassFlux << endl;
        cout << "sum of mass flux absolute value: " << totalAbsMassFlux << endl;
      }

      prevTimeFlow->setSolution(solution); // reset previous time solution to current time sol
      timestepCount++;
    }

    if (refIndex < numRefs){
      if (rank==0){
        cout << "Performing refinement number " << refIndex << endl;
      }     
      refinementStrategy->refine(rank==0);    
      // RESET solution every refinement - make sure discretization error doesn't creep in
      // prevTimeFlow->projectOntoMesh(functionMap);
    }
  }

  return 0;
}
Example #10
0
bool LobattoBasisTests::testSimpleStiffnessMatrix() {
  bool success = true;
  
  int rank = Teuchos::GlobalMPISession::getRank();
  
  VarFactory varFactory;
  VarPtr u = varFactory.fieldVar("u");
  VarPtr un = varFactory.fluxVar("un_hat");
  VarPtr v = varFactory.testVar("v", HGRAD);
  
  BFPtr bf = Teuchos::rcp( new BF(varFactory) );
  vector<double> beta;
  beta.push_back(1);
  beta.push_back(1);
  bf->addTerm(beta * u, v->grad());
  bf->addTerm(un, v);
  
  DofOrderingPtr trialSpace = Teuchos::rcp( new DofOrdering );
  DofOrderingPtr testSpace = Teuchos::rcp( new DofOrdering );
  
  const int numSides = 4;
  const int spaceDim = 2;
  
  int fieldOrder = 3;
  int testOrder = fieldOrder+2;
  BasisPtr fieldBasis = Camellia::intrepidQuadHGRAD(fieldOrder);
  BasisPtr fluxBasis = Camellia::intrepidLineHGRAD(fieldOrder);
  trialSpace->addEntry(u->ID(), fieldBasis, fieldBasis->rangeRank());
  for (int i=0; i<numSides; i++) {
    trialSpace->addEntry(un->ID(), fluxBasis, fluxBasis->rangeRank(), i);
  }
  
  BasisPtr testBasis = Camellia::lobattoQuadHGRAD(testOrder+1,false); // +1 because it lives in HGRAD
  testSpace->addEntry(v->ID(), testBasis, testBasis->rangeRank());
  
  int numTrialDofs = trialSpace->totalDofs();
  int numTestDofs = testSpace->totalDofs();
  int numCells = 1;
  
  FieldContainer<double> cellNodes(numCells,numSides,spaceDim);
  cellNodes(0,0,0) = 0;
  cellNodes(0,0,1) = 0;
  cellNodes(0,1,0) = 1;
  cellNodes(0,1,1) = 0;
  cellNodes(0,2,0) = 1;
  cellNodes(0,2,1) = 1;
  cellNodes(0,3,0) = 0;
  cellNodes(0,3,1) = 1;
  
  FieldContainer<double> stiffness(numCells,numTestDofs,numTrialDofs);
  
  FieldContainer<double> cellSideParities(numCells,numSides);
  cellSideParities.initialize(1.0);
  
  Teuchos::RCP<shards::CellTopology> quad_4 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ) );
  Teuchos::RCP<ElementType> elemType = Teuchos::rcp( new ElementType(trialSpace, testSpace, quad_4));
  
  BasisCachePtr basisCache = Teuchos::rcp( new BasisCache(elemType) );
  vector<GlobalIndexType> cellIDs;
  cellIDs.push_back(0);
  basisCache->setPhysicalCellNodes(cellNodes, cellIDs, true);
  bf->stiffnessMatrix(stiffness, elemType, cellSideParities, basisCache);

  // TODO: finish this test
  
//  cout << stiffness;
  if (rank==0)
    cout << "Warning: testSimpleStiffnessMatrix() unfinished.\n";
  
  return success;
}
Example #11
0
// tests to make sure that the rieszNorm computed via matrices is the same as the one computed thru direct integration
bool ScratchPadTests::testRieszIntegration()
{
  double tol = 1e-11;
  bool success = true;

  int nCells = 2;
  double eps = .25;

  ////////////////////   DECLARE VARIABLES   ///////////////////////

  // define test variables
  VarFactoryPtr varFactory = VarFactory::varFactory();
  VarPtr tau = varFactory->testVar("\\tau", HDIV);
  VarPtr v = varFactory->testVar("v", HGRAD);

  // define trial variables
  VarPtr uhat = varFactory->traceVar("\\widehat{u}");
  VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
  VarPtr u = varFactory->fieldVar("u");
  VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
  VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");

  vector<double> beta;
  beta.push_back(1.0);
  beta.push_back(0.0);

  ////////////////////   DEFINE BILINEAR FORM   ///////////////////////

  BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
  // tau terms:
  confusionBF->addTerm(sigma1 / eps, tau->x());
  confusionBF->addTerm(sigma2 / eps, tau->y());
  confusionBF->addTerm(u, tau->div());
  confusionBF->addTerm(uhat, -tau->dot_normal());

  // v terms:
  confusionBF->addTerm( sigma1, v->dx() );
  confusionBF->addTerm( sigma2, v->dy() );
  confusionBF->addTerm( -u, beta * v->grad() );
  confusionBF->addTerm( beta_n_u_minus_sigma_n, v);

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////

  // robust test norm
  IPPtr ip = Teuchos::rcp(new IP);

  // just H1 projection
  ip->addTerm(v->grad());
  ip->addTerm(v);
  ip->addTerm(tau);
  ip->addTerm(tau->div());

  ////////////////////   SPECIFY RHS AND HELPFUL FUNCTIONS   ///////////////////////

  FunctionPtr n = Function::normal();
  vector<double> e1,e2;
  e1.push_back(1.0);
  e1.push_back(0.0);
  e2.push_back(0.0);
  e2.push_back(1.0);
  FunctionPtr one = Function::constant(1.0);

  FunctionPtr zero = Function::constant(0.0);
  RHSPtr rhs = RHS::rhs();
  FunctionPtr f = one;
  rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!

  ////////////////////   CREATE BCs   ///////////////////////
  BCPtr bc = BC::bc();
  SpatialFilterPtr squareBoundary = Teuchos::rcp( new SquareBoundary );

  bc->addDirichlet(uhat, squareBoundary, zero);

  ////////////////////   BUILD MESH   ///////////////////////

  // define nodes for mesh
  int order = 2;
  int H1Order = order+1;
  int pToAdd = 2;

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);

  ////////////////////   SOLVE & REFINE   ///////////////////////

  LinearTermPtr lt = Teuchos::rcp(new LinearTerm);
  FunctionPtr fxn = Function::xn(1); // fxn = x
  lt->addTerm(fxn*v + fxn->grad()*v->grad());
  lt->addTerm(fxn*tau->x() + fxn*tau->y() + (fxn->dx() + fxn->dy())*tau->div());
  Teuchos::RCP<RieszRep> rieszLT = Teuchos::rcp(new RieszRep(mesh, ip, lt));
  rieszLT->computeRieszRep();
  double rieszNorm = rieszLT->getNorm();
  FunctionPtr e_v = RieszRep::repFunction(v,rieszLT);
  FunctionPtr e_tau = RieszRep::repFunction(tau,rieszLT);
  map<int,FunctionPtr> repFxns;
  repFxns[v->ID()] = e_v;
  repFxns[tau->ID()] = e_tau;

  double integratedNorm = sqrt((lt->evaluate(repFxns,false))->integrate(mesh,5,true));
  success = abs(rieszNorm-integratedNorm)<tol;
  if (success==false)
  {
    cout << "Failed testRieszIntegration; riesz norm is computed to be = " << rieszNorm << ", while using integration it's computed to be " << integratedNorm << endl;
    return success;
  }
  return success;
}
Example #12
0
bool ScratchPadTests::testGalerkinOrthogonality()
{

  double tol = 1e-11;
  bool success = true;

  ////////////////////   DECLARE VARIABLES   ///////////////////////
  // define test variables
  VarFactoryPtr varFactory = VarFactory::varFactory();
  VarPtr v = varFactory->testVar("v", HGRAD);

  vector<double> beta;
  beta.push_back(1.0);
  beta.push_back(1.0);

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////

  // robust test norm
  IPPtr ip = Teuchos::rcp(new IP);
  ip->addTerm(v);
  ip->addTerm(beta*v->grad());

  // define trial variables
  VarPtr beta_n_u = varFactory->fluxVar("\\widehat{\\beta \\cdot n }");
  VarPtr u = varFactory->fieldVar("u");

  ////////////////////   BUILD MESH   ///////////////////////

  BFPtr convectionBF = Teuchos::rcp( new BF(varFactory) );

  FunctionPtr n = Function::normal();
  // v terms:
  convectionBF->addTerm( -u, beta * v->grad() );
  convectionBF->addTerm( beta_n_u, v);

  // define nodes for mesh
  int order = 2;
  int H1Order = order+1;
  int pToAdd = 1;

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(4, convectionBF, H1Order, H1Order+pToAdd);

  ////////////////////   SOLVE   ///////////////////////

  RHSPtr rhs = RHS::rhs();
  BCPtr bc = BC::bc();
  SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
  SpatialFilterPtr outflowBoundary = Teuchos::rcp( new NegatedSpatialFilter(inflowBoundary) );

  FunctionPtr uIn;
  uIn = Teuchos::rcp(new Uinflow); // uses a discontinuous piecewise-constant basis function on left and bottom sides of square
  bc->addDirichlet(beta_n_u, inflowBoundary, beta*n*uIn);

  Teuchos::RCP<Solution> solution;
  solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
  solution->solve(false);
  FunctionPtr uFxn = Function::solution(u, solution);
  FunctionPtr fnhatFxn = Function::solution(beta_n_u,solution);

  // make residual for riesz representation function
  LinearTermPtr residual = Teuchos::rcp(new LinearTerm);// residual
  FunctionPtr parity = Function::sideParity();
  residual->addTerm(-fnhatFxn*v + (beta*uFxn)*v->grad());
  Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(mesh, ip, residual));
  riesz->computeRieszRep();
  map<int,FunctionPtr> err_rep_map;
  err_rep_map[v->ID()] = RieszRep::repFunction(v,riesz);

  ////////////////////   GET BOUNDARY CONDITION DATA    ///////////////////////

  FieldContainer<GlobalIndexType> bcGlobalIndices;
  FieldContainer<double> bcGlobalValues;
  mesh->boundary().bcsToImpose(bcGlobalIndices,bcGlobalValues,*(solution->bc()), NULL);
  set<int> bcInds;
  for (int i=0; i<bcGlobalIndices.dimension(0); i++)
  {
    bcInds.insert(bcGlobalIndices(i));
  }

  ////////////////////   CHECK GALERKIN ORTHOGONALITY   ///////////////////////

  BCPtr nullBC;
  RHSPtr nullRHS;
  IPPtr nullIP;
  SolutionPtr solnPerturbation = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );

  map< int, vector<DofInfo> > infoMap = constructGlobalDofToLocalDofInfoMap(mesh);

  for (map< int, vector<DofInfo> >::iterator mapIt = infoMap.begin();
       mapIt != infoMap.end(); mapIt++)
  {
    int dofIndex = mapIt->first;
    vector< DofInfo > dofInfoVector = mapIt->second; // all the local dofs that map to dofIndex
    // create perturbation in direction du
    solnPerturbation->clear(); // clear all solns
    // set each corresponding local dof to 1.0
    for (vector< DofInfo >::iterator dofInfoIt = dofInfoVector.begin();
         dofInfoIt != dofInfoVector.end(); dofInfoIt++)
    {
      DofInfo info = *dofInfoIt;
      FieldContainer<double> solnCoeffs(info.basisCardinality);
      solnCoeffs(info.basisOrdinal) = 1.0;
      solnPerturbation->setSolnCoeffsForCellID(solnCoeffs, info.cellID, info.trialID, info.sideIndex);
    }
    //    solnPerturbation->setSolnCoeffForGlobalDofIndex(1.0,dofIndex);

    LinearTermPtr b_du =  convectionBF->testFunctional(solnPerturbation);
    FunctionPtr gradient = b_du->evaluate(err_rep_map, TestingUtilities::isFluxOrTraceDof(mesh,dofIndex)); // use boundary part only if flux
    double grad = gradient->integrate(mesh,10);
    if (!TestingUtilities::isFluxOrTraceDof(mesh,dofIndex) && abs(grad)>tol)  // if we're not single-precision zero FOR FIELDS
    {
      //      int cellID = mesh->getGlobalToLocalMap()[dofIndex].first;
      cout << "Failed testGalerkinOrthogonality() for fields with diff " << abs(grad) << " at dof " << dofIndex << "; info:" << endl;
      cout << dofInfoString(infoMap[dofIndex]);
      success = false;
    }
  }
  FieldContainer<double> errorJumps(mesh->numGlobalDofs()); //initialized to zero
  // just test fluxes ON INTERNAL SKELETON here
  set<GlobalIndexType> activeCellIDs = mesh->getActiveCellIDsGlobal();
  for (GlobalIndexType activeCellID : activeCellIDs)
  {
    ElementPtr elem = mesh->getElement(activeCellID);
    for (int sideIndex = 0; sideIndex < 4; sideIndex++)
    {
      ElementTypePtr elemType = elem->elementType();
      vector<int> localDofIndices = elemType->trialOrderPtr->getDofIndices(beta_n_u->ID(), sideIndex);
      for (int i = 0; i<localDofIndices.size(); i++)
      {
        int globalDofIndex = mesh->globalDofIndex(elem->cellID(), localDofIndices[i]);
        vector< DofInfo > dofInfoVector = infoMap[globalDofIndex];

        solnPerturbation->clear();
        TestingUtilities::setSolnCoeffForGlobalDofIndex(solnPerturbation,1.0,globalDofIndex);
        // also add in BCs
        for (int i = 0; i<bcGlobalIndices.dimension(0); i++)
        {
          TestingUtilities::setSolnCoeffForGlobalDofIndex(solnPerturbation,bcGlobalValues(i),bcGlobalIndices(i));
        }

        LinearTermPtr b_du =  convectionBF->testFunctional(solnPerturbation);
        FunctionPtr gradient = b_du->evaluate(err_rep_map, TestingUtilities::isFluxOrTraceDof(mesh,globalDofIndex)); // use boundary part only if flux
        double jump = gradient->integrate(mesh,10);
        errorJumps(globalDofIndex) += jump;
      }
    }
  }
  for (int i = 0; i<mesh->numGlobalDofs(); i++)
  {
    if (abs(errorJumps(i))>tol)
    {
      cout << "Failing Galerkin orthogonality test for fluxes with diff " << errorJumps(i) << " at dof " << i << endl;
      cout << dofInfoString(infoMap[i]);
      success = false;
    }
  }

  return success;
}
Example #13
0
// tests whether a mixed type LT
bool ScratchPadTests::testIntegrateDiscontinuousFunction()
{
  bool success = true;

  ////////////////////   DECLARE VARIABLES   ///////////////////////
  // define test variables
  VarFactoryPtr varFactory = VarFactory::varFactory();
  VarPtr v = varFactory->testVar("v", HGRAD);

  vector<double> beta;
  beta.push_back(1.0);
  beta.push_back(1.0);

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////

  // robust test norm
  IPPtr ip = Teuchos::rcp(new IP);
  ip->addTerm(v);
  ip->addTerm(beta*v->grad());

  // for projections
  IPPtr ipL2 = Teuchos::rcp(new IP);
  ipL2->addTerm(v);

  // define trial variables
  VarPtr beta_n_u = varFactory->fluxVar("\\widehat{\\beta \\cdot n }");
  VarPtr u = varFactory->fieldVar("u");

  ////////////////////   BUILD MESH   ///////////////////////

  BFPtr convectionBF = Teuchos::rcp( new BF(varFactory) );

  // v terms:
  convectionBF->addTerm( -u, beta * v->grad() );
  convectionBF->addTerm( beta_n_u, v);

  // define nodes for mesh
  int order = 1;
  int H1Order = order+1;
  int pToAdd = 1;

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(2, 1, convectionBF, H1Order, H1Order+pToAdd);

  ////////////////////   integrate discontinuous function - cellIDFunction   ///////////////////////

  //  FunctionPtr cellIDFxn = Teuchos::rcp(new CellIDFunction); // should be 0 on cellID 0, 1 on cellID 1
  set<int> cellIDs;
  cellIDs.insert(1); // 0 on cell 0, 1 on cell 1
  FunctionPtr indicator = Teuchos::rcp(new IndicatorFunction(cellIDs)); // should be 0 on cellID 0, 1 on cellID 1
  double jumpWeight = 13.3; // some random number
  FunctionPtr edgeRestrictionFxn = Teuchos::rcp(new EdgeFunction);
  FunctionPtr X = Function::xn(1);
  LinearTermPtr integrandLT = Function::constant(1.0)*v + Function::constant(jumpWeight)*X*edgeRestrictionFxn*v;

  // make riesz representation function to more closely emulate the error rep
  LinearTermPtr indicatorLT = Teuchos::rcp(new LinearTerm);// residual
  indicatorLT->addTerm(indicator*v);
  Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(mesh, ipL2, indicatorLT));
  riesz->computeRieszRep();
  map<int,FunctionPtr> vmap;
  vmap[v->ID()] = RieszRep::repFunction(v,riesz); // SHOULD BE L2 projection = same thing!!!

  FunctionPtr volumeIntegrand = integrandLT->evaluate(vmap,false);
  FunctionPtr edgeRestrictedIntegrand = integrandLT->evaluate(vmap,true);

  double edgeRestrictedValue = volumeIntegrand->integrate(mesh,10) + edgeRestrictedIntegrand->integrate(mesh,10);

  double expectedValue = .5 + .5*jumpWeight;
  double diff = abs(expectedValue-edgeRestrictedValue);
  if (abs(diff)>1e-11)
  {
    success = false;
    cout << "Failed testIntegrateDiscontinuousFunction() with expectedValue = " << expectedValue << " and actual value = " << edgeRestrictedValue << endl;
  }
  return success;
}
Example #14
0
// tests whether a mixed type LT
bool ScratchPadTests::testLinearTermEvaluationConsistency()
{
  bool success = true;

  ////////////////////   DECLARE VARIABLES   ///////////////////////
  // define test variables
  VarFactoryPtr varFactory = VarFactory::varFactory();
  VarPtr v = varFactory->testVar("v", HGRAD);

  vector<double> beta;
  beta.push_back(1.0);
  beta.push_back(1.0);

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////

  // robust test norm
  IPPtr ip = Teuchos::rcp(new IP);
  ip->addTerm(v);
  ip->addTerm(beta*v->grad());

  // define trial variables
  VarPtr beta_n_u = varFactory->fluxVar("\\widehat{\\beta \\cdot n }");
  VarPtr u = varFactory->fieldVar("u");

  ////////////////////   BUILD MESH   ///////////////////////

  BFPtr convectionBF = Teuchos::rcp( new BF(varFactory) );

  // v terms:
  convectionBF->addTerm( -u, beta * v->grad() );
  convectionBF->addTerm( beta_n_u, v);

  // define nodes for mesh
  int order = 1;
  int H1Order = order+1;
  int pToAdd = 1;

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(1, convectionBF, H1Order, H1Order+pToAdd);

  ////////////////////   get fake residual   ///////////////////////

  LinearTermPtr lt = Teuchos::rcp(new LinearTerm);
  FunctionPtr edgeFxn = Teuchos::rcp(new EdgeFunction);
  FunctionPtr Xsq = Function::xn(2);
  FunctionPtr Ysq = Function::yn(2);
  FunctionPtr XYsq = Xsq*Ysq;
  lt->addTerm(edgeFxn*v + (beta*XYsq)*v->grad());

  Teuchos::RCP<RieszRep> ltRiesz = Teuchos::rcp(new RieszRep(mesh, ip, lt));
  ltRiesz->computeRieszRep();
  FunctionPtr repFxn = RieszRep::repFunction(v,ltRiesz);
  map<int,FunctionPtr> rep_map;
  rep_map[v->ID()] = repFxn;

  FunctionPtr edgeLt = lt->evaluate(rep_map, true) ;
  FunctionPtr elemLt = lt->evaluate(rep_map, false);

  double edgeVal = edgeLt->integrate(mesh,10);
  double elemVal = elemLt->integrate(mesh,10);
  LinearTermPtr edgeOnlyLt = Teuchos::rcp(new LinearTerm);// residual
  edgeOnlyLt->addTerm(edgeFxn*v);
  FunctionPtr edgeOnly = edgeOnlyLt->evaluate(rep_map,true);
  double edgeOnlyVal = edgeOnly->integrate(mesh,10);

  double diff = edgeOnlyVal-edgeVal;
  if (abs(diff)>1e-11)
  {
    success = false;
    cout << "Failed testLinearTermEvaluationConsistency() with diff = " << diff << endl;
  }

  return success;
}
Example #15
0
// tests to make sure the energy error calculated thru direct integration works for vector valued test functions too
bool ScratchPadTests::testLTResidual()
{
  double tol = 1e-11;
  int rank = Teuchos::GlobalMPISession::getRank();

  bool success = true;

  int nCells = 2;
  double eps = .1;

  ////////////////////   DECLARE VARIABLES   ///////////////////////

  // define test variables
  VarFactoryPtr varFactory = VarFactory::varFactory();
  VarPtr tau = varFactory->testVar("\\tau", HDIV);
  VarPtr v = varFactory->testVar("v", HGRAD);

  // define trial variables
  VarPtr uhat = varFactory->traceVar("\\widehat{u}");
  VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
  VarPtr u = varFactory->fieldVar("u");
  VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
  VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");

  vector<double> beta;
  beta.push_back(1.0);
  beta.push_back(0.0);

  ////////////////////   DEFINE BILINEAR FORM   ///////////////////////

  BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
  // tau terms:
  confusionBF->addTerm(sigma1 / eps, tau->x());
  confusionBF->addTerm(sigma2 / eps, tau->y());
  confusionBF->addTerm(u, tau->div());
  confusionBF->addTerm(uhat, -tau->dot_normal());

  // v terms:
  confusionBF->addTerm( sigma1, v->dx() );
  confusionBF->addTerm( sigma2, v->dy() );
  confusionBF->addTerm( -u, beta * v->grad() );
  confusionBF->addTerm( beta_n_u_minus_sigma_n, v);

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////

  // robust test norm
  IPPtr ip = Teuchos::rcp(new IP);

  // choose the mesh-independent norm even though it may have boundary layers
  ip->addTerm(v->grad());
  ip->addTerm(v);
  ip->addTerm(tau);
  ip->addTerm(tau->div());

  ////////////////////   SPECIFY RHS AND HELPFUL FUNCTIONS   ///////////////////////

  FunctionPtr n = Function::normal();
  vector<double> e1,e2;
  e1.push_back(1.0);
  e1.push_back(0.0);
  e2.push_back(0.0);
  e2.push_back(1.0);
  FunctionPtr one = Function::constant(1.0);

  FunctionPtr zero = Function::constant(0.0);
  RHSPtr rhs = RHS::rhs();
  FunctionPtr f = one; // if this is set to zero instead, we pass the test (a clue?)
  rhs->addTerm( f * v );

  ////////////////////   CREATE BCs   ///////////////////////
  BCPtr bc = BC::bc();
  SpatialFilterPtr squareBoundary = Teuchos::rcp( new SquareBoundary );

  bc->addDirichlet(uhat, squareBoundary, one);

  ////////////////////   BUILD MESH   ///////////////////////
  // define nodes for mesh
  int order = 2;
  int H1Order = order+1;
  int pToAdd = 2;

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);

  ////////////////////   SOLVE & REFINE   ///////////////////////

  Teuchos::RCP<Solution> solution;
  solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
  solution->solve(false);
  double energyError = solution->energyErrorTotal();

  LinearTermPtr residual = rhs->linearTermCopy();
  residual->addTerm(-confusionBF->testFunctional(solution),true);

//  FunctionPtr uh = Function::solution(uhat,solution);
//  FunctionPtr fn = Function::solution(beta_n_u_minus_sigma_n,solution);
//  FunctionPtr uF = Function::solution(u,solution);
//  FunctionPtr sigma = e1*Function::solution(sigma1,solution)+e2*Function::solution(sigma2,solution);
//  residual->addTerm(- (fn*v - uh*tau->dot_normal()));
//  residual->addTerm(- (uF*(tau->div() - beta*v->grad()) + sigma*((1/eps)*tau + v->grad())));
//  residual->addTerm(-(fn*v - uF*beta*v->grad() + sigma*v->grad())); // just v portion
//  residual->addTerm(uh*tau->dot_normal() - uF*tau->div() - sigma*((1/eps)*tau)); // just tau portion

  Teuchos::RCP<RieszRep> rieszResidual = Teuchos::rcp(new RieszRep(mesh, ip, residual));
  rieszResidual->computeRieszRep();
  double energyErrorLT = rieszResidual->getNorm();

  int cubEnrich = 0;
  bool testVsTest = true;
  FunctionPtr e_v = RieszRep::repFunction(v,rieszResidual);
  FunctionPtr e_tau = RieszRep::repFunction(tau,rieszResidual);
  // experiment by Nate: manually specify the error (this appears to produce identical results, as it should)
//  FunctionPtr err = e_v * e_v + e_tau * e_tau + e_v->grad() * e_v->grad() + e_tau->div() * e_tau->div();
  map<int,FunctionPtr> errFxns;
  errFxns[v->ID()] = e_v;
  errFxns[tau->ID()] = e_tau;
  LinearTermPtr ipAtErrFxns = ip->evaluate(errFxns);
  FunctionPtr err = ip->evaluate(errFxns)->evaluate(errFxns);
  double energyErrorIntegrated = sqrt(err->integrate(mesh,cubEnrich,testVsTest));

  // check that energy error computed thru Solution and through rieszRep are the same
  bool success1 = abs(energyError-energyErrorLT)<tol;
  // checks that matrix-computed and integrated errors are the same
  bool success2 = abs(energyErrorLT-energyErrorIntegrated)<tol;
  success = success1==true && success2==true;
  if (!success)
  {
    if (rank==0)
      cout << "Failed testLTResidual; energy error = " << energyError << ", while linearTerm error is computed to be " << energyErrorLT << ", and when computing through integration of the Riesz rep function, error = " << energyErrorIntegrated << endl;
  }
  //  VTKExporter exporter(solution, mesh, varFactory);
  //  exporter.exportSolution("testLTRes");
  //  cout << endl;

  return success;
}
Example #16
0
// tests residual computation on simple convection
bool ScratchPadTests::testLTResidualSimple()
{
  double tol = 1e-11;
  int rank = Teuchos::GlobalMPISession::getRank();

  bool success = true;

  int nCells = 2;

  ////////////////////   DECLARE VARIABLES   ///////////////////////

  // define test variables
  VarFactoryPtr varFactory = VarFactory::varFactory();
  VarPtr v = varFactory->testVar("v", HGRAD);

  // define trial variables
  VarPtr beta_n_u = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
  VarPtr u = varFactory->fieldVar("u");

  vector<double> beta;
  beta.push_back(1.0);
  beta.push_back(1.0);

  ////////////////////   DEFINE BILINEAR FORM   ///////////////////////

  BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
  // v terms:
  confusionBF->addTerm( -u, beta * v->grad() );
  confusionBF->addTerm( beta_n_u, v);

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////

  // robust test norm
  IPPtr ip = Teuchos::rcp(new IP);

  // choose the mesh-independent norm even though it may have BLs
  ip->addTerm(v->grad());
  ip->addTerm(v);

  ////////////////////   SPECIFY RHS AND HELPFUL FUNCTIONS   ///////////////////////

  FunctionPtr n = Function::normal();
  vector<double> e1,e2;
  e1.push_back(1.0);
  e1.push_back(0.0);
  e2.push_back(0.0);
  e2.push_back(1.0);
  FunctionPtr one = Function::constant(1.0);

  FunctionPtr zero = Function::constant(0.0);
  RHSPtr rhs = RHS::rhs();
  FunctionPtr f = one;
  rhs->addTerm( f * v );

  ////////////////////   CREATE BCs   ///////////////////////
  BCPtr bc = BC::bc();
  SpatialFilterPtr boundary = Teuchos::rcp( new InflowSquareBoundary );
  FunctionPtr u_in = Teuchos::rcp(new Uinflow);
  bc->addDirichlet(beta_n_u, boundary, beta*n*u_in);

  ////////////////////   BUILD MESH   ///////////////////////
  // define nodes for mesh
  int order = 2;
  int H1Order = order+1;
  int pToAdd = 2;

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);

  ////////////////////   SOLVE & REFINE   ///////////////////////

  int cubEnrich = 0;

  Teuchos::RCP<Solution> solution;
  solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
  solution->solve(false);
  double energyError = solution->energyErrorTotal();

  LinearTermPtr residual = rhs->linearTermCopy();
  residual->addTerm(-confusionBF->testFunctional(solution),true);

  Teuchos::RCP<RieszRep> rieszResidual = Teuchos::rcp(new RieszRep(mesh, ip, residual));
  rieszResidual->computeRieszRep(cubEnrich);
  double energyErrorLT = rieszResidual->getNorm();

  bool testVsTest = true;
  FunctionPtr e_v = RieszRep::repFunction(v,rieszResidual);
  map<int,FunctionPtr> errFxns;
  errFxns[v->ID()] = e_v;
  FunctionPtr err = (ip->evaluate(errFxns,false))->evaluate(errFxns,false); // don't need boundary terms unless they're in IP
  double energyErrorIntegrated = sqrt(err->integrate(mesh,cubEnrich,testVsTest));
  // check that energy error computed thru Solution and through rieszRep are the same
  success = abs(energyError-energyErrorLT) < tol;
  if (success==false)
  {
    if (rank==0)
      cout << "Failed testLTResidualSimple; energy error = " << energyError << ", while linearTerm error is computed to be " << energyErrorLT << endl;
    return success;
  }
  // checks that matrix-computed and integrated errors are the same
  success = abs(energyErrorLT-energyErrorIntegrated)<tol;
  if (success==false)
  {
    if (rank==0)
      cout << "Failed testLTResidualSimple; energy error = " << energyError << ", while error computed via integration is " << energyErrorIntegrated << endl;
    return success;
  }
  return success;
}
Example #17
0
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
  Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
  choice::MpiArgs args( argc, argv );
#else
  choice::Args args( argc, argv );
#endif
  int commRank = Teuchos::GlobalMPISession::getRank();
  int numProcs = Teuchos::GlobalMPISession::getNProc();

  // Required arguments
  int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
  int norm = args.Input<int>("--norm", "0 = graph\n    1 = robust\n    2 = coupled robust");

  // Optional arguments (have defaults)
  int uniformRefinements = args.Input("--uniformRefinements", "number of uniform refinements", 0);
  bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation", false);
  double radius = args.Input("--r", "cylinder radius", 0.6);
  int Re = args.Input("--Re", "Reynolds number", 1);
  int maxNewtonIterations = args.Input("--maxIterations", "maximum number of Newton iterations", 1);
  int polyOrder = args.Input("--polyOrder", "polynomial order for field variables", 2);
  int deltaP = args.Input("--deltaP", "how much to enrich test space", 2);
  // string saveFile = args.Input<string>("--meshSaveFile", "file to which to save refinement history", "");
  // string replayFile = args.Input<string>("--meshLoadFile", "file with refinement history to replay", "");
  args.Process();

  ////////////////////   PROBLEM DEFINITIONS   ///////////////////////
  int H1Order = polyOrder+1;

  ////////////////////   DECLARE VARIABLES   ///////////////////////
  // define test variables
  VarFactory varFactory;
  VarPtr tau1 = varFactory.testVar("tau1", HDIV);
  VarPtr tau2 = varFactory.testVar("tau2", HDIV);
  VarPtr v1 = varFactory.testVar("v1", HGRAD);
  VarPtr v2 = varFactory.testVar("v2", HGRAD);
  VarPtr vc = varFactory.testVar("vc", HGRAD);

  // define trial variables
  VarPtr u1 = varFactory.fieldVar("u1");
  VarPtr u2 = varFactory.fieldVar("u2");
  VarPtr p = varFactory.fieldVar("p");
  VarPtr u1hat = varFactory.traceVar("u1hat");
  VarPtr u2hat = varFactory.traceVar("u2hat");
  VarPtr t1hat = varFactory.fluxVar("t1hat");
  VarPtr t2hat = varFactory.fluxVar("t2hat");
  VarPtr sigma1 = varFactory.fieldVar("sigma1", VECTOR_L2);
  VarPtr sigma2 = varFactory.fieldVar("sigma2", VECTOR_L2);

  ////////////////////   BUILD MESH   ///////////////////////
  BFPtr bf = Teuchos::rcp( new BF(varFactory) );

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = MeshFactory::shiftedHemkerMesh(-1, 3, 2, radius, bf, H1Order, deltaP);

  ////////////////////////////////////////////////////////////////////
  // INITIALIZE BACKGROUND FLOW FUNCTIONS
  ////////////////////////////////////////////////////////////////////

  BCPtr nullBC = Teuchos::rcp((BC*)NULL);
  RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
  IPPtr nullIP = Teuchos::rcp((IP*)NULL);
  SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );

  vector<double> e1(2); // (1,0)
  e1[0] = 1;
  vector<double> e2(2); // (0,1)
  e2[1] = 1;

  FunctionPtr u1_prev = Function::solution(u1, backgroundFlow);
  FunctionPtr u2_prev = Function::solution(u2, backgroundFlow);
  FunctionPtr sigma1_prev = Function::solution(sigma1, backgroundFlow);
  FunctionPtr sigma2_prev = Function::solution(sigma2, backgroundFlow);

  FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
  FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
  FunctionPtr beta = e1 * u1_prev + e2 * u2_prev;

  // ==================== SET INITIAL GUESS ==========================
  map<int, Teuchos::RCP<Function> > functionMap;
  functionMap[u1->ID()] = one;
  functionMap[u2->ID()] = zero;
  functionMap[sigma1->ID()] = Function::vectorize(zero,zero);
  functionMap[sigma2->ID()] = Function::vectorize(zero,zero);
  functionMap[p->ID()] = zero;

  backgroundFlow->projectOntoMesh(functionMap);

  ////////////////////   DEFINE BILINEAR FORM   ///////////////////////

  // // stress equation
  bf->addTerm( sigma1, tau1 );
  bf->addTerm( sigma2, tau2 );
  bf->addTerm( u1, tau1->div() );
  bf->addTerm( u2, tau2->div() );
  bf->addTerm( -u1hat, tau1->dot_normal() );
  bf->addTerm( -u2hat, tau2->dot_normal() );

  // momentum equation
  // bf->addTerm( Function::xPart(sigma1_prev)*u1, v1 );
  // bf->addTerm( Function::yPart(sigma1_prev)*u2, v1 );
  // bf->addTerm( Function::xPart(sigma2_prev)*u1, v2 );
  // bf->addTerm( Function::yPart(sigma2_prev)*u2, v2 );
  // bf->addTerm( beta*sigma1, v1);
  // bf->addTerm( beta*sigma2, v2);
  bf->addTerm( 1./Re*sigma1, v1->grad() );
  bf->addTerm( 1./Re*sigma2, v2->grad() );
  bf->addTerm( t1hat, v1);
  bf->addTerm( t2hat, v2);
  bf->addTerm( -p, v1->dx() );
  bf->addTerm( -p, v2->dy() );

  // continuity equation
  bf->addTerm( -u1, vc->dx() );
  bf->addTerm( -u2, vc->dy() );
  bf->addTerm( u1hat, vc->times_normal_x() );
  bf->addTerm( u2hat, vc->times_normal_y() );

  ////////////////////   SPECIFY RHS   ///////////////////////
  Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );

  // stress equation
  rhs->addTerm( -sigma1_prev * tau1 );
  rhs->addTerm( -sigma2_prev * tau2 );
  rhs->addTerm( -u1_prev * tau1->div() );
  rhs->addTerm( -u2_prev * tau2->div() );

  // momentum equation
  // rhs->addTerm( -beta*sigma1_prev * v1 );
  // rhs->addTerm( -beta*sigma2_prev * v2 );
  rhs->addTerm( -1./Re*sigma1_prev * v1->grad() );
  rhs->addTerm( -1./Re*sigma2_prev * v2->grad() );

  // continuity equation
  rhs->addTerm( u1_prev * vc->dx() );
  rhs->addTerm( u2_prev * vc->dy() );

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////
  IPPtr ip = Teuchos::rcp(new IP);
  if (norm == 0)
  {
    ip = bf->graphNorm();
  }
  else if (norm == 1)
  {
    // ip = bf->l2Norm();
  }

  ////////////////////   CREATE BCs   ///////////////////////
  Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
  SpatialFilterPtr left = Teuchos::rcp( new ConstantXBoundary(-1) );
  SpatialFilterPtr right = Teuchos::rcp( new ConstantXBoundary(3) );
  SpatialFilterPtr top = Teuchos::rcp( new ConstantYBoundary(1) );
  SpatialFilterPtr bottom = Teuchos::rcp( new ConstantYBoundary(-1) );
  SpatialFilterPtr circle = Teuchos::rcp( new CircleBoundary(radius) );
  FunctionPtr boundaryU1 = Teuchos::rcp( new BoundaryU1 );
  bc->addDirichlet(u1hat, left, boundaryU1);
  bc->addDirichlet(u2hat, left, zero);
  bc->addDirichlet(u1hat, right, boundaryU1);
  bc->addDirichlet(u2hat, right, zero);
  bc->addDirichlet(u1hat, top, zero);
  bc->addDirichlet(u2hat, top, zero);
  bc->addDirichlet(u1hat, bottom, zero);
  bc->addDirichlet(u2hat, bottom, zero);
  bc->addDirichlet(u1hat, circle, zero);
  bc->addDirichlet(u2hat, circle, zero);

  // zero mean constraint on pressure
  bc->addZeroMeanConstraint(p);

  Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );

  if (enforceLocalConservation)
  {
    solution->lagrangeConstraints()->addConstraint(u1hat->times_normal_x() + u2hat->times_normal_y() == zero);
  }

  // ==================== Register Solutions ==========================
  mesh->registerSolution(solution);
  mesh->registerSolution(backgroundFlow);

  // Teuchos::RCP< RefinementHistory > refHistory = Teuchos::rcp( new RefinementHistory );
  // mesh->registerObserver(refHistory);

  ////////////////////   SOLVE & REFINE   ///////////////////////
  double energyThreshold = 0.2; // for mesh refinements
  RefinementStrategy refinementStrategy( solution, energyThreshold );
  VTKExporter exporter(backgroundFlow, mesh, varFactory);
  ofstream errOut;
  ofstream fluxOut;
  if (commRank == 0)
  {
    errOut.open("stokeshemker_err.txt");
    fluxOut.open("stokeshemker_flux.txt");
  }
  errOut.precision(15);
  fluxOut.precision(15);

  // Cell IDs for flux calculations
  vector< pair<ElementPtr, int> > cellFace0;
  vector< pair<ElementPtr, int> > cellFace1;
  vector< pair<ElementPtr, int> > cellFace2;
  vector< pair<ElementPtr, int> > cellFace3;
  vector< pair<ElementPtr, int> > cellFace4;
  cellFace0.push_back(make_pair(mesh->getElement(12), 3));
  cellFace0.push_back(make_pair(mesh->getElement(13), 3));
  cellFace0.push_back(make_pair(mesh->getElement(14), 3));
  cellFace0.push_back(make_pair(mesh->getElement(15), 3));
  cellFace1.push_back(make_pair(mesh->getElement(12), 1));
  cellFace1.push_back(make_pair(mesh->getElement(13), 1));
  cellFace1.push_back(make_pair(mesh->getElement(14), 1));
  cellFace1.push_back(make_pair(mesh->getElement(15), 1));
  cellFace2.push_back(make_pair(mesh->getElement(11), 1));
  cellFace2.push_back(make_pair(mesh->getElement(2 ), 0));
  cellFace2.push_back(make_pair(mesh->getElement(5 ), 2));
  cellFace2.push_back(make_pair(mesh->getElement(16), 1));
  cellFace3.push_back(make_pair(mesh->getElement(9 ), 3));
  cellFace3.push_back(make_pair(mesh->getElement(8 ), 3));
  cellFace3.push_back(make_pair(mesh->getElement(19), 3));
  cellFace3.push_back(make_pair(mesh->getElement(18), 3));
  cellFace4.push_back(make_pair(mesh->getElement(9 ), 1));
  cellFace4.push_back(make_pair(mesh->getElement(8 ), 1));
  cellFace4.push_back(make_pair(mesh->getElement(19), 1));
  cellFace4.push_back(make_pair(mesh->getElement(18), 1));

  // // for loading refinement history
  // if (replayFile.length() > 0) {
  //   RefinementHistory refHistory;
  //   replayFile = replayFile;
  //   refHistory.loadFromFile(replayFile);
  //   refHistory.playback(mesh);
  //   int numElems = mesh->numActiveElements();
  //   if (commRank==0){
  //     double minSideLength = meshInfo.getMinCellSideLength() ;
  //     cout << "after replay, num elems = " << numElems << " and min side length = " << minSideLength << endl;
  //   }
  // }

  for (int i = 0; i < uniformRefinements; i++)
    refinementStrategy.hRefineUniformly(mesh);

  double nonlinearRelativeEnergyTolerance = 1e-5; // used to determine convergence of the nonlinear solution
  for (int refIndex=0; refIndex<=numRefs; refIndex++)
  {
    double L2Update = 1e10;
    int iterCount = 0;
    while (L2Update > nonlinearRelativeEnergyTolerance && iterCount < maxNewtonIterations)
    {
      solution->solve(false);
      double u1L2Update = solution->L2NormOfSolutionGlobal(u1->ID());
      double u2L2Update = solution->L2NormOfSolutionGlobal(u2->ID());
      L2Update = sqrt(u1L2Update*u1L2Update + u2L2Update*u2L2Update);
      double energy_error = solution->energyErrorTotal();

      // Check local conservation
      if (commRank == 0)
      {
        FunctionPtr n = Function::normal();
        FunctionPtr u1_prev = Function::solution(u1hat, solution);
        FunctionPtr u2_prev = Function::solution(u2hat, solution);
        FunctionPtr flux = u1_prev*n->x() + u2_prev*n->y();
        Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, mesh);
        // cout << "Mass flux: Largest Local = " << fluxImbalances[0]
        //   << ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;

        errOut << mesh->numGlobalDofs() << " " << energy_error << " "
               << fluxImbalances[0] << " " << fluxImbalances[1] << " " << fluxImbalances[2] << endl;

        double massFlux0 = computeFluxOverElementSides(u1_prev, mesh, cellFace0);
        double massFlux1 = computeFluxOverElementSides(u1_prev, mesh, cellFace1);
        double massFlux2 = computeFluxOverElementSides(u1_prev, mesh, cellFace2);
        double massFlux3 = computeFluxOverElementSides(u1_prev, mesh, cellFace3);
        double massFlux4 = computeFluxOverElementSides(u1_prev, mesh, cellFace4);
        fluxOut << massFlux0 << " " << massFlux1 << " " << massFlux2 << " " << massFlux3 << " " << massFlux4 << " " << endl;
        cout << "Total mass flux = " << massFlux0 << " " << massFlux1 << " " << massFlux2 << " " << massFlux3 << " " << massFlux4 << " " << endl;

        // if (saveFile.length() > 0) {
        //   std::ostringstream oss;
        //   oss << string(saveFile) << refIndex ;
        //   cout << "on refinement " << refIndex << " saving mesh file to " << oss.str() << endl;
        //   refHistory->saveToFile(oss.str());
        // }
      }

      // line search algorithm
      double alpha = 1.0;
      // bool useLineSearch = false;
      // int posEnrich = 5; // amount of enriching of grid points on which to ensure positivity
      // if (useLineSearch){ // to enforce positivity of density rho
      //   double lineSearchFactor = .5; double eps = .001; // arbitrary
      //   FunctionPtr rhoTemp = Function::solution(rho,backgroundFlow) + alpha*Function::solution(rho,solution) - Function::constant(eps);
      //   FunctionPtr eTemp = Function::solution(e,backgroundFlow) + alpha*Function::solution(e,solution) - Function::constant(eps);
      //   bool rhoIsPositive = rhoTemp->isPositive(mesh,posEnrich);
      //   bool eIsPositive = eTemp->isPositive(mesh,posEnrich);
      //   int iter = 0; int maxIter = 20;
      //   while (!(rhoIsPositive && eIsPositive) && iter < maxIter){
      //     alpha = alpha*lineSearchFactor;
      //     rhoTemp = Function::solution(rho,backgroundFlow) + alpha*Function::solution(rho,solution);
      //     eTemp = Function::solution(e,backgroundFlow) + alpha*Function::solution(e,solution);
      //     rhoIsPositive = rhoTemp->isPositive(mesh,posEnrich);
      //     eIsPositive = eTemp->isPositive(mesh,posEnrich);
      //     iter++;
      //   }
      //   if (commRank==0 && alpha < 1.0){
      //     cout << "line search factor alpha = " << alpha << endl;
      //   }
      // }

      backgroundFlow->addSolution(solution, alpha, false, true);
      iterCount++;
      // if (commRank == 0)
      //   cout << "L2 Norm of Update = " << L2Update << endl;
    }
    if (commRank == 0)
      cout << endl;

    if (commRank == 0)
    {
      stringstream outfile;
      outfile << "stokeshemker" << uniformRefinements << "_" << refIndex;
      exporter.exportSolution(outfile.str());
    }

    if (refIndex < numRefs)
      refinementStrategy.refine(commRank==0); // print to console on commRank 0
  }
  if (commRank == 0)
  {
    errOut.close();
    fluxOut.close();
  }

  return 0;
}
Example #18
0
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
  Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
  int rank=mpiSession.getRank();
  int numProcs=mpiSession.getNProc();
#else
  int rank = 0;
  int numProcs = 1;
#endif
  ////////////////////   DECLARE VARIABLES   ///////////////////////
  // define test variables
  VarFactory varFactory;
  VarPtr tau = varFactory.testVar("\\tau", HDIV);
  VarPtr v = varFactory.testVar("v", HGRAD);

  // define trial variables
  VarPtr uhat = varFactory.traceVar("\\widehat{u}");
  VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
  VarPtr u = varFactory.fieldVar("u");
  VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
  VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");

  vector<double> beta_const;
  double c = sqrt(1.25);
  beta_const.push_back(1.0/c);
  beta_const.push_back(.5/c);
//  FunctionPtr beta = Teuchos::rcp(new Beta());

  double eps = 1e-3;

  ////////////////////   DEFINE BILINEAR FORM   ///////////////////////

  BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
  // tau terms:
  confusionBF->addTerm(sigma1 / eps, tau->x());
  confusionBF->addTerm(sigma2 / eps, tau->y());
  confusionBF->addTerm(u, tau->div());
  confusionBF->addTerm(-uhat, tau->dot_normal());

  // v terms:
  confusionBF->addTerm( sigma1, v->dx() );
  confusionBF->addTerm( sigma2, v->dy() );
  confusionBF->addTerm( beta_const * u, - v->grad() );
  confusionBF->addTerm( beta_n_u_minus_sigma_n, v);

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////

  // quasi-optimal norm
  IPPtr qoptIP = Teuchos::rcp(new IP);
  qoptIP->addTerm( v );
  qoptIP->addTerm( tau / eps + v->grad() );
  qoptIP->addTerm( beta_const * v->grad() - tau->div() );

  // robust test norm
  IPPtr robIP = Teuchos::rcp(new IP);
  FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(eps) );
  if (enforceLocalConservation)
  {
    robIP->addZeroMeanTerm( v );
  }
  else
  {
    robIP->addTerm( ip_scaling * v );
  }
  robIP->addTerm( sqrt(eps) * v->grad() );

  bool useNewBC = false;
  FunctionPtr weight = Teuchos::rcp( new SqrtWeight(eps) );
  if (useNewBC)
  {
    robIP->addTerm( beta_const * v->grad() );
    robIP->addTerm( tau->div() );
    robIP->addTerm( ip_scaling/sqrt(eps) * tau );
  }
  else
  {
    robIP->addTerm( weight * beta_const * v->grad() );
    robIP->addTerm( weight * tau->div() );
    robIP->addTerm( weight * ip_scaling/sqrt(eps) * tau );
  }


  ////////////////////   SPECIFY RHS   ///////////////////////
  FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
  Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
  FunctionPtr f = zero;
  rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!

  ////////////////////   CREATE BCs   ///////////////////////
  Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
  SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
  SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary );

  FunctionPtr u0 = Teuchos::rcp( new U0 );
  FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
  bc->addDirichlet(uhat, outflowBoundary, zero);
  if (useNewBC)
  {
    bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, beta_const*n*u0);
  }
  else
  {
    SpatialFilterPtr inflowBot = Teuchos::rcp( new InflowSquareBot );
    SpatialFilterPtr inflowLeft = Teuchos::rcp( new InflowSquareLeft );

    bc->addDirichlet(beta_n_u_minus_sigma_n, inflowLeft, beta_const*n*u0);
    bc->addDirichlet(uhat, inflowBot, u0);
  }

  // Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp(new PenaltyConstraints);
  // pc->addConstraint(uhat==u0,inflowBoundary);

  ////////////////////   BUILD MESH   ///////////////////////
  // define nodes for mesh
  int H1Order = 2, pToAdd = 2;

  FieldContainer<double> quadPoints(4,2);

  quadPoints(0,0) = 0.0; // x1
  quadPoints(0,1) = 0.0; // y1
  quadPoints(1,0) = 1.0;
  quadPoints(1,1) = 0.0;
  quadPoints(2,0) = 1.0;
  quadPoints(2,1) = 1.0;
  quadPoints(3,0) = 0.0;
  quadPoints(3,1) = 1.0;

  int nCells = 2;
  int horizontalCells = nCells, verticalCells = nCells;

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
                            confusionBF, H1Order, H1Order+pToAdd);


  ////////////////////   SOLVE & REFINE   ///////////////////////
  Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) );
  // solution->setFilter(pc);

  if (enforceLocalConservation)
  {
    FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
    solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero);
  }

  double energyThreshold = 0.2; // for mesh refinements
  RefinementStrategy refinementStrategy( solution, energyThreshold );

  int numRefs = 9;

  for (int refIndex=0; refIndex<numRefs; refIndex++)
  {
    solution->solve(false);
    refinementStrategy.refine(rank==0); // print to console on rank 0
  }
  // one more solve on the final refined mesh:
  solution->solve(false);

  if (rank==0)
  {
    solution->writeToVTK("Hughes.vtu",min(H1Order+1,4));
    solution->writeFluxesToFile(uhat->ID(), "uhat.dat");

    cout << "wrote files: u.m, uhat.dat\n";
  }

  return 0;
}
Example #19
0
void Projector::projectFunctionOntoBasis(FieldContainer<double> &basisCoefficients, FunctionPtr fxn, 
                                         BasisPtr basis, BasisCachePtr basisCache, IPPtr ip, VarPtr v,
                                         set<int> fieldIndicesToSkip) {
  CellTopoPtr cellTopo = basis->domainTopology();
  DofOrderingPtr dofOrderPtr = Teuchos::rcp(new DofOrdering());
  
  if (! fxn.get()) {
    TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "fxn cannot be null!");
  }
  
  int cardinality = basis->getCardinality();
  int numCells = basisCache->getPhysicalCubaturePoints().dimension(0);
  int numDofs = cardinality - fieldIndicesToSkip.size();
  if (numDofs==0) {
    // we're skipping all the fields, so just initialize basisCoefficients to 0 and return
    basisCoefficients.resize(numCells,cardinality);
    basisCoefficients.initialize(0);
    return;
  }
  
  FieldContainer<double> gramMatrix(numCells,cardinality,cardinality);
  FieldContainer<double> ipVector(numCells,cardinality);

  // fake a DofOrdering
  DofOrderingPtr dofOrdering = Teuchos::rcp( new DofOrdering );
  if (! basisCache->isSideCache()) {
    dofOrdering->addEntry(v->ID(), basis, v->rank());
  } else {
    dofOrdering->addEntry(v->ID(), basis, v->rank(), basisCache->getSideIndex());
  }
  
  ip->computeInnerProductMatrix(gramMatrix, dofOrdering, basisCache);
  ip->computeInnerProductVector(ipVector, v, fxn, dofOrdering, basisCache);
  
//  cout << "physical points for projection:\n" << basisCache->getPhysicalCubaturePoints();
//  cout << "gramMatrix:\n" << gramMatrix;
//  cout << "ipVector:\n" << ipVector;
  
  map<int,int> oldToNewIndices;
  if (fieldIndicesToSkip.size() > 0) {
    // the code to do with fieldIndicesToSkip might not be terribly efficient...
    // (but it's not likely to be called too frequently)
    int i_indices_skipped = 0;
    for (int i=0; i<cardinality; i++) {
      int new_index;
      if (fieldIndicesToSkip.find(i) != fieldIndicesToSkip.end()) {
        i_indices_skipped++;
        new_index = -1;
      } else {
        new_index = i - i_indices_skipped;
      }
      oldToNewIndices[i] = new_index;
    }
    
    FieldContainer<double> gramMatrixFiltered(numCells,numDofs,numDofs);
    FieldContainer<double> ipVectorFiltered(numCells,numDofs);
    // now filter out the values that we're to skip
    
    for (int cellIndex=0; cellIndex<numCells; cellIndex++) {
      for (int i=0; i<cardinality; i++) {
        int i_filtered = oldToNewIndices[i];
        if (i_filtered == -1) {
          continue;
        }
        ipVectorFiltered(cellIndex,i_filtered) = ipVector(cellIndex,i);
        
        for (int j=0; j<cardinality; j++) {
          int j_filtered = oldToNewIndices[j];
          if (j_filtered == -1) {
            continue;
          }
          gramMatrixFiltered(cellIndex,i_filtered,j_filtered) = gramMatrix(cellIndex,i,j);
        }
      }
    }
//    cout << "gramMatrixFiltered:\n" << gramMatrixFiltered;
//    cout << "ipVectorFiltered:\n" << ipVectorFiltered;
    gramMatrix = gramMatrixFiltered;
    ipVector = ipVectorFiltered;
  }
  
  for (int cellIndex=0; cellIndex<numCells; cellIndex++){
    
    // TODO: rewrite to take advantage of SerialDenseWrapper...
    Epetra_SerialDenseSolver solver;
    
    Epetra_SerialDenseMatrix A(Copy,
                               &gramMatrix(cellIndex,0,0),
                               gramMatrix.dimension(2), 
                               gramMatrix.dimension(2),  
                               gramMatrix.dimension(1)); // stride -- fc stores in row-major order (a.o.t. SDM)
    
    Epetra_SerialDenseVector b(Copy,
                               &ipVector(cellIndex,0),
                               ipVector.dimension(1));
    
    Epetra_SerialDenseVector x(gramMatrix.dimension(1));
    
    solver.SetMatrix(A);
    int info = solver.SetVectors(x,b);
    if (info!=0){
      cout << "projectFunctionOntoBasis: failed to SetVectors with error " << info << endl;
    }
    
    bool equilibrated = false;
    if (solver.ShouldEquilibrate()){
      solver.EquilibrateMatrix();
      solver.EquilibrateRHS();      
      equilibrated = true;
    }   
    
    info = solver.Solve();
    if (info!=0){
      cout << "projectFunctionOntoBasis: failed to solve with error " << info << endl;
    }
    
    if (equilibrated) {
      int successLocal = solver.UnequilibrateLHS();
      if (successLocal != 0) {
        cout << "projection: unequilibration FAILED with error: " << successLocal << endl;
      }
    }
    
    basisCoefficients.resize(numCells,cardinality);
    for (int i=0;i<cardinality;i++) {
      if (fieldIndicesToSkip.size()==0) {
        basisCoefficients(cellIndex,i) = x(i);
      } else {
        int i_filtered = oldToNewIndices[i];
        if (i_filtered==-1) {
          basisCoefficients(cellIndex,i) = 0.0;
        } else {
          basisCoefficients(cellIndex,i) = x(i_filtered);
        }
      }
    }
    
  }
}
Example #20
0
void Boundary::bcsToImpose(FieldContainer<GlobalIndexType> &globalIndices,
                           FieldContainer<Scalar> &globalValues, TBC<Scalar> &bc,
                           DofInterpreter* dofInterpreter)
{
  set< GlobalIndexType > rankLocalCells = _mesh->cellIDsInPartition();
  map< GlobalIndexType, double> bcGlobalIndicesAndValues;

  for (GlobalIndexType cellID : rankLocalCells)
  {
    bcsToImpose(bcGlobalIndicesAndValues, bc, cellID, dofInterpreter);
  }
  singletonBCsToImpose(bcGlobalIndicesAndValues, bc, dofInterpreter);
  
  // ****** New, tag-based BC imposition follows ******
  map< GlobalIndexType, double> bcTagGlobalIndicesAndValues;
  
  map< int, vector<pair<VarPtr, TFunctionPtr<Scalar>>>> tagBCs = bc.getDirichletTagBCs(); // keys are tags
  
  MeshTopology* meshTopo = dynamic_cast<MeshTopology*>(_mesh->getTopology().get());
  
  TEUCHOS_TEST_FOR_EXCEPTION(!meshTopo, std::invalid_argument, "pure MeshTopologyViews are not yet supported by new tag-based BC imposition");
  
  for (auto tagBC : tagBCs)
  {
    int tagID = tagBC.first;
    
    vector<EntitySetPtr> entitySets = meshTopo->getEntitySetsForTagID(DIRICHLET_SET_TAG_NAME, tagID);
    for (EntitySetPtr entitySet : entitySets)
    {
      // get rank-local cells that match the entity set:
      set<IndexType> matchingCellIDs = entitySet->cellIDsThatMatch(_mesh->getTopology(), rankLocalCells);
      for (IndexType cellID : matchingCellIDs)
      {
        ElementTypePtr elemType = _mesh->getElementType(cellID);
        BasisCachePtr basisCache = BasisCache::basisCacheForCell(_mesh, cellID);
        
        for (auto varFunctionPair : tagBC.second)
        {
          VarPtr var = varFunctionPair.first;
          FunctionPtr f = varFunctionPair.second;
          
          vector<int> sideOrdinals = elemType->trialOrderPtr->getSidesForVarID(var->ID());
          
          for (int sideOrdinal : sideOrdinals)
          {
            BasisPtr basis = elemType->trialOrderPtr->getBasis(var->ID(), sideOrdinal);
            bool isVolume = basis->domainTopology()->getDimension() == _mesh->getDimension();
            for (int d=0; d<_mesh->getDimension(); d++)
            {
              vector<unsigned> matchingSubcells;
              if (isVolume)
                matchingSubcells = entitySet->subcellOrdinals(_mesh->getTopology(), cellID, d);
              else
              {
                CellTopoPtr cellTopo = elemType->cellTopoPtr;
                int sideDim = cellTopo->getDimension() - 1;
                vector<unsigned> matchingSubcellsOnSide = entitySet->subcellOrdinalsOnSide(_mesh->getTopology(), cellID, sideOrdinal, d);
                for (unsigned sideSubcellOrdinal : matchingSubcellsOnSide)
                {
                  unsigned cellSubcellOrdinal = CamelliaCellTools::subcellOrdinalMap(cellTopo, sideDim, sideOrdinal, d, sideSubcellOrdinal);
                  matchingSubcells.push_back(cellSubcellOrdinal);
                }
              }
              
              if (matchingSubcells.size() == 0) continue; // nothing to impose
              
              /*
               What follows - projecting the function onto the basis on the whole domain - is more expensive than necessary,
               in the general case: we can do the projection on just the matching subcells, and if we had a way of taking the
               restriction of a basis to a subcell of the domain, then we could avoid computing the whole basis as well.
               
               But for now, this should work, and it's simple to implement.
               */
              BasisCachePtr basisCacheForImposition = isVolume ? basisCache : basisCache->getSideBasisCache(sideOrdinal);
              int numCells = 1;
              FieldContainer<double> basisCoefficients(numCells,basis->getCardinality());
              Projector<double>::projectFunctionOntoBasisInterpolating(basisCoefficients, f, basis, basisCacheForImposition);
              basisCoefficients.resize(basis->getCardinality());
              
              set<GlobalIndexType> matchingGlobalIndices;
              for (unsigned matchingSubcell : matchingSubcells)
              {
                set<GlobalIndexType> subcellGlobalIndices = dofInterpreter->globalDofIndicesForVarOnSubcell(var->ID(),cellID,d,matchingSubcell);
                matchingGlobalIndices.insert(subcellGlobalIndices.begin(),subcellGlobalIndices.end());
              }
              
              FieldContainer<double> globalData;
              FieldContainer<GlobalIndexType> globalDofIndices;
//              dofInterpreter->interpretLocalBasisCoefficients(cellID, var->ID(), sideOrdinal, basisCoefficientsToImpose, globalData, globalDofIndices);
              dofInterpreter->interpretLocalBasisCoefficients(cellID, var->ID(), sideOrdinal, basisCoefficients, globalData, globalDofIndices);
              for (int globalDofOrdinal=0; globalDofOrdinal<globalDofIndices.size(); globalDofOrdinal++)
              {
                GlobalIndexType globalDofIndex = globalDofIndices(globalDofOrdinal);
                if (matchingGlobalIndices.find(globalDofIndex) != matchingGlobalIndices.end())
                  bcTagGlobalIndicesAndValues[globalDofIndex] = globalData(globalDofOrdinal);
              }
            }
          }
        }
      }
    }
  }
  
  // merge tag-based and legacy BC maps
  double tol = 1e-15;
  for (auto tagEntry : bcTagGlobalIndicesAndValues)
  {
    if (bcGlobalIndicesAndValues.find(tagEntry.first) != bcGlobalIndicesAndValues.end())
    {
      // then check that they match, within tolerance
      double diff = abs(bcGlobalIndicesAndValues[tagEntry.first] - tagEntry.second);
      TEUCHOS_TEST_FOR_EXCEPTION(diff > tol, std::invalid_argument, "Incompatible BC entries encountered");
    }
    else
    {
      bcGlobalIndicesAndValues[tagEntry.first] = tagEntry.second;
    }
  }
  
  globalIndices.resize(bcGlobalIndicesAndValues.size());
  globalValues.resize(bcGlobalIndicesAndValues.size());
  globalIndices.initialize(0);
  globalValues.initialize(0.0);
  int entryOrdinal = 0;
  for (auto bcEntry : bcGlobalIndicesAndValues)
  {
    globalIndices[entryOrdinal] = bcEntry.first;
    globalValues[entryOrdinal] = bcEntry.second;
    entryOrdinal++;
  }
}
Example #21
0
bool FunctionTests::testValuesDottedWithTensor()
{
  bool success = true;

  vector< FunctionPtr > vectorFxns;

  double xValue = 3, yValue = 4;
  FunctionPtr simpleVector = Function::vectorize(Function::constant(xValue), Function::constant(yValue));
  vectorFxns.push_back(simpleVector);
  FunctionPtr x = Function::xn(1);
  FunctionPtr y = Function::yn(1);
  vectorFxns.push_back( Function::vectorize(x*x, x*y) );

  VGPStokesFormulation vgpStokes = VGPStokesFormulation(1.0);
  BFPtr bf = vgpStokes.bf();

  int h1Order = 1;
  MeshPtr mesh = MeshFactory::quadMesh(bf, h1Order);

  int cellID=0; // the only cell
  BasisCachePtr basisCache = BasisCache::basisCacheForCell(mesh, cellID);

  for (int i=0; i<vectorFxns.size(); i++)
  {
    FunctionPtr vectorFxn_i = vectorFxns[i];
    for (int j=0; j<vectorFxns.size(); j++)
    {
      FunctionPtr vectorFxn_j = vectorFxns[j];
      FunctionPtr dotProduct = vectorFxn_i * vectorFxn_j;
      FunctionPtr expectedDotProduct = vectorFxn_i->x() * vectorFxn_j->x() + vectorFxn_i->y() * vectorFxn_j->y();
      if (! expectedDotProduct->equals(dotProduct, basisCache))
      {
        cout << "testValuesDottedWithTensor() failed: expected dot product does not match dotProduct.\n";
        success = false;
        double tol = 1e-14;
        reportFunctionValueDifferences(dotProduct, expectedDotProduct, basisCache, tol);
      }
    }
  }

  // now, let's try the same thing, but for a LinearTerm dot product
  VarFactoryPtr vf = VarFactory::varFactory();
  VarPtr v = vf->testVar("v", HGRAD);

  DofOrderingPtr dofOrdering = Teuchos::rcp( new DofOrdering(CellTopology::quad()) );
  shards::CellTopology quad_4(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
  BasisPtr basis = BasisFactory::basisFactory()->getBasis(h1Order, quad_4.getKey(), Camellia::FUNCTION_SPACE_HGRAD);
  dofOrdering->addEntry(v->ID(), basis, v->rank());

  int numCells = 1;
  int numFields = basis->getCardinality();

  for (int i=0; i<vectorFxns.size(); i++)
  {
    FunctionPtr f_i = vectorFxns[i];
    LinearTermPtr lt_i = f_i * v;
    LinearTermPtr lt_i_x = f_i->x() * v;
    LinearTermPtr lt_i_y = f_i->y() * v;
    for (int j=0; j<vectorFxns.size(); j++)
    {
      FunctionPtr f_j = vectorFxns[j];
      LinearTermPtr lt_j = f_j * v;
      LinearTermPtr lt_j_x = f_j->x() * v;
      LinearTermPtr lt_j_y = f_j->y() * v;
      FieldContainer<double> values(numCells,numFields,numFields);
      lt_i->integrate(values, dofOrdering, lt_j, dofOrdering, basisCache);
      FieldContainer<double> values_expected(numCells,numFields,numFields);
      lt_i_x->integrate(values_expected,dofOrdering,lt_j_x,dofOrdering,basisCache);
      lt_i_y->integrate(values_expected,dofOrdering,lt_j_y,dofOrdering,basisCache);
      double tol = 1e-14;
      double maxDiff = 0;
      if (!fcsAgree(values, values_expected, tol, maxDiff))
      {
        cout << "FunctionTests::testValuesDottedWithTensor: ";
        cout << "dot product and sum of the products of scalar components differ by maxDiff " << maxDiff;
        cout << " in LinearTerm::integrate().\n";
        success = false;
      }
    }
  }

//  // finally, let's try the same sort of thing, but now with a vector-valued basis
//  BasisPtr vectorBasisTemp = BasisFactory::basisFactory()->getBasis(h1Order, quad_4.getKey(), Camellia::FUNCTION_SPACE_VECTOR_HGRAD);
//  VectorBasisPtr vectorBasis = Teuchos::rcp( (VectorizedBasis<double, FieldContainer<double> > *)vectorBasisTemp.get(),false);
//
//  BasisPtr compBasis = vectorBasis->getComponentBasis();
//
//  // create a new v, and a new dofOrdering
//  VarPtr v_vector = vf->testVar("v_vector", VECTOR_HGRAD);
//  dofOrdering = Teuchos::rcp( new DofOrdering );
//  dofOrdering->addEntry(v_vector->ID(), vectorBasis, v_vector->rank());
//
//  DofOrderingPtr dofOrderingComp = Teuchos::rcp( new DofOrdering );
//  dofOrderingComp->addEntry(v->ID(), compBasis, v->rank());
//

  return success;
}
Example #22
0
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
    Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
    int rank=mpiSession.getRank();
    int numProcs=mpiSession.getNProc();
#else
    int rank = 0;
    int numProcs = 1;
#endif
    int polyOrder = 2;

    // define our manufactured solution or problem bilinear form:
    double epsilon = 1e-3;
    bool useTriangles = false;

    int pToAdd = 2;
    int nCells = 2;
    if ( argc > 1)
    {
        nCells = atoi(argv[1]);
        if (rank==0)
        {
            cout << "numCells = " << nCells << endl;
        }
    }
    int numSteps = 20;
    if ( argc > 2)
    {
        numSteps = atoi(argv[2]);
        if (rank==0)
        {
            cout << "num NR steps = " << numSteps << endl;
        }
    }
    int useHessian = 0; // defaults to "not use"
    if ( argc > 3)
    {
        useHessian = atoi(argv[3]);
        if (rank==0)
        {
            cout << "useHessian = " << useHessian << endl;
        }
    }

    int thresh = numSteps; // threshhold for when to apply linesearch/hessian
    if ( argc > 4)
    {
        thresh = atoi(argv[4]);
        if (rank==0)
        {
            cout << "thresh = " << thresh << endl;
        }
    }

    int H1Order = polyOrder + 1;

    double energyThreshold = 0.2; // for mesh refinements
    double nonlinearStepSize = 0.5;
    double nonlinearRelativeEnergyTolerance = 1e-8; // used to determine convergence of the nonlinear solution

    ////////////////////////////////////////////////////////////////////
    // DEFINE VARIABLES
    ////////////////////////////////////////////////////////////////////

    // new-style bilinear form definition
    VarFactory varFactory;
    VarPtr uhat = varFactory.traceVar("\\widehat{u}");
    VarPtr beta_n_u_minus_sigma_hat = varFactory.fluxVar("\\widehat{\\beta_n u - \\sigma_n}");
    VarPtr u = varFactory.fieldVar("u");
    VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
    VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");

    VarPtr tau = varFactory.testVar("\\tau",HDIV);
    VarPtr v = varFactory.testVar("v",HGRAD);
    BFPtr bf = Teuchos::rcp( new BF(varFactory) ); // initialize bilinear form

    ////////////////////////////////////////////////////////////////////
    // CREATE MESH
    ////////////////////////////////////////////////////////////////////

    // create a pointer to a new mesh:
    Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells, bf, H1Order, H1Order+pToAdd);
    mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));

    ////////////////////////////////////////////////////////////////////
    // INITIALIZE BACKGROUND FLOW FUNCTIONS
    ////////////////////////////////////////////////////////////////////
    BCPtr nullBC = Teuchos::rcp((BC*)NULL);
    RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
    IPPtr nullIP = Teuchos::rcp((IP*)NULL);
    SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC,
                                 nullRHS, nullIP) );

    vector<double> e1(2); // (1,0)
    e1[0] = 1;
    vector<double> e2(2); // (0,1)
    e2[1] = 1;

    FunctionPtr u_prev = Teuchos::rcp( new PreviousSolutionFunction(backgroundFlow, u) );
    FunctionPtr beta = e1 * u_prev + Teuchos::rcp( new ConstantVectorFunction( e2 ) );

    ////////////////////////////////////////////////////////////////////
    // DEFINE BILINEAR FORM
    ////////////////////////////////////////////////////////////////////

    // tau parts:
    // 1/eps (sigma, tau)_K + (u, div tau)_K - (u_hat, tau_n)_dK
    bf->addTerm(sigma1 / epsilon, tau->x());
    bf->addTerm(sigma2 / epsilon, tau->y());
    bf->addTerm(u, tau->div());
    bf->addTerm( - uhat, tau->dot_normal() );

    // v:
    // (sigma, grad v)_K - (sigma_hat_n, v)_dK - (u, beta dot grad v) + (u_hat * n dot beta, v)_dK
    bf->addTerm( sigma1, v->dx() );
    bf->addTerm( sigma2, v->dy() );
    bf->addTerm( -u, beta * v->grad());
    bf->addTerm( beta_n_u_minus_sigma_hat, v);

    // ==================== SET INITIAL GUESS ==========================
    mesh->registerSolution(backgroundFlow);
    FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
    FunctionPtr u0 = Teuchos::rcp( new U0 );

    map<int, Teuchos::RCP<Function> > functionMap;
    functionMap[u->ID()] = u0;
    functionMap[sigma1->ID()] = zero;
    functionMap[sigma2->ID()] = zero;

    backgroundFlow->projectOntoMesh(functionMap);
    // ==================== END SET INITIAL GUESS ==========================

    ////////////////////////////////////////////////////////////////////
    // DEFINE INNER PRODUCT
    ////////////////////////////////////////////////////////////////////
    // function to scale the squared guy by epsilon/h
    FunctionPtr epsilonOverHScaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
    IPPtr ip = Teuchos::rcp( new IP );
    ip->addTerm( epsilonOverHScaling * (1.0/sqrt(epsilon))* tau);
    ip->addTerm( tau->div());
    //  ip->addTerm( epsilonOverHScaling * v );
    ip->addTerm( v );
    ip->addTerm( sqrt(epsilon) * v->grad() );
    ip->addTerm(v->grad());
    //  ip->addTerm( beta * v->grad() );

    ////////////////////////////////////////////////////////////////////
    // DEFINE RHS
    ////////////////////////////////////////////////////////////////////
    RHSPtr rhs = RHS::rhs();
    FunctionPtr u_prev_squared_div2 = 0.5 * u_prev * u_prev;

    rhs->addTerm((e1 * u_prev_squared_div2 + e2 * u_prev) * v->grad() - u_prev * tau->div());

    ////////////////////////////////////////////////////////////////////
    // DEFINE DIRICHLET BC
    ////////////////////////////////////////////////////////////////////
    FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
    SpatialFilterPtr outflowBoundary = Teuchos::rcp( new TopBoundary);
    SpatialFilterPtr inflowBoundary = Teuchos::rcp( new NegatedSpatialFilter(outflowBoundary) );
    BCPtr inflowBC = BC::bc();
    FunctionPtr u0_squared_div_2 = 0.5 * u0 * u0;
    inflowBC->addDirichlet(beta_n_u_minus_sigma_hat,inflowBoundary,
                           ( e1 * u0_squared_div_2 + e2 * u0) * n );

    ////////////////////////////////////////////////////////////////////
    // CREATE SOLUTION OBJECT
    ////////////////////////////////////////////////////////////////////
    Teuchos::RCP<Solution> solution = Teuchos::rcp(new Solution(mesh, inflowBC, rhs, ip));
    mesh->registerSolution(solution);

    ////////////////////////////////////////////////////////////////////
    // WARNING: UNFINISHED HESSIAN BIT
    ////////////////////////////////////////////////////////////////////
    VarFactory hessianVars = varFactory.getBubnovFactory(VarFactory::BUBNOV_TRIAL);
    VarPtr du = hessianVars.test(u->ID());
    BFPtr hessianBF = Teuchos::rcp( new BF(hessianVars) ); // initialize bilinear form
    //  FunctionPtr e_v = Function::constant(1.0); // dummy error rep function for now - should do nothing

    FunctionPtr u_current  = Teuchos::rcp( new PreviousSolutionFunction(solution, u) );

    FunctionPtr sig1_prev = Teuchos::rcp( new PreviousSolutionFunction(solution, sigma1) );
    FunctionPtr sig2_prev = Teuchos::rcp( new PreviousSolutionFunction(solution, sigma2) );
    FunctionPtr sig_prev = (e1*sig1_prev + e2*sig2_prev);
    FunctionPtr fnhat = Teuchos::rcp(new PreviousSolutionFunction(solution,beta_n_u_minus_sigma_hat));
    FunctionPtr uhat_prev = Teuchos::rcp(new PreviousSolutionFunction(solution,uhat));
    LinearTermPtr residual = Teuchos::rcp(new LinearTerm);// residual
    residual->addTerm(fnhat*v - (e1 * (u_prev_squared_div2 - sig1_prev) + e2 * (u_prev - sig2_prev)) * v->grad());
    residual->addTerm((1/epsilon)*sig_prev * tau + u_prev * tau->div() - uhat_prev*tau->dot_normal());

    LinearTermPtr Bdu = Teuchos::rcp(new LinearTerm);// residual
    Bdu->addTerm( u_current*tau->div() - u_current*(beta*v->grad()));

    Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(mesh, ip, residual));
    Teuchos::RCP<RieszRep> duRiesz = Teuchos::rcp(new RieszRep(mesh, ip, Bdu));
    riesz->computeRieszRep();
    FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,riesz));
    e_v->writeValuesToMATLABFile(mesh, "e_v.m");
    FunctionPtr posErrPart = Teuchos::rcp(new PositivePart(e_v->dx()));
    hessianBF->addTerm(e_v->dx()*u,du);
    //  hessianBF->addTerm(posErrPart*u,du);
    Teuchos::RCP<HessianFilter> hessianFilter = Teuchos::rcp(new HessianFilter(hessianBF));

    if (useHessian)
    {
        solution->setWriteMatrixToFile(true,"hessianStiffness.dat");
    }
    else
    {
        solution->setWriteMatrixToFile(true,"stiffness.dat");
    }

    Teuchos::RCP< LineSearchStep > LS_Step = Teuchos::rcp(new LineSearchStep(riesz));
    ofstream out;
    out.open("Burgers.txt");
    double NL_residual = 9e99;
    for (int i = 0; i<numSteps; i++)
    {
        solution->solve(false); // do one solve to initialize things...
        double stepLength = 1.0;
        stepLength = LS_Step->stepSize(backgroundFlow,solution, NL_residual);
        if (useHessian)
        {
            solution->setFilter(hessianFilter);
        }
        backgroundFlow->addSolution(solution,stepLength);
        NL_residual = LS_Step->getNLResidual();
        if (rank==0)
        {
            cout << "NL residual after adding = " << NL_residual << " with step size " << stepLength << endl;
            out << NL_residual << endl; // saves initial NL error
        }
    }
    out.close();


    ////////////////////////////////////////////////////////////////////
    // DEFINE REFINEMENT STRATEGY
    ////////////////////////////////////////////////////////////////////
    Teuchos::RCP<RefinementStrategy> refinementStrategy;
    refinementStrategy = Teuchos::rcp(new RefinementStrategy(solution,energyThreshold));

    int numRefs = 0;

    Teuchos::RCP<NonlinearStepSize> stepSize = Teuchos::rcp(new NonlinearStepSize(nonlinearStepSize));
    Teuchos::RCP<NonlinearSolveStrategy> solveStrategy;
    solveStrategy = Teuchos::rcp( new NonlinearSolveStrategy(backgroundFlow, solution, stepSize,
                                  nonlinearRelativeEnergyTolerance));

    ////////////////////////////////////////////////////////////////////
    // SOLVE
    ////////////////////////////////////////////////////////////////////

    for (int refIndex=0; refIndex<numRefs; refIndex++)
    {
        solveStrategy->solve(rank==0);       // print to console on rank 0
        refinementStrategy->refine(rank==0); // print to console on rank 0
    }
    //  solveStrategy->solve(rank==0);

    if (rank==0)
    {
        backgroundFlow->writeToVTK("Burgers.vtu",min(H1Order+1,4));
        solution->writeFluxesToFile(uhat->ID(), "burgers.dat");
        cout << "wrote solution files" << endl;
    }

    return 0;
}
Example #23
0
int main(int argc, char *argv[]) {
 
#ifdef HAVE_MPI
  Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
  choice::MpiArgs args( argc, argv );
#else
  choice::Args args( argc, argv );
#endif
  int rank = Teuchos::GlobalMPISession::getRank();
  int numProcs = Teuchos::GlobalMPISession::getNProc();
  
  int nCells = args.Input<int>("--nCells", "num cells",2);  
  int numRefs = args.Input<int>("--numRefs","num adaptive refinements",0);
  int numPreRefs = args.Input<int>("--numPreRefs","num preemptive adaptive refinements",0);
  int order = args.Input<int>("--order","order of approximation",2);
  double eps = args.Input<double>("--epsilon","diffusion parameter",1e-2);
  double energyThreshold = args.Input<double>("-energyThreshold","energy thresh for adaptivity", .5);
  double rampHeight = args.Input<double>("--rampHeight","ramp height at x = 2", 0.0);
  double ipSwitch = args.Input<double>("--ipSwitch","point at which to switch to graph norm", 0.0); // default to 0 to remain on robust norm
  bool useAnisotropy = args.Input<bool>("--useAnisotropy","aniso flag ", false);

  int H1Order = order+1; 
  int pToAdd = args.Input<int>("--pToAdd","test space enrichment", 2);

  FunctionPtr zero = Function::constant(0.0);
  FunctionPtr one = Function::constant(1.0);
  FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
  vector<double> e1,e2;
  e1.push_back(1.0);e1.push_back(0.0);
  e2.push_back(0.0);e2.push_back(1.0);

  ////////////////////   DECLARE VARIABLES   ///////////////////////
  // define test variables
  VarFactory varFactory; 
  VarPtr tau = varFactory.testVar("\\tau", HDIV);
  VarPtr v = varFactory.testVar("v", HGRAD);
  
  // define trial variables
  VarPtr uhat = varFactory.traceVar("\\widehat{u}");
  VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
  VarPtr u = varFactory.fieldVar("u");
  VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
  VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");

  vector<double> beta;
  beta.push_back(1.0);
  beta.push_back(0.0);
  
  ////////////////////   DEFINE BILINEAR FORM   ///////////////////////

  BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
  // tau terms:
  confusionBF->addTerm(sigma1 / eps, tau->x());
  confusionBF->addTerm(sigma2 / eps, tau->y());
  confusionBF->addTerm(u, tau->div());
  confusionBF->addTerm(uhat, -tau->dot_normal());
  
  // v terms:
  confusionBF->addTerm( sigma1, v->dx() );
  confusionBF->addTerm( sigma2, v->dy() );
  confusionBF->addTerm( -u, beta * v->grad() );
  confusionBF->addTerm( beta_n_u_minus_sigma_n, v);

  // first order term with magnitude alpha
  double alpha = 0.0;
  //  confusionBF->addTerm(alpha * u, v);

  ////////////////////   BUILD MESH   ///////////////////////


  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);
  mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));  
  MeshInfo meshInfo(mesh); // gets info like cell measure, etc

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////
  IPPtr ip = Teuchos::rcp(new IP);

  /*
   // robust test norm
  FunctionPtr C_h = Teuchos::rcp( new EpsilonScaling(eps) );  
  FunctionPtr invH = Teuchos::rcp(new InvHScaling);
  FunctionPtr invSqrtH = Teuchos::rcp(new InvSqrtHScaling);
  FunctionPtr sqrtH = Teuchos::rcp(new SqrtHScaling);
  FunctionPtr hSwitch = Teuchos::rcp(new HSwitch(ipSwitch,mesh));
  ip->addTerm(hSwitch*sqrt(eps) * v->grad() );
  ip->addTerm(hSwitch*beta * v->grad() );
  ip->addTerm(hSwitch*tau->div() );
  
  // graph norm
  ip->addTerm( (one-hSwitch)*((1.0/eps) * tau + v->grad()));
  ip->addTerm( (one-hSwitch)*(beta * v->grad() - tau->div()));

  // regularizing terms
  ip->addTerm(C_h/sqrt(eps) * tau );    
  ip->addTerm(invSqrtH*v);
  */

   // robust test norm
  IPPtr robIP = Teuchos::rcp(new IP);
  FunctionPtr C_h = Teuchos::rcp( new EpsilonScaling(eps) );  
  FunctionPtr invH = Teuchos::rcp(new InvHScaling);
  FunctionPtr invSqrtH = Teuchos::rcp(new InvSqrtHScaling);
  FunctionPtr sqrtH = Teuchos::rcp(new SqrtHScaling);
  FunctionPtr hSwitch = Teuchos::rcp(new HSwitch(ipSwitch,mesh));
  robIP->addTerm(sqrt(eps) * v->grad() );
  robIP->addTerm(beta * v->grad() );
  robIP->addTerm(tau->div() );
  // regularizing terms
  robIP->addTerm(C_h/sqrt(eps) * tau );    
  robIP->addTerm(invSqrtH*v);

  IPPtr graphIP = confusionBF->graphNorm();
  graphIP->addTerm(invSqrtH*v);
  //  graphIP->addTerm(C_h/sqrt(eps) * tau );    
  IPPtr switchIP = Teuchos::rcp(new IPSwitcher(robIP,graphIP,ipSwitch)); // rob IP for h>ipSwitch mesh size, graph norm o/w
  ip = switchIP;
    
  LinearTermPtr vVecLT = Teuchos::rcp(new LinearTerm);
  LinearTermPtr tauVecLT = Teuchos::rcp(new LinearTerm);
  vVecLT->addTerm(sqrt(eps)*v->grad());
  tauVecLT->addTerm(C_h/sqrt(eps)*tau);

  LinearTermPtr restLT = Teuchos::rcp(new LinearTerm);
  restLT->addTerm(alpha*v);
  restLT->addTerm(invSqrtH*v);
  restLT = restLT + beta * v->grad();
  restLT = restLT + tau->div();

  ////////////////////   SPECIFY RHS   ///////////////////////

  Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
  FunctionPtr f = zero;
  //  f = one;
  rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!

  ////////////////////   CREATE BCs   ///////////////////////
  Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );

  SpatialFilterPtr Inflow = Teuchos::rcp(new LeftInflow);
  SpatialFilterPtr wallBoundary = Teuchos::rcp(new WallBoundary);//MeshUtilities::rampBoundary(rampHeight);
  SpatialFilterPtr freeStream = Teuchos::rcp(new FreeStreamBoundary);

  bc->addDirichlet(uhat, wallBoundary, one);
  //  bc->addDirichlet(uhat, wallBoundary, Teuchos::rcp(new WallSmoothBC(eps)));
  bc->addDirichlet(beta_n_u_minus_sigma_n, Inflow, zero);
  bc->addDirichlet(beta_n_u_minus_sigma_n, freeStream, zero);

  ////////////////////   SOLVE & REFINE   ///////////////////////

  Teuchos::RCP<Solution> solution;
  solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
  BCPtr nullBC = Teuchos::rcp((BC*)NULL); RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL); IPPtr nullIP = Teuchos::rcp((IP*)NULL);
  SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );  
  mesh->registerSolution(backgroundFlow); // to trigger issue with p-refinements
  map<int, Teuchos::RCP<Function> > functionMap; functionMap[u->ID()] = Function::constant(3.14);
  backgroundFlow->projectOntoMesh(functionMap);

  // lower p to p = 1 at SINGULARITY only
  vector<int> ids;
  /*
  for (int i = 0;i<mesh->numActiveElements();i++){
    bool cellIDset = false;
    int cellID = mesh->activeElements()[i]->cellID();
    int elemOrder = mesh->cellPolyOrder(cellID)-1;
    FieldContainer<double> vv(4,2); mesh->verticesForCell(vv, cellID);
    bool vertexOnWall = false; bool vertexAtSingularity = false;
    for (int j = 0;j<4;j++){
      if ((abs(vv(j,0)-.5) + abs(vv(j,1)))<1e-10){
	vertexAtSingularity = true;     
	cellIDset = true;
      }
    }	
    if (!vertexAtSingularity && elemOrder<2 && !cellIDset ){
      ids.push_back(cellID);
      cout << "celliD = " << cellID << endl;
    }
  }
  */
  ids.push_back(1);
  ids.push_back(3);
  mesh->pRefine(ids); // to put order = 1

  return 0;
  
  LinearTermPtr residual = rhs->linearTermCopy();
  residual->addTerm(-confusionBF->testFunctional(solution));  
  RieszRepPtr rieszResidual = Teuchos::rcp(new RieszRep(mesh, ip, residual));
  rieszResidual->computeRieszRep();
  FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,rieszResidual));
  FunctionPtr e_tau = Teuchos::rcp(new RepFunction(tau,rieszResidual));
  map<int,FunctionPtr> errRepMap;
  errRepMap[v->ID()] = e_v;
  errRepMap[tau->ID()] = e_tau;
  FunctionPtr errTau = tauVecLT->evaluate(errRepMap,false);
  FunctionPtr errV = vVecLT->evaluate(errRepMap,false);
  FunctionPtr errRest = restLT->evaluate(errRepMap,false);
  FunctionPtr xErr = (errTau->x())*(errTau->x()) + (errV->dx())*(errV->dx());
  FunctionPtr yErr = (errTau->y())*(errTau->y()) + (errV->dy())*(errV->dy());
  FunctionPtr restErr = errRest*errRest;

  RefinementStrategy refinementStrategy( solution, energyThreshold );    

  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
  //                     PRE REFINEMENTS 
  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////  

  if (rank==0){
    cout << "Number of pre-refinements = " << numPreRefs << endl;
  }
  for (int i =0;i<=numPreRefs;i++){   
    vector<ElementPtr> elems = mesh->activeElements();
    vector<ElementPtr>::iterator elemIt;
    vector<int> wallCells;    
    for (elemIt=elems.begin();elemIt != elems.end();elemIt++){
      int cellID = (*elemIt)->cellID();
      int numSides = mesh->getElement(cellID)->numSides();
      FieldContainer<double> vertices(numSides,2); //for quads

      mesh->verticesForCell(vertices, cellID);
      bool cellIDset = false;	
      for (int j = 0;j<numSides;j++){ 	
	if ((abs(vertices(j,0)-.5)<1e-7) && (abs(vertices(j,1))<1e-7) && !cellIDset){ // if at singularity, i.e. if a vertex is (1,0)
	  wallCells.push_back(cellID);
	  cellIDset = true;
	}
      }
    }
    if (i<numPreRefs){
      refinementStrategy.refineCells(wallCells);
    }
  }

  double minSideLength = meshInfo.getMinCellSideLength() ;
  double minCellMeasure = meshInfo.getMinCellMeasure() ;
  if (rank==0){
    cout << "after prerefs, sqrt min cell measure = " << sqrt(minCellMeasure) << ", min side length = " << minSideLength << endl;
  }

  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

  VTKExporter exporter(solution, mesh, varFactory);

  for (int refIndex=0;refIndex<numRefs;refIndex++){
    if (rank==0){
      cout << "on ref index " << refIndex << endl;
    }    
    rieszResidual->computeRieszRep(); // in preparation to get anisotropy    

    vector<int> cellIDs;
    refinementStrategy.getCellsAboveErrorThreshhold(cellIDs);

    map<int,double> energyError = solution->energyError();  

    map<int,double> xErrMap = xErr->cellIntegrals(cellIDs,mesh,5,true);
    map<int,double> yErrMap = yErr->cellIntegrals(cellIDs,mesh,5,true);
    map<int,double> restErrMap = restErr->cellIntegrals(cellIDs,mesh,5,true);    
    for (vector<ElementPtr>::iterator elemIt = mesh->activeElements().begin();elemIt!=mesh->activeElements().end();elemIt++){
      int cellID = (*elemIt)->cellID();
      double err = xErrMap[cellID]+ yErrMap[cellID] + restErrMap[cellID];
      //      if (rank==0)
	//      cout << "err thru LT = " << sqrt(err) << ", while energy err = " << energyError[cellID] << endl;
    }

    /*
    map<int,double> ratio,xErr,yErr;
    vector<ElementPtr> elems = mesh->activeElements();
    for (vector<ElementPtr>::iterator elemIt = elems.begin();elemIt!=elems.end();elemIt++){
      int cellID = (*elemIt)->cellID();
      ratio[cellID] = 0.0;
      xErr[cellID] = 0.0;
      yErr[cellID] = 0.0;
      if (std::find(cellIDs.begin(),cellIDs.end(),cellID)!=cellIDs.end()){ // if this cell is above energy thresh
	ratio[cellID] = yErrMap[cellID]/xErrMap[cellID];
	xErr[cellID] = xErrMap[cellID];
	yErr[cellID] = yErrMap[cellID];
      }
    }   
    FunctionPtr ratioFxn = Teuchos::rcp(new EnergyErrorFunction(ratio));
    FunctionPtr xErrFxn = Teuchos::rcp(new EnergyErrorFunction(xErr));
    FunctionPtr yErrFxn = Teuchos::rcp(new EnergyErrorFunction(yErr));
    exporter.exportFunction(ratioFxn, string("ratio")+oss.str());
    exporter.exportFunction(xErrFxn, string("xErr")+oss.str());
    exporter.exportFunction(yErrFxn, string("yErr")+oss.str());
    */
    if (useAnisotropy){
      refinementStrategy.refine(rank==0,xErrMap,yErrMap); //anisotropic refinements
    }else{
      refinementStrategy.refine(rank==0); // no anisotropy
    }

    // lower p to p = 1 at SINGULARITY only
    vector<int> ids;
    for (int i = 0;i<mesh->numActiveElements();i++){
      int cellID = mesh->activeElements()[i]->cellID();
      int elemOrder = mesh->cellPolyOrder(cellID)-1;
      FieldContainer<double> vv(4,2); mesh->verticesForCell(vv, cellID);
      bool vertexOnWall = false; bool vertexAtSingularity = false;
      for (int j = 0;j<4;j++){
	if ((abs(vv(j,0)-.5) + abs(vv(j,1)))<1e-10)
	  vertexAtSingularity = true;
      }	
      if (!vertexAtSingularity && elemOrder<2){
	ids.push_back(cellID);
      }
    }
    mesh->pRefine(ids); // to put order = 1
    /*
      if (elemOrder>1){
	if (vertexAtSingularity){
	  vector<int> ids;
	  ids.push_back(cellID);
	  mesh->pRefine(ids,1-(elemOrder-1)); // to put order = 1
	  //	  mesh->pRefine(ids); // to put order = 1
	  if (rank==0)
	    cout << "p unrefining elem with elemOrder = " << elemOrder << endl;
	}
      }else{
	if (!vertexAtSingularity){
	  vector<int> ids;
	  ids.push_back(cellID);	    
	  mesh->pRefine(ids,2-elemOrder);
	}	  
      }
      */



    double minSideLength = meshInfo.getMinCellSideLength() ;
    if (rank==0)
      cout << "minSideLength is " << minSideLength << endl;

    solution->condensedSolve();
    std::ostringstream oss;
    oss << refIndex;
    
  }

  // final solve on final mesh
  solution->setWriteMatrixToFile(true,"K.mat");
  solution->condensedSolve();

  ////////////////////////////////////////////////////////////////////////////////////////////////////////////
  //                                          CHECK CONDITIONING 
  ////////////////////////////////////////////////////////////////////////////////////////////////////////////

  bool checkConditioning = true;
  if (checkConditioning){
    double minSideLength = meshInfo.getMinCellSideLength() ;
    StandardAssembler assembler(solution);
    double maxCond = 0.0;
    int maxCellID = 0;
    for (int i = 0;i<mesh->numActiveElements();i++){
      int cellID = mesh->getActiveElement(i)->cellID();
      FieldContainer<double> ipMat = assembler.getIPMatrix(mesh->getElement(cellID));
      double cond = SerialDenseWrapper::getMatrixConditionNumber(ipMat);
      if (cond>maxCond){
	maxCond = cond;
	maxCellID = cellID;
      }
    }
    if (rank==0){
      cout << "cell ID  " << maxCellID << " has minCellLength " << minSideLength << " and condition estimate " << maxCond << endl;
    }
    string ipMatName = string("ipMat.mat");
    ElementPtr maxCondElem = mesh->getElement(maxCellID);
    FieldContainer<double> ipMat = assembler.getIPMatrix(maxCondElem);
    SerialDenseWrapper::writeMatrixToMatlabFile(ipMatName,ipMat);   
  }
  ////////////////////   print to file   ///////////////////////
  
  if (rank==0){
    exporter.exportSolution(string("robustIP"));
    cout << endl;
  }
 
  return 0;
} 
Example #24
0
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
  Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
  int rank=mpiSession.getRank();
  int numProcs=mpiSession.getNProc();
#else
  int rank = 0;
  int numProcs = 1;
#endif
  ////////////////////   DECLARE VARIABLES   ///////////////////////
  // define test variables
  VarFactory varFactory;
  VarPtr tau = varFactory.testVar("\\tau", HDIV);
  VarPtr v = varFactory.testVar("v", HGRAD);

  // define trial variables
  VarPtr uhat = varFactory.traceVar("\\widehat{u}");
  VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
  VarPtr u = varFactory.fieldVar("u");
  VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
  VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");

  vector<double> beta_const;
  beta_const.push_back(1.0);
  beta_const.push_back(0.0);
//  FunctionPtr beta = Teuchos::rcp(new Beta());

  double eps = 1e-2;

  ////////////////////   DEFINE BILINEAR FORM   ///////////////////////
  BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
  // tau terms:
  confusionBF->addTerm(sigma1 / eps, tau->x());
  confusionBF->addTerm(sigma2 / eps, tau->y());
  confusionBF->addTerm(u, tau->div());
  confusionBF->addTerm(-uhat, tau->dot_normal());

  // v terms:
  confusionBF->addTerm( sigma1, v->dx() );
  confusionBF->addTerm( sigma2, v->dy() );
  confusionBF->addTerm( beta_const * u, - v->grad() );
  confusionBF->addTerm( beta_n_u_minus_sigma_n, v);

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////
  // mathematician's norm
  IPPtr mathIP = Teuchos::rcp(new IP());
  mathIP->addTerm(tau);
  mathIP->addTerm(tau->div());

  mathIP->addTerm(v);
  mathIP->addTerm(v->grad());

  // quasi-optimal norm
  IPPtr qoptIP = Teuchos::rcp(new IP);
  qoptIP->addTerm( v );
  qoptIP->addTerm( tau / eps + v->grad() );
  qoptIP->addTerm( beta_const * v->grad() - tau->div() );

  // robust test norm
  IPPtr robIP = Teuchos::rcp(new IP);
  FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(eps) );
  if (enforceLocalConservation)
  {
    robIP->addZeroMeanTerm( v );
  }
  else
  {
    robIP->addTerm( ip_scaling * v );
  }

  robIP->addTerm( sqrt(eps) * v->grad() );
  robIP->addTerm( beta_const * v->grad() );
  robIP->addTerm( tau->div() );
  robIP->addTerm( ip_scaling/sqrt(eps) * tau );

  ////////////////////   SPECIFY RHS   ///////////////////////
  FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
  Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
  FunctionPtr f = zero;
  rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!

  ////////////////////   CREATE BCs   ///////////////////////
  Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
  //  SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
  //  SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary );

  SpatialFilterPtr inflowTop = Teuchos::rcp(new InflowLshapeTop);
  SpatialFilterPtr inflowBot = Teuchos::rcp(new InflowLshapeBottom);
  SpatialFilterPtr LshapeBot1 = Teuchos::rcp(new LshapeBottom1);
  SpatialFilterPtr LshapeBot2 = Teuchos::rcp(new LshapeBottom2);
  SpatialFilterPtr Top = Teuchos::rcp(new LshapeTop);
  SpatialFilterPtr Out = Teuchos::rcp(new LshapeOutflow);

  FunctionPtr u0 = Teuchos::rcp( new U0 );
  bc->addDirichlet(uhat, LshapeBot1, u0);
  bc->addDirichlet(uhat, LshapeBot2, u0);
  bc->addDirichlet(uhat, Top, u0);
  bc->addDirichlet(uhat, Out, u0);

  FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
  //  bc->addDirichlet(uhat, inflowBot, u0);
  FunctionPtr u0Top = Teuchos::rcp(new ParabolicProfile);
  FunctionPtr u0Bot = Teuchos::rcp(new LinearProfile);
  bc->addDirichlet(beta_n_u_minus_sigma_n, inflowTop, beta_const*n*u0Top);
  //  bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBot, beta_const*n*u0Bot);
  bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBot, beta_const*n*zero);

  ////////////////////   BUILD MESH   ///////////////////////
  // define nodes for mesh
  int H1Order = 2, pToAdd = 2;
  /*
  FieldContainer<double> quadPoints(4,2);

  quadPoints(0,0) = 0.0; // x1
  quadPoints(0,1) = 0.0; // y1
  quadPoints(1,0) = 1.0;
  quadPoints(1,1) = 0.0;
  quadPoints(2,0) = 1.0;
  quadPoints(2,1) = 1.0;
  quadPoints(3,0) = 0.0;
  quadPoints(3,1) = 1.0;

  int horizontalCells = 1, verticalCells = 1;

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
                                                confusionBF, H1Order, H1Order+pToAdd);
  */

  Teuchos::RCP<Mesh> mesh;
  // L-shaped domain for double ramp problem
  FieldContainer<double> A(2), B(2), C(2), D(2), E(2), F(2), G(2), H(2);
  A(0) = 0.0;
  A(1) = 0.5;
  B(0) = 0.0;
  B(1) = 1.0;
  C(0) = 0.5;
  C(1) = 1.0;
  D(0) = 1.0;
  D(1) = 1.0;
  E(0) = 1.0;
  E(1) = 0.5;
  F(0) = 1.0;
  F(1) = 0.0;
  G(0) = 0.5;
  G(1) = 0.0;
  H(0) = 0.5;
  H(1) = 0.5;
  vector<FieldContainer<double> > vertices;
  vertices.push_back(A);
  int A_index = 0;
  vertices.push_back(B);
  int B_index = 1;
  vertices.push_back(C);
  int C_index = 2;
  vertices.push_back(D);
  int D_index = 3;
  vertices.push_back(E);
  int E_index = 4;
  vertices.push_back(F);
  int F_index = 5;
  vertices.push_back(G);
  int G_index = 6;
  vertices.push_back(H);
  int H_index = 7;
  vector< vector<int> > elementVertices;
  vector<int> el1, el2, el3, el4, el5;
  // left patch:
  el1.push_back(A_index);
  el1.push_back(H_index);
  el1.push_back(C_index);
  el1.push_back(B_index);
  // top right:
  el2.push_back(H_index);
  el2.push_back(E_index);
  el2.push_back(D_index);
  el2.push_back(C_index);
  // bottom right:
  el3.push_back(G_index);
  el3.push_back(F_index);
  el3.push_back(E_index);
  el3.push_back(H_index);

  elementVertices.push_back(el1);
  elementVertices.push_back(el2);
  elementVertices.push_back(el3);

  mesh = Teuchos::rcp( new Mesh(vertices, elementVertices, confusionBF, H1Order, pToAdd) );

  ////////////////////   SOLVE & REFINE   ///////////////////////
  // Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, qoptIP) );
  Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) );
  // solution->setFilter(pc);

  if (enforceLocalConservation)
  {
    FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
    solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero);
  }

  double energyThreshold = 0.2; // for mesh refinements
  RefinementStrategy refinementStrategy( solution, energyThreshold );

  int numRefs = 8;

  for (int refIndex=0; refIndex<numRefs; refIndex++)
  {
    solution->solve(false);
    refinementStrategy.refine(rank==0); // print to console on rank 0
  }
  // one more solve on the final refined mesh:
  solution->solve(false);

  if (rank==0)
  {
    solution->writeToVTK("step.vtu",min(H1Order+1,4));
    solution->writeFluxesToFile(uhat->ID(), "uhat.dat");

    cout << "wrote files: u.m, uhat.dat\n";
  }

  return 0;
}
Example #25
0
int main(int argc, char *argv[])
{
  // Process command line arguments
#ifdef HAVE_MPI
  Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
  int rank=mpiSession.getRank();
  int numProcs=mpiSession.getNProc();
#else
  int rank = 0;
  int numProcs = 1;
#endif

  ////////////////////   DECLARE VARIABLES   ///////////////////////
  // define test variables
  VarFactory varFactory;
  VarPtr v = varFactory.testVar("v", HGRAD);

  // define trial variables
  VarPtr beta_n_u_hat = varFactory.fluxVar("\\widehat{\\beta \\cdot n }");
  VarPtr u = varFactory.fieldVar("u");

  FunctionPtr beta = Teuchos::rcp(new Beta());

  ////////////////////   BUILD MESH   ///////////////////////
  BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
  // define nodes for mesh
  FieldContainer<double> meshBoundary(4,2);

  meshBoundary(0,0) = -1.0; // x1
  meshBoundary(0,1) = -1.0; // y1
  meshBoundary(1,0) =  1.0;
  meshBoundary(1,1) = -1.0;
  meshBoundary(2,0) =  1.0;
  meshBoundary(2,1) =  1.0;
  meshBoundary(3,0) = -1.0;
  meshBoundary(3,1) =  1.0;

  int horizontalCells = 32, verticalCells = 32;

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
                            confusionBF, H1Order, H1Order+pToAdd);

  ////////////////////////////////////////////////////////////////////
  // INITIALIZE FLOW FUNCTIONS
  ////////////////////////////////////////////////////////////////////

  BCPtr nullBC = Teuchos::rcp((BC*)NULL);
  RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
  IPPtr nullIP = Teuchos::rcp((IP*)NULL);
  SolutionPtr prevTimeFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
  SolutionPtr flowResidual = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );

  FunctionPtr u_prev_time = Teuchos::rcp( new PreviousSolutionFunction(prevTimeFlow, u) );

  ////////////////////   DEFINE BILINEAR FORM   ///////////////////////
  Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
  FunctionPtr invDt = Teuchos::rcp(new ScalarParamFunction(1.0/dt));

  // v terms:
  confusionBF->addTerm( beta * u, - v->grad() );
  confusionBF->addTerm( beta_n_u_hat, v);

  confusionBF->addTerm( u, invDt*v );
  rhs->addTerm( u_prev_time * invDt * v );

  ////////////////////   SPECIFY RHS   ///////////////////////
  FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
  rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////
  // robust test norm
  IPPtr ip = confusionBF->graphNorm();
  // IPPtr ip = Teuchos::rcp(new IP);
  // ip->addTerm(v);
  // ip->addTerm(invDt*v - beta*v->grad());

  ////////////////////   CREATE BCs   ///////////////////////
  Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
  SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary(beta) );
  FunctionPtr u0 = Teuchos::rcp( new ConstantScalarFunction(0) );
  FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );

  bc->addDirichlet(beta_n_u_hat, inflowBoundary, beta*n*u0);

  Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );

  // ==================== Register Solutions ==========================
  mesh->registerSolution(solution);
  mesh->registerSolution(prevTimeFlow);
  mesh->registerSolution(flowResidual);

  // ==================== SET INITIAL GUESS ==========================
  FunctionPtr u_init = Teuchos::rcp(new InitialCondition());
  map<int, Teuchos::RCP<Function> > functionMap;
  functionMap[u->ID()]      = u_init;

  prevTimeFlow->projectOntoMesh(functionMap);

  ////////////////////   SOLVE & REFINE   ///////////////////////
  // if (enforceLocalConservation) {
  //   // FunctionPtr parity = Teuchos::rcp<Function>( new SideParityFunction );
  //   // LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(parity, beta_n_u_minus_sigma_n) );
  //   LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(1.0, beta_n_u_minus_sigma_n) );
  //   LinearTermPtr sourcePart = Teuchos::rcp<LinearTerm>( new LinearTerm(invDt, u) );
  //   conservedQuantity->addTerm(sourcePart, true);
  //   solution->lagrangeConstraints()->addConstraint(conservedQuantity == u_prev_time * invDt);
  // }

  int timestepCount = 0;
  double time_tol = 1e-8;
  double L2_time_residual = 1e9;
  while((L2_time_residual > time_tol) && (timestepCount < numTimeSteps))
  {
    solution->solve(false);
    // Subtract solutions to get residual
    flowResidual->setSolution(solution);
    flowResidual->addSolution(prevTimeFlow, -1.0);
    L2_time_residual = flowResidual->L2NormOfSolutionGlobal(u->ID());

    if (rank == 0)
    {
      cout << endl << "Timestep: " << timestepCount << ", dt = " << dt << ", Time residual = " << L2_time_residual << endl;

      stringstream outfile;
      outfile << "rotatingCylinder_" << timestepCount;
      solution->writeToVTK(outfile.str(), 5);

      // Check local conservation
      FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_hat) );
      FunctionPtr source = Teuchos::rcp( new PreviousSolutionFunction(flowResidual, u) );
      source = invDt * source;
      Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, source, varFactory, mesh);
      cout << "Mass flux: Largest Local = " << fluxImbalances[0]
           << ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
    }

    prevTimeFlow->setSolution(solution); // reset previous time solution to current time sol
    timestepCount++;
  }

  return 0;
}
Example #26
0
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
  Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
  choice::MpiArgs args( argc, argv );
#else
  choice::Args args( argc, argv );
#endif
  int commRank = Teuchos::GlobalMPISession::getRank();
  int numProcs = Teuchos::GlobalMPISession::getNProc();

  // Required arguments
  int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
  bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation");
  bool steady = args.Input<bool>("--steady", "run steady rather than transient");

  // Optional arguments (have defaults)
  double dt = args.Input("--dt", "time step", 0.25);
  int numTimeSteps = args.Input("--nt", "number of time steps", 20);
  halfWidth = args.Input("--halfWidth", "half width of inlet profile", 1.0);
  args.Process();

  ////////////////////   DECLARE VARIABLES   ///////////////////////
  // define test variables
  VarFactory varFactory;
  VarPtr v = varFactory.testVar("v", HGRAD);

  // define trial variables
  VarPtr beta_n_u_hat = varFactory.fluxVar("\\widehat{\\beta \\cdot n }");
  VarPtr u = varFactory.fieldVar("u");

  vector<double> beta;
  beta.push_back(1.0);
  beta.push_back(0.0);

  ////////////////////   BUILD MESH   ///////////////////////
  BFPtr bf = Teuchos::rcp( new BF(varFactory) );
  // define nodes for mesh
  FieldContainer<double> meshBoundary(4,2);

  meshBoundary(0,0) =  0.0; // x1
  meshBoundary(0,1) = -2.0; // y1
  meshBoundary(1,0) =  4.0;
  meshBoundary(1,1) = -2.0;
  meshBoundary(2,0) =  4.0;
  meshBoundary(2,1) =  2.0;
  meshBoundary(3,0) =  0.0;
  meshBoundary(3,1) =  2.0;

  int horizontalCells = 8, verticalCells = 8;

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
                            bf, H1Order, H1Order+pToAdd);

  ////////////////////////////////////////////////////////////////////
  // INITIALIZE FLOW FUNCTIONS
  ////////////////////////////////////////////////////////////////////

  BCPtr nullBC = Teuchos::rcp((BC*)NULL);
  RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
  IPPtr nullIP = Teuchos::rcp((IP*)NULL);
  SolutionPtr prevTimeFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
  SolutionPtr flowResidual = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );

  FunctionPtr u_prev_time = Teuchos::rcp( new PreviousSolutionFunction(prevTimeFlow, u) );

  ////////////////////   DEFINE BILINEAR FORM   ///////////////////////
  Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
  FunctionPtr invDt = Teuchos::rcp(new ScalarParamFunction(1.0/dt));

  // v terms:
  bf->addTerm( beta * u, - v->grad() );
  bf->addTerm( beta_n_u_hat, v);

  if (!steady)
  {
    bf->addTerm( u, invDt*v );
    rhs->addTerm( u_prev_time * invDt * v );
  }

  ////////////////////   SPECIFY RHS   ///////////////////////
  FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
  rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////
  IPPtr ip = bf->graphNorm();
  // ip->addTerm(v);
  // ip->addTerm(beta*v->grad());

  ////////////////////   CREATE BCs   ///////////////////////
  Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
  SpatialFilterPtr lBoundary = Teuchos::rcp( new LeftBoundary );
  FunctionPtr u1 = Teuchos::rcp( new InletBC );
  bc->addDirichlet(beta_n_u_hat, lBoundary, -u1);

  Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );

  // ==================== Register Solutions ==========================
  mesh->registerSolution(solution);
  mesh->registerSolution(prevTimeFlow);
  mesh->registerSolution(flowResidual);

  // ==================== SET INITIAL GUESS ==========================
  double u_free = 0.0;
  map<int, Teuchos::RCP<Function> > functionMap;
  // functionMap[u->ID()]      = Teuchos::rcp( new ConInletBC
  functionMap[u->ID()]      = Teuchos::rcp( new InletBC );

  prevTimeFlow->projectOntoMesh(functionMap);

  ////////////////////   SOLVE & REFINE   ///////////////////////
  if (enforceLocalConservation)
  {
    if (steady)
    {
      FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
      solution->lagrangeConstraints()->addConstraint(beta_n_u_hat == zero);
    }
    else
    {
      // FunctionPtr parity = Teuchos::rcp<Function>( new SideParityFunction );
      // LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(parity, beta_n_u_minus_sigma_n) );
      LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(1.0, beta_n_u_hat) );
      LinearTermPtr sourcePart = Teuchos::rcp<LinearTerm>( new LinearTerm(invDt, u) );
      conservedQuantity->addTerm(sourcePart, true);
      solution->lagrangeConstraints()->addConstraint(conservedQuantity == u_prev_time * invDt);
    }
  }

  double energyThreshold = 0.2; // for mesh refinements
  RefinementStrategy refinementStrategy( solution, energyThreshold );
  VTKExporter exporter(solution, mesh, varFactory);

  for (int refIndex=0; refIndex<=numRefs; refIndex++)
  {
    if (steady)
    {
      solution->solve(false);

      if (commRank == 0)
      {
        stringstream outfile;
        outfile << "Convection_" << refIndex;
        exporter.exportSolution(outfile.str());

        // Check local conservation
        FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_hat) );
        FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
        Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, varFactory, mesh);
        cout << "Mass flux: Largest Local = " << fluxImbalances[0]
             << ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
      }
    }
    else
    {
      int timestepCount = 0;
      double time_tol = 1e-8;
      double L2_time_residual = 1e9;
      // cout << L2_time_residual <<" "<< time_tol << timestepCount << numTimeSteps << endl;
      while((L2_time_residual > time_tol) && (timestepCount < numTimeSteps))
      {
        solution->solve(false);
        // Subtract solutions to get residual
        flowResidual->setSolution(solution);
        flowResidual->addSolution(prevTimeFlow, -1.0);
        L2_time_residual = flowResidual->L2NormOfSolutionGlobal(u->ID());

        if (commRank == 0)
        {
          cout << endl << "Timestep: " << timestepCount << ", dt = " << dt << ", Time residual = " << L2_time_residual << endl;

          stringstream outfile;
          outfile << "TransientConvection_" << refIndex << "-" << timestepCount;
          exporter.exportSolution(outfile.str());

          // Check local conservation
          FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_hat) );
          FunctionPtr source = Teuchos::rcp( new PreviousSolutionFunction(flowResidual, u) );
          source = -invDt * source;
          Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, source, varFactory, mesh);
          cout << "Mass flux: Largest Local = " << fluxImbalances[0]
               << ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
        }

        prevTimeFlow->setSolution(solution); // reset previous time solution to current time sol
        timestepCount++;
      }
    }

    if (refIndex < numRefs)
      refinementStrategy.refine(commRank==0); // print to console on commRank 0
  }

  return 0;
}
Example #27
0
bool LinearTermTests::testIntegrateMixedBasis()
{
  bool success = true;

  ////////////////////   DECLARE VARIABLES   ///////////////////////
  // define test variables
  VarFactoryPtr varFactory = VarFactory::varFactory();
  VarPtr v = varFactory->testVar("v", HGRAD);

  // define trial variables
  VarPtr beta_n_u_hat = varFactory->fluxVar("\\widehat{\\beta \\cdot n }");
  VarPtr u = varFactory->fieldVar("u");

  vector<double> beta;
  beta.push_back(1.0);
  beta.push_back(1.0);

  ////////////////////   DEFINE BILINEAR FORM/Mesh   ///////////////////////

  BFPtr convectionBF = Teuchos::rcp( new BF(varFactory) );

  // v terms:
  convectionBF->addTerm( -u, beta * v->grad() );
  convectionBF->addTerm( beta_n_u_hat, v);
  convectionBF->addTerm( u, v);

  // build CONSTANT SINGLE ELEMENT MESH
  int order = 0;
  int H1Order = order+1;
  int pToAdd = 1;
  int nCells = 2; // along a side

  // create a pointer to a new mesh:
  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,convectionBF, H1Order, H1Order+pToAdd);
  ElementTypePtr elemType = mesh->getElement(0)->elementType();
  BasisCachePtr basisCache = Teuchos::rcp(new BasisCache(elemType, mesh));
  vector<GlobalIndexType> cellIDs;
  vector< ElementPtr > allElems = mesh->activeElements();
  vector< ElementPtr >::iterator elemIt;
  for (elemIt=allElems.begin(); elemIt!=allElems.end(); elemIt++)
  {
    cellIDs.push_back((*elemIt)->cellID());
  }
  bool createSideCacheToo = true;
  basisCache->setPhysicalCellNodes(mesh->physicalCellNodesGlobal(elemType), cellIDs, createSideCacheToo);

  int numTrialDofs = elemType->trialOrderPtr->totalDofs();
  int numCells = mesh->numActiveElements();
  double areaPerCell = 1.0 / numCells;
  FieldContainer<double> integrals(numCells,numTrialDofs);
  FieldContainer<double> expectedIntegrals(numCells,numTrialDofs);
  double sidelengthOfCell = 1.0 / nCells;
  DofOrderingPtr trialOrdering = elemType->trialOrderPtr;
  int dofForField = trialOrdering->getDofIndex(u->ID(), 0);
  vector<int> dofsForFlux;
  const vector<int>* sidesForFlux = &trialOrdering->getSidesForVarID(beta_n_u_hat->ID());
  for (vector<int>::const_iterator sideIt = sidesForFlux->begin(); sideIt != sidesForFlux->end(); sideIt++)
  {
    int sideIndex = *sideIt;
    dofsForFlux.push_back(trialOrdering->getDofIndex(beta_n_u_hat->ID(), 0, sideIndex));
  }
  for (int cellIndex = 0; cellIndex < numCells; cellIndex++)
  {
    expectedIntegrals(cellIndex, dofForField) = areaPerCell;
    for (vector<int>::iterator dofIt = dofsForFlux.begin(); dofIt != dofsForFlux.end(); dofIt++)
    {
      int fluxDofIndex = *dofIt;
      expectedIntegrals(cellIndex, fluxDofIndex) = sidelengthOfCell;
    }
  }

//  cout << "expectedIntegrals:\n" << expectedIntegrals;

  // setup: with constant degrees of freedom, we expect that the integral of int_dK (flux) + int_K (field) will be ones for each degree of freedom, assuming the basis functions for these constants field/flux variables are just C = 1.0.
  //
  //On a unit square, int_K (constant) = 1.0, and int_dK (u_i) = 1, for i = 0,...,3.

  LinearTermPtr lt = 1.0 * beta_n_u_hat;
  LinearTermPtr field =  1.0 * u;
  lt->addTerm(field,true);
  lt->integrate(integrals, elemType->trialOrderPtr, basisCache);

  double tol = 1e-12;
  double maxDiff;
  success = TestSuite::fcsAgree(integrals,expectedIntegrals,tol,maxDiff);
  if (success==false)
  {
    cout << "Failed testIntegrateMixedBasis with maxDiff = " << maxDiff << endl;
  }

  return success;
}
Example #28
0
int main(int argc, char *argv[])
{

#ifdef HAVE_MPI
  Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
  choice::MpiArgs args( argc, argv );
#else
  choice::Args args( argc, argv );
#endif
  int rank = Teuchos::GlobalMPISession::getRank();
  int numProcs = Teuchos::GlobalMPISession::getNProc();

  int nCells = args.Input<int>("--nCells", "num cells",2);
  int numRefs = args.Input<int>("--numRefs","num adaptive refinements",0);
  int numPreRefs = args.Input<int>("--numPreRefs","num preemptive adaptive refinements",0);
  int order = args.Input<int>("--order","order of approximation",2);
  double eps = args.Input<double>("--epsilon","diffusion parameter",1e-2);
  double energyThreshold = args.Input<double>("-energyThreshold","energy thresh for adaptivity", .5);
  double rampHeight = args.Input<double>("--rampHeight","ramp height at x = 2", 0.0);
  bool useAnisotropy = args.Input<bool>("--useAnisotropy","aniso flag ", false);

  FunctionPtr zero = Function::constant(0.0);
  FunctionPtr one = Function::constant(1.0);
  FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
  vector<double> e1,e2;
  e1.push_back(1.0);
  e1.push_back(0.0);
  e2.push_back(0.0);
  e2.push_back(1.0);

  ////////////////////   DECLARE VARIABLES   ///////////////////////
  // define test variables
  VarFactory varFactory;
  VarPtr tau = varFactory.testVar("\\tau", HDIV);
  VarPtr v = varFactory.testVar("v", HGRAD);

  // define trial variables
  VarPtr uhat = varFactory.traceVar("\\widehat{u}");
  VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
  VarPtr u = varFactory.fieldVar("u");
  VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
  VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");

  vector<double> beta;
  beta.push_back(1.0);
  beta.push_back(0.0);

  ////////////////////   DEFINE BILINEAR FORM   ///////////////////////

  BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
  // tau terms:
  confusionBF->addTerm(sigma1 / eps, tau->x());
  confusionBF->addTerm(sigma2 / eps, tau->y());
  confusionBF->addTerm(u, tau->div());
  confusionBF->addTerm(uhat, -tau->dot_normal());

  // v terms:
  confusionBF->addTerm( sigma1, v->dx() );
  confusionBF->addTerm( sigma2, v->dy() );
  confusionBF->addTerm( -u, beta * v->grad() );
  confusionBF->addTerm( beta_n_u_minus_sigma_n, v);

  // first order term with magnitude alpha
  double alpha = 0.0;
  confusionBF->addTerm(alpha * u, v);

  ////////////////////   DEFINE INNER PRODUCT(S)   ///////////////////////

  // robust test norm
  IPPtr robIP = Teuchos::rcp(new IP);
  FunctionPtr C_h = Teuchos::rcp( new EpsilonScaling(eps) );
  FunctionPtr invH = Teuchos::rcp(new InvHScaling);
  FunctionPtr invSqrtH = Teuchos::rcp(new InvSqrtHScaling);
  FunctionPtr sqrtH = Teuchos::rcp(new SqrtHScaling);
  robIP->addTerm(v*alpha);
  robIP->addTerm(invSqrtH*v);
  //  robIP->addTerm(v);
  robIP->addTerm(sqrt(eps) * v->grad() );
  robIP->addTerm(beta * v->grad() );
  robIP->addTerm(tau->div() );
  robIP->addTerm(C_h/sqrt(eps) * tau );

  LinearTermPtr vVecLT = Teuchos::rcp(new LinearTerm);
  LinearTermPtr tauVecLT = Teuchos::rcp(new LinearTerm);
  vVecLT->addTerm(sqrt(eps)*v->grad());
  tauVecLT->addTerm(C_h/sqrt(eps)*tau);

  LinearTermPtr restLT = Teuchos::rcp(new LinearTerm);
  restLT->addTerm(alpha*v);
  restLT->addTerm(invSqrtH*v);
  restLT = restLT + beta * v->grad();
  restLT = restLT + tau->div();

  ////////////////////   SPECIFY RHS   ///////////////////////

  Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
  FunctionPtr f = zero;
  //  f = one;
  rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!

  ////////////////////   CREATE BCs   ///////////////////////
  Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );

  //  SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
  //  SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary);
  //  bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, zero);
  //  bc->addDirichlet(uhat, outflowBoundary, zero);

  SpatialFilterPtr rampInflow = Teuchos::rcp(new LeftInflow);
  SpatialFilterPtr rampBoundary = MeshUtilities::rampBoundary(rampHeight);
  SpatialFilterPtr freeStream = Teuchos::rcp(new FreeStreamBoundary);
  SpatialFilterPtr outflowBoundary = Teuchos::rcp(new OutflowBoundary);
  bc->addDirichlet(uhat, rampBoundary, one);
  //  bc->addDirichlet(uhat, outflowBoundary, one);
  bc->addDirichlet(beta_n_u_minus_sigma_n, rampInflow, zero);
  bc->addDirichlet(beta_n_u_minus_sigma_n, freeStream, zero);

  ////////////////////   BUILD MESH   ///////////////////////
  // define nodes for mesh
  int H1Order = order+1;
  int pToAdd = 2;

  // create a pointer to a new mesh:
  //  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);
  Teuchos::RCP<Mesh> mesh = MeshUtilities::buildRampMesh(rampHeight,confusionBF, H1Order, H1Order+pToAdd);
  mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));

  ////////////////////   SOLVE & REFINE   ///////////////////////

  Teuchos::RCP<Solution> solution;
  solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) );
  //  solution->solve(false);
  solution->condensedSolve();

  LinearTermPtr residual = rhs->linearTermCopy();
  residual->addTerm(-confusionBF->testFunctional(solution));
  RieszRepPtr rieszResidual = Teuchos::rcp(new RieszRep(mesh, robIP, residual));
  rieszResidual->computeRieszRep();
  FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,rieszResidual));
  FunctionPtr e_tau = Teuchos::rcp(new RepFunction(tau,rieszResidual));
  map<int,FunctionPtr> errRepMap;
  errRepMap[v->ID()] = e_v;
  errRepMap[tau->ID()] = e_tau;
  FunctionPtr errTau = tauVecLT->evaluate(errRepMap,false);
  FunctionPtr errV = vVecLT->evaluate(errRepMap,false);
  FunctionPtr errRest = restLT->evaluate(errRepMap,false);
  FunctionPtr xErr = (errTau->x())*(errTau->x()) + (errV->dx())*(errV->dx());
  FunctionPtr yErr = (errTau->y())*(errTau->y()) + (errV->dy())*(errV->dy());
  FunctionPtr restErr = errRest*errRest;

  RefinementStrategy refinementStrategy( solution, energyThreshold );

  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
  //                     PRE REFINEMENTS
  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

  if (rank==0)
  {
    cout << "Number of pre-refinements = " << numPreRefs << endl;
  }
  for (int i =0; i<=numPreRefs; i++)
  {
    vector<ElementPtr> elems = mesh->activeElements();
    vector<ElementPtr>::iterator elemIt;
    vector<int> wallCells;
    for (elemIt=elems.begin(); elemIt != elems.end(); elemIt++)
    {
      int cellID = (*elemIt)->cellID();
      int numSides = mesh->getElement(cellID)->numSides();
      FieldContainer<double> vertices(numSides,2); //for quads

      mesh->verticesForCell(vertices, cellID);
      bool cellIDset = false;
      for (int j = 0; j<numSides; j++)
      {
        if ((abs(vertices(j,0)-1.0)<1e-7) && (abs(vertices(j,1))<1e-7) && !cellIDset)  // if at singularity, i.e. if a vertex is (1,0)
        {
          wallCells.push_back(cellID);
          cellIDset = true;
        }
      }
    }
    if (i<numPreRefs)
    {
      refinementStrategy.refineCells(wallCells);
    }
  }

  ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
  VTKExporter exporter(solution, mesh, varFactory);

  for (int refIndex=0; refIndex<numRefs; refIndex++)
  {
    if (rank==0)
    {
      cout << "on ref index " << refIndex << endl;
    }
    rieszResidual->computeRieszRep(); // in preparation to get anisotropy

    vector<int> cellIDs;
    refinementStrategy.getCellsAboveErrorThreshhold(cellIDs);

    map<int,double> energyError = solution->energyError();

    map<int,double> xErrMap = xErr->cellIntegrals(cellIDs,mesh,5,true);
    map<int,double> yErrMap = yErr->cellIntegrals(cellIDs,mesh,5,true);
    map<int,double> restErrMap = restErr->cellIntegrals(cellIDs,mesh,5,true);
    for (vector<ElementPtr>::iterator elemIt = mesh->activeElements().begin(); elemIt!=mesh->activeElements().end(); elemIt++)
    {
      int cellID = (*elemIt)->cellID();
      double err = xErrMap[cellID]+ yErrMap[cellID] + restErrMap[cellID];
      if (rank==0)
        cout << "err thru LT = " << sqrt(err) << ", while energy err = " << energyError[cellID] << endl;
    }

    map<int,double> ratio,xErr,yErr;
    vector<ElementPtr> elems = mesh->activeElements();
    for (vector<ElementPtr>::iterator elemIt = elems.begin(); elemIt!=elems.end(); elemIt++)
    {
      int cellID = (*elemIt)->cellID();
      ratio[cellID] = 0.0;
      xErr[cellID] = 0.0;
      yErr[cellID] = 0.0;
      if (std::find(cellIDs.begin(),cellIDs.end(),cellID)!=cellIDs.end())  // if this cell is above energy thresh
      {
        ratio[cellID] = yErrMap[cellID]/xErrMap[cellID];
        xErr[cellID] = xErrMap[cellID];
        yErr[cellID] = yErrMap[cellID];
      }
    }
    FunctionPtr ratioFxn = Teuchos::rcp(new EnergyErrorFunction(ratio));
    FunctionPtr xErrFxn = Teuchos::rcp(new EnergyErrorFunction(xErr));
    FunctionPtr yErrFxn = Teuchos::rcp(new EnergyErrorFunction(yErr));
    std::ostringstream oss;
    oss << refIndex;
    exporter.exportFunction(ratioFxn, string("ratio")+oss.str());
    exporter.exportFunction(xErrFxn, string("xErr")+oss.str());
    exporter.exportFunction(yErrFxn, string("yErr")+oss.str());

    if (useAnisotropy)
    {
      refinementStrategy.refine(rank==0,xErrMap,yErrMap); //anisotropic refinements
    }
    else
    {
      refinementStrategy.refine(rank==0); // no anisotropy
    }

    solution->condensedSolve();
  }

  // final solve on final mesh
  solution->condensedSolve();

  ////////////////////   print to file   ///////////////////////

  FunctionPtr orderFxn = Teuchos::rcp(new MeshPolyOrderFunction(mesh));
  std::ostringstream oss;
  oss << nCells;
  if (rank==0)
  {
    exporter.exportSolution(string("robustIP")+oss.str());
    exporter.exportFunction(orderFxn, "meshOrder");
    cout << endl;
  }

  return 0;
}
Example #29
0
int main(int argc, char *argv[])
{
#ifdef ENABLE_INTEL_FLOATING_POINT_EXCEPTIONS
  cout << "NOTE: enabling floating point exceptions for divide by zero.\n";
  _MM_SET_EXCEPTION_MASK(_MM_GET_EXCEPTION_MASK() & ~_MM_MASK_INVALID);
#endif

  Teuchos::GlobalMPISession mpiSession(&argc, &argv);
  int rank = Teuchos::GlobalMPISession::getRank();

#ifdef HAVE_MPI
  Epetra_MpiComm Comm(MPI_COMM_WORLD);
  //cout << "rank: " << rank << " of " << numProcs << endl;
#else
  Epetra_SerialComm Comm;
#endif

  Comm.Barrier(); // set breakpoint here to allow debugger attachment to other MPI processes than the one you automatically attached to.

  Teuchos::CommandLineProcessor cmdp(false,true); // false: don't throw exceptions; true: do return errors for unrecognized options

  double minTol = 1e-8;

  bool use3D = false;
  int refCount = 10;

  int k = 4; // poly order for field variables
  int delta_k = use3D ? 3 : 2;   // test space enrichment
  int k_coarse = 0;

  bool useMumps = true;
  bool useGMGSolver = true;

  bool enforceOneIrregularity = true;
  bool useStaticCondensation = false;
  bool conformingTraces = false;
  bool useDiagonalScaling = false; // of the global stiffness matrix in GMGSolver

  bool printRefinementDetails = false;

  bool useWeightedGraphNorm = true; // graph norm scaled according to units, more or less

  int numCells = 2;

  int AztecOutputLevel = 1;
  int gmgMaxIterations = 10000;
  int smootherOverlap = 0;
  double relativeTol = 1e-6;
  double D = 1.0; // characteristic length scale

  cmdp.setOption("polyOrder",&k,"polynomial order for field variable u");
  cmdp.setOption("delta_k", &delta_k, "test space polynomial order enrichment");
  cmdp.setOption("k_coarse", &k_coarse, "polynomial order for field variables on coarse mesh");
  cmdp.setOption("numRefs",&refCount,"number of refinements");
  cmdp.setOption("D", &D, "domain dimension");
  cmdp.setOption("useConformingTraces", "useNonConformingTraces", &conformingTraces);
  cmdp.setOption("enforceOneIrregularity", "dontEnforceOneIrregularity", &enforceOneIrregularity);

  cmdp.setOption("smootherOverlap", &smootherOverlap, "overlap for smoother");

  cmdp.setOption("printRefinementDetails", "dontPrintRefinementDetails", &printRefinementDetails);
  cmdp.setOption("azOutput", &AztecOutputLevel, "Aztec output level");
  cmdp.setOption("numCells", &numCells, "number of cells in the initial mesh");
  cmdp.setOption("useScaledGraphNorm", "dontUseScaledGraphNorm", &useWeightedGraphNorm);
//  cmdp.setOption("gmgTol", &gmgTolerance, "tolerance for GMG convergence");
  cmdp.setOption("relativeTol", &relativeTol, "Energy error-relative tolerance for iterative solver.");
  cmdp.setOption("gmgMaxIterations", &gmgMaxIterations, "tolerance for GMG convergence");

  bool enhanceUField = false;
  cmdp.setOption("enhanceUField", "dontEnhanceUField", &enhanceUField);
  cmdp.setOption("useStaticCondensation", "dontUseStaticCondensation", &useStaticCondensation);

  if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL)
  {
#ifdef HAVE_MPI
    MPI_Finalize();
#endif
    return -1;
  }

  double width = D, height = D, depth = D;

  VarFactory varFactory;
  // fields:
  VarPtr u = varFactory.fieldVar("u", L2);
  VarPtr sigma = varFactory.fieldVar("\\sigma", VECTOR_L2);

  FunctionPtr n = Function::normal();
  // traces:
  VarPtr u_hat;

  if (conformingTraces)
  {
    u_hat = varFactory.traceVar("\\widehat{u}", u);
  }
  else
  {
    cout << "Note: using non-conforming traces.\n";
    u_hat = varFactory.traceVar("\\widehat{u}", u, L2);
  }
  VarPtr sigma_n_hat = varFactory.fluxVar("\\widehat{\\sigma}_{n}", sigma * n);

  // test functions:
  VarPtr tau = varFactory.testVar("\\tau", HDIV);
  VarPtr v = varFactory.testVar("v", HGRAD);

  BFPtr poissonBF = Teuchos::rcp( new BF(varFactory) );
  FunctionPtr alpha = Function::constant(1); // viscosity

  // tau terms:
  poissonBF->addTerm(sigma / alpha, tau);
  poissonBF->addTerm(-u, tau->div()); // (sigma1, tau1)
  poissonBF->addTerm(u_hat, tau * n);

  // v terms:
  poissonBF->addTerm(- sigma, v->grad()); // (mu sigma1, grad v1)
  poissonBF->addTerm( sigma_n_hat, v);

  int horizontalCells = numCells, verticalCells = numCells, depthCells = numCells;

  vector<double> domainDimensions;
  domainDimensions.push_back(width);
  domainDimensions.push_back(height);

  vector<int> elementCounts;
  elementCounts.push_back(horizontalCells);
  elementCounts.push_back(verticalCells);

  if (use3D)
  {
    domainDimensions.push_back(depth);
    elementCounts.push_back(depthCells);
  }

  MeshPtr mesh, k0Mesh;

  int H1Order = k + 1;
  int H1Order_coarse = k_coarse + 1;
  if (!use3D)
  {
    Teuchos::ParameterList pl;

    map<int,int> trialOrderEnhancements;

    if (enhanceUField)
    {
      trialOrderEnhancements[u->ID()] = 1;
    }

    BFPtr poissonBilinearForm = poissonBF;

    pl.set("useMinRule", true);
    pl.set("bf",poissonBilinearForm);
    pl.set("H1Order", H1Order);
    pl.set("delta_k", delta_k);
    pl.set("horizontalElements", horizontalCells);
    pl.set("verticalElements", verticalCells);
    pl.set("divideIntoTriangles", false);
    pl.set("useConformingTraces", conformingTraces);
    pl.set("trialOrderEnhancements", &trialOrderEnhancements);
    pl.set("x0",(double)0);
    pl.set("y0",(double)0);
    pl.set("width", width);
    pl.set("height",height);

    mesh = MeshFactory::quadMesh(pl);

    pl.set("H1Order", H1Order_coarse);
    k0Mesh = MeshFactory::quadMesh(pl);

  }
  else
  {
    mesh = MeshFactory::rectilinearMesh(poissonBF, domainDimensions, elementCounts, H1Order, delta_k);
    k0Mesh = MeshFactory::rectilinearMesh(poissonBF, domainDimensions, elementCounts, H1Order_coarse, delta_k);
  }

  mesh->registerObserver(k0Mesh); // ensure that the k0 mesh refinements track those of the solution mesh

  RHSPtr rhs = RHS::rhs(); // zero
  FunctionPtr sin_pi_x = Teuchos::rcp( new Sin_ax(PI/D) );
  FunctionPtr sin_pi_y = Teuchos::rcp( new Sin_ay(PI/D) );
  FunctionPtr u_exact = sin_pi_x * sin_pi_y;
  FunctionPtr f = -(2.0 * PI * PI / (D * D)) * sin_pi_x * sin_pi_y;
  rhs->addTerm( f * v );

  BCPtr bc = BC::bc();
  SpatialFilterPtr boundary = SpatialFilter::allSpace();

  bc->addDirichlet(u_hat, boundary, u_exact);

  IPPtr graphNorm;

  FunctionPtr h = Teuchos::rcp( new hFunction() );

  if (useWeightedGraphNorm)
  {
    graphNorm = IP::ip();
    graphNorm->addTerm( tau->div() ); // u
    graphNorm->addTerm( (h / alpha) * tau - h * v->grad() ); // sigma
    graphNorm->addTerm( v ); // boundary term (adjoint to u)
    graphNorm->addTerm( h * tau );

//    // new effort, with the idea that the test norm should be considered in reference space, basically
//    graphNorm = IP::ip();
//    graphNorm->addTerm( tau->div() ); // u
//    graphNorm->addTerm( tau / h - v->grad() ); // sigma
//    graphNorm->addTerm( v / h ); // boundary term (adjoint to u)
//    graphNorm->addTerm( tau / h );
  }
  else
  {
    map<int, double> trialWeights; // on the squared terms in the trial space norm
    trialWeights[u->ID()] = 1.0 / (D * D);
    trialWeights[sigma->ID()] = 1.0;
    graphNorm = poissonBF->graphNorm(trialWeights, 1.0); // 1.0: weight on the L^2 terms
  }

  SolutionPtr solution = Solution::solution(mesh, bc, rhs, graphNorm);
  solution->setUseCondensedSolve(useStaticCondensation);

  mesh->registerSolution(solution); // sign up for projection of old solution onto refined cells.

  double energyThreshold = 0.2;
  RefinementStrategy refinementStrategy( solution, energyThreshold );

  refinementStrategy.setReportPerCellErrors(true);
  refinementStrategy.setEnforceOneIrregularity(enforceOneIrregularity);

  Teuchos::RCP<Solver> coarseSolver, fineSolver;
  if (useMumps)
  {
#ifdef HAVE_AMESOS_MUMPS
    coarseSolver = Teuchos::rcp( new MumpsSolver(512, true) );
#else
    cout << "useMumps=true, but MUMPS is not available!\n";
    exit(0);
#endif
  }
  else
  {
    coarseSolver = Teuchos::rcp( new KluSolver );
  }
  GMGSolver* gmgSolver;

  if (useGMGSolver)
  {
    double tol = relativeTol;
    int maxIters = gmgMaxIterations;
    BCPtr zeroBCs = bc->copyImposingZero();
    gmgSolver = new GMGSolver(zeroBCs, k0Mesh, graphNorm, mesh, solution->getDofInterpreter(),
                              solution->getPartitionMap(), maxIters, tol, coarseSolver,
                              useStaticCondensation);

    gmgSolver->setAztecOutput(AztecOutputLevel);
    gmgSolver->setUseConjugateGradient(true);
    gmgSolver->gmgOperator()->setSmootherType(GMGOperator::IFPACK_ADDITIVE_SCHWARZ);
    gmgSolver->gmgOperator()->setSmootherOverlap(smootherOverlap);

    fineSolver = Teuchos::rcp( gmgSolver );
  }
  else
  {
    fineSolver = coarseSolver;
  }

//  if (rank==0) cout << "experimentally starting by solving with MUMPS on the fine mesh.\n";
//  solution->solve( Teuchos::rcp( new MumpsSolver) );

  solution->solve(fineSolver);

#ifdef HAVE_EPETRAEXT_HDF5
  ostringstream dir_name;
  dir_name << "poissonCavityFlow_k" << k;
  HDF5Exporter exporter(mesh,dir_name.str());
  exporter.exportSolution(solution,varFactory,0);
#endif

#ifdef HAVE_AMESOS_MUMPS
  if (useMumps) coarseSolver = Teuchos::rcp( new MumpsSolver(512, true) );
#endif

  solution->reportTimings();
  if (useGMGSolver) gmgSolver->gmgOperator()->reportTimings();
  for (int refIndex=0; refIndex < refCount; refIndex++)
  {
    double energyError = solution->energyErrorTotal();
    GlobalIndexType numFluxDofs = mesh->numFluxDofs();
    if (rank==0)
    {
      cout << "Before refinement " << refIndex << ", energy error = " << energyError;
      cout << " (using " << numFluxDofs << " trace degrees of freedom)." << endl;
    }
    bool printToConsole = printRefinementDetails && (rank==0);
    refinementStrategy.refine(printToConsole);

    if (useStaticCondensation)
    {
      CondensedDofInterpreter* condensedDofInterpreter = dynamic_cast<CondensedDofInterpreter*>(solution->getDofInterpreter().get());
      if (condensedDofInterpreter != NULL)
      {
        condensedDofInterpreter->reinitialize();
      }
    }

    GlobalIndexType fineDofs = mesh->globalDofCount();
    GlobalIndexType coarseDofs = k0Mesh->globalDofCount();
    if (rank==0)
    {
      cout << "After refinement, coarse mesh has " << k0Mesh->numActiveElements() << " elements and " << coarseDofs << " dofs.\n";
      cout << "  Fine mesh has " << mesh->numActiveElements() << " elements and " << fineDofs << " dofs.\n";
    }

    if (!use3D)
    {
      ostringstream fineMeshLocation, coarseMeshLocation;
      fineMeshLocation << "poissonFineMesh_k" << k << "_ref" << refIndex;
      GnuPlotUtil::writeComputationalMeshSkeleton(fineMeshLocation.str(), mesh, true); // true: label cells
      coarseMeshLocation << "poissonCoarseMesh_k" << k << "_ref" << refIndex;
      GnuPlotUtil::writeComputationalMeshSkeleton(coarseMeshLocation.str(), k0Mesh, true); // true: label cells
    }

    if (useGMGSolver)   // create fresh fineSolver now that the meshes have changed:
    {
#ifdef HAVE_AMESOS_MUMPS
      if (useMumps) coarseSolver = Teuchos::rcp( new MumpsSolver(512, true) );
#endif
      double tol = max(relativeTol * energyError, minTol);
      int maxIters = gmgMaxIterations;
      BCPtr zeroBCs = bc->copyImposingZero();
      gmgSolver = new GMGSolver(zeroBCs, k0Mesh, graphNorm, mesh, solution->getDofInterpreter(),
                                solution->getPartitionMap(), maxIters, tol, coarseSolver, useStaticCondensation);
      gmgSolver->setAztecOutput(AztecOutputLevel);
      gmgSolver->setUseDiagonalScaling(useDiagonalScaling);
      fineSolver = Teuchos::rcp( gmgSolver );
    }

    solution->solve(fineSolver);
    solution->reportTimings();
    if (useGMGSolver) gmgSolver->gmgOperator()->reportTimings();

#ifdef HAVE_EPETRAEXT_HDF5
    exporter.exportSolution(solution,varFactory,refIndex+1);
#endif
  }
  double energyErrorTotal = solution->energyErrorTotal();

  GlobalIndexType numFluxDofs = mesh->numFluxDofs();
  GlobalIndexType numGlobalDofs = mesh->numGlobalDofs();
  if (rank==0)
  {
    cout << "Final mesh has " << mesh->numActiveElements() << " elements and " << numFluxDofs << " trace dofs (";
    cout << numGlobalDofs << " total dofs, including fields).\n";
    cout << "Final energy error: " << energyErrorTotal << endl;
  }

#ifdef HAVE_EPETRAEXT_HDF5
  exporter.exportSolution(solution,varFactory,0);
#endif

  if (!use3D)
  {
    GnuPlotUtil::writeComputationalMeshSkeleton("poissonRefinedMesh", mesh, true);
  }

  coarseSolver = Teuchos::rcp((Solver*) NULL); // without this when useMumps = true and running on one rank, we see a crash on exit, which may have to do with MPI being finalized before coarseSolver is deleted.

  return 0;
}
Example #30
0
void ExactSolution::setSolutionFunction( VarPtr var, FunctionPtr varFunction ) {
  _exactFunctions[var->ID()] = varFunction;
}