int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
#endif
{
// 1D tests
CellTopoPtr line_2 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >() ) );
// let's draw a line
vector<double> v0 = makeVertex(0);
vector<double> v1 = makeVertex(1);
vector<double> v2 = makeVertex(2);
vector< vector<double> > vertices;
vertices.push_back(v0);
vertices.push_back(v1);
vertices.push_back(v2);
vector<unsigned> line1VertexList;
vector<unsigned> line2VertexList;
line1VertexList.push_back(0);
line1VertexList.push_back(1);
line2VertexList.push_back(1);
line2VertexList.push_back(2);
vector< vector<unsigned> > elementVertices;
elementVertices.push_back(line1VertexList);
elementVertices.push_back(line2VertexList);
vector< CellTopoPtr > cellTopos;
cellTopos.push_back(line_2);
cellTopos.push_back(line_2);
MeshGeometryPtr meshGeometry = Teuchos::rcp( new MeshGeometry(vertices, elementVertices, cellTopos) );
MeshTopologyPtr meshTopology = Teuchos::rcp( new MeshTopology(meshGeometry) );
FunctionPtr x = Function::xn(1);
FunctionPtr function = x;
FunctionPtr fbdr = Function::restrictToCellBoundary(function);
vector<FunctionPtr> functions;
functions.push_back(function);
functions.push_back(function);
vector<string> functionNames;
functionNames.push_back("function1");
functionNames.push_back("function2");
{
XDMFExporter exporter(meshTopology, "function1", false);
exporter.exportFunction(function, "function1");
}
{
XDMFExporter exporter(meshTopology, "boundary1", false);
exporter.exportFunction(fbdr, "boundary1");
}
{
XDMFExporter exporter(meshTopology, "functions1", false);
exporter.exportFunction(functions, functionNames);
}
}
{
// 2D tests
CellTopoPtr quad_4 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ) );
CellTopoPtr tri_3 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() ) );
// let's draw a little house
vector<double> v0 = makeVertex(-1,0);
vector<double> v1 = makeVertex(1,0);
vector<double> v2 = makeVertex(1,2);
vector<double> v3 = makeVertex(-1,2);
vector<double> v4 = makeVertex(0.0,3);
vector< vector<double> > vertices;
vertices.push_back(v0);
vertices.push_back(v1);
vertices.push_back(v2);
vertices.push_back(v3);
vertices.push_back(v4);
vector<unsigned> quadVertexList;
quadVertexList.push_back(0);
quadVertexList.push_back(1);
quadVertexList.push_back(2);
quadVertexList.push_back(3);
vector<unsigned> triVertexList;
triVertexList.push_back(3);
triVertexList.push_back(2);
triVertexList.push_back(4);
vector< vector<unsigned> > elementVertices;
elementVertices.push_back(quadVertexList);
elementVertices.push_back(triVertexList);
vector< CellTopoPtr > cellTopos;
cellTopos.push_back(quad_4);
cellTopos.push_back(tri_3);
MeshGeometryPtr meshGeometry = Teuchos::rcp( new MeshGeometry(vertices, elementVertices, cellTopos) );
MeshTopologyPtr meshTopology = Teuchos::rcp( new MeshTopology(meshGeometry) );
FunctionPtr x2 = Function::xn(2);
FunctionPtr y2 = Function::yn(2);
FunctionPtr function = x2 + y2;
FunctionPtr vect = Function::vectorize(x2, y2);
FunctionPtr fbdr = Function::restrictToCellBoundary(function);
vector<FunctionPtr> functions;
functions.push_back(function);
functions.push_back(vect);
vector<string> functionNames;
functionNames.push_back("function");
functionNames.push_back("vect");
vector<FunctionPtr> bdrfunctions;
bdrfunctions.push_back(fbdr);
bdrfunctions.push_back(fbdr);
vector<string> bdrfunctionNames;
bdrfunctionNames.push_back("bdr1");
bdrfunctionNames.push_back("bdr2");
map<int, int> cellIDToNum1DPts;
cellIDToNum1DPts[1] = 4;
{
XDMFExporter exporter(meshTopology, "Grid2D", false);
// exporter.exportFunction(function, "function2", 0, 10);
// exporter.exportFunction(vect, "vect2", 1, 10, cellIDToNum1DPts);
// exporter.exportFunction(fbdr, "boundary2", 0);
exporter.exportFunction(functions, functionNames, 1, 10);
}
{
XDMFExporter exporter(meshTopology, "BdrGrid2D", false);
// exporter.exportFunction(function, "function2", 0, 10);
// exporter.exportFunction(vect, "vect2", 1, 10, cellIDToNum1DPts);
// exporter.exportFunction(fbdr, "boundary2", 0);
exporter.exportFunction(bdrfunctions, bdrfunctionNames, 1, 10);
}
//////////////////// 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("uhat");
VarPtr fhat = varFactory.fluxVar("fhat");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma = varFactory.fieldVar("sigma", VECTOR_L2);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// tau terms:
bf->addTerm(sigma, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( fhat, v);
//////////////////// BUILD MESH ///////////////////////
int H1Order = 4, pToAdd = 2;
Teuchos::RCP<Mesh> mesh = Teuchos::rcp( new Mesh (meshTopology, bf, H1Order, pToAdd) );
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = bf->graphNorm();
//////////////////// SPECIFY RHS ///////////////////////
RHSPtr rhs = RHS::rhs();
// Teuchos::RCP<RHS> rhs = Teuchos::rcp( new RHS );
FunctionPtr one = Function::constant(1.0);
rhs->addTerm( one * v );
//////////////////// CREATE BCs ///////////////////////
// Teuchos::RCP<BC> bc = Teuchos::rcp( new BCEasy );
BCPtr bc = BC::bc();
FunctionPtr zero = Function::zero();
SpatialFilterPtr entireBoundary = Teuchos::rcp( new EntireBoundary );
bc->addDirichlet(uhat, entireBoundary, zero);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
solution->solve(false);
RefinementStrategy refinementStrategy( solution, 0.2);
// Output solution
FunctionPtr uSoln = Function::solution(u, solution);
FunctionPtr sigmaSoln = Function::solution(sigma, solution);
FunctionPtr uhatSoln = Function::solution(uhat, solution);
FunctionPtr fhatSoln = Function::solution(fhat, solution);
{
XDMFExporter exporter(meshTopology, "Poisson", false);
exporter.exportFunction(uSoln, "u", 0, 4);
exporter.exportFunction(uSoln, "u", 1, 5);
exporter.exportFunction(uhatSoln, "uhat", 0, 4);
exporter.exportFunction(uhatSoln, "uhat", 1, 5);
// exporter.exportFunction(fhatSoln, "fhat", 0, 4);
// exporter.exportFunction(fhatSoln, "fhat", 1, 5);
}
{
XDMFExporter exporter(meshTopology, "PoissonSolution", false);
exporter.exportSolution(solution, mesh, varFactory, 0, 2, cellIDToSubdivision(mesh, 10));
refinementStrategy.refine(true);
solution->solve(false);
exporter.exportSolution(solution, mesh, varFactory, 1, 2, cellIDToSubdivision(mesh, 10));
}
// exporter.exportFunction(sigmaSoln, "Poisson-s", "sigma", 0, 5);
// exporter.exportFunction(uhatSoln, "Poisson-uhat", "uhat", 1, 6);
}
{
// 3D tests
CellTopoPtr hex = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Hexahedron<8> >() ));
// let's draw a little box
vector<double> v0 = makeVertex(0,0,0);
vector<double> v1 = makeVertex(1,0,0);
vector<double> v2 = makeVertex(1,1,0);
vector<double> v3 = makeVertex(0,1,0);
vector<double> v4 = makeVertex(0,0,1);
vector<double> v5 = makeVertex(1,0,1);
vector<double> v6 = makeVertex(1,1,1);
vector<double> v7 = makeVertex(0,1,1);
vector< vector<double> > vertices;
vertices.push_back(v0);
vertices.push_back(v1);
vertices.push_back(v2);
vertices.push_back(v3);
vertices.push_back(v4);
vertices.push_back(v5);
vertices.push_back(v6);
vertices.push_back(v7);
vector<unsigned> hexVertexList;
hexVertexList.push_back(0);
hexVertexList.push_back(1);
hexVertexList.push_back(2);
hexVertexList.push_back(3);
hexVertexList.push_back(4);
hexVertexList.push_back(5);
hexVertexList.push_back(6);
hexVertexList.push_back(7);
// vector<unsigned> triVertexList;
// triVertexList.push_back(2);
// triVertexList.push_back(3);
// triVertexList.push_back(4);
vector< vector<unsigned> > elementVertices;
elementVertices.push_back(hexVertexList);
// elementVertices.push_back(triVertexList);
vector< CellTopoPtr > cellTopos;
cellTopos.push_back(hex);
// cellTopos.push_back(tri_3);
MeshGeometryPtr meshGeometry = Teuchos::rcp( new MeshGeometry(vertices, elementVertices, cellTopos) );
MeshTopologyPtr meshTopology = Teuchos::rcp( new MeshTopology(meshGeometry) );
FunctionPtr x = Function::xn(1);
FunctionPtr y = Function::yn(1);
FunctionPtr z = Function::zn(1);
FunctionPtr function = x + y + z;
FunctionPtr fbdr = Function::restrictToCellBoundary(function);
FunctionPtr vect = Function::vectorize(x, y, z);
vector<FunctionPtr> functions;
functions.push_back(function);
functions.push_back(vect);
vector<string> functionNames;
functionNames.push_back("function");
functionNames.push_back("vect");
{
XDMFExporter exporter(meshTopology, "function3", false);
exporter.exportFunction(function, "function3");
}
{
XDMFExporter exporter(meshTopology, "boundary3", false);
exporter.exportFunction(fbdr, "boundary3");
}
{
XDMFExporter exporter(meshTopology, "vect3", false);
exporter.exportFunction(vect, "vect3");
}
{
XDMFExporter exporter(meshTopology, "functions3", false);
exporter.exportFunction(functions, functionNames);
}
}
}
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)
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation", false);
double Re = args.Input("--Re", "Reynolds number", 40);
double nu = 1./Re;
double lambda = Re/2.-sqrt(Re*Re/4+4*pi*pi);
int maxNewtonIterations = args.Input("--maxIterations", "maximum number of Newton iterations", 20);
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();
// if (commRank==0)
// {
// cout << "saveFile is " << saveFile << endl;
// cout << "loadFile is " << replayFile << endl;
// }
//////////////////// PROBLEM DEFINITIONS ///////////////////////
int H1Order = polyOrder+1;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau11 = varFactory.testVar("tau11", HGRAD);
VarPtr tau12 = varFactory.testVar("tau12", HGRAD);
VarPtr tau22 = varFactory.testVar("tau22", HGRAD);
VarPtr v1 = varFactory.testVar("v1", HGRAD);
VarPtr v2 = varFactory.testVar("v2", HGRAD);
// define trial variables
VarPtr u1 = varFactory.fieldVar("u1");
VarPtr u2 = varFactory.fieldVar("u2");
VarPtr sigma11 = varFactory.fieldVar("sigma11");
VarPtr sigma12 = varFactory.fieldVar("sigma12");
VarPtr sigma22 = varFactory.fieldVar("sigma22");
VarPtr u1hat = varFactory.traceVar("u1hat");
VarPtr u2hat = varFactory.traceVar("u2hat");
VarPtr t1hat = varFactory.fluxVar("t1hat");
VarPtr t2hat = varFactory.fluxVar("t2hat");
//////////////////// BUILD MESH ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// define nodes for mesh
FieldContainer<double> meshBoundary(4,2);
double xmin = -0.5;
double xmax = 1.0;
double ymin = -0.5;
double ymax = 1.5;
meshBoundary(0,0) = xmin; // x1
meshBoundary(0,1) = ymin; // y1
meshBoundary(1,0) = xmax;
meshBoundary(1,1) = ymin;
meshBoundary(2,0) = xmax;
meshBoundary(2,1) = ymax;
meshBoundary(3,0) = xmin;
meshBoundary(3,1) = ymax;
int horizontalCells = 6, verticalCells = 8;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshFactory::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
bf, H1Order, 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 sigma11_prev = Function::solution(sigma11, backgroundFlow);
// FunctionPtr sigma12_prev = Function::solution(sigma12, backgroundFlow);
// FunctionPtr sigma22_prev = Function::solution(sigma22, backgroundFlow);
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
FunctionPtr u1Exact = Teuchos::rcp( new ExactU1(lambda) );
FunctionPtr u2Exact = Teuchos::rcp( new ExactU2(lambda) );
// ==================== SET INITIAL GUESS ==========================
map<int, Teuchos::RCP<Function> > functionMap;
// functionMap[u1->ID()] = u1Exact;
// functionMap[u2->ID()] = u2Exact;
functionMap[u1->ID()] = zero;
functionMap[u2->ID()] = zero;
backgroundFlow->projectOntoMesh(functionMap);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
// stress equation
bf->addTerm( 1./nu*sigma11, tau11 );
bf->addTerm( 1./nu*sigma12, tau12 );
bf->addTerm( 1./nu*sigma12, tau12 );
bf->addTerm( 1./nu*sigma22, tau22 );
bf->addTerm( -0.5/nu*sigma11, tau11 );
bf->addTerm( -0.5/nu*sigma22, tau11 );
bf->addTerm( -0.5/nu*sigma11, tau22 );
bf->addTerm( -0.5/nu*sigma22, tau22 );
bf->addTerm( 2*u1, tau11->dx() );
bf->addTerm( 2*u1, tau12->dy() );
bf->addTerm( 2*u2, tau12->dx() );
bf->addTerm( 2*u2, tau22->dy() );
bf->addTerm( -2*u1hat, tau11->times_normal_x() );
bf->addTerm( -2*u1hat, tau12->times_normal_y() );
bf->addTerm( -2*u2hat, tau12->times_normal_x() );
bf->addTerm( -2*u2hat, tau22->times_normal_y() );
// momentum equation
bf->addTerm( -2.*u1_prev*u1, v1->dx() );
bf->addTerm( -u2_prev*u1, v1->dy() );
bf->addTerm( -u1_prev*u2, v1->dy() );
bf->addTerm( -u2_prev*u1, v2->dx() );
bf->addTerm( -u1_prev*u2, v2->dx() );
bf->addTerm( -2.*u2_prev*u2, v2->dy() );
bf->addTerm( sigma11, v1->dx() );
bf->addTerm( sigma12, v1->dy() );
bf->addTerm( sigma12, v2->dx() );
bf->addTerm( sigma22, v2->dy() );
bf->addTerm( t1hat, v1);
bf->addTerm( t2hat, v2);
//////////////////// SPECIFY RHS ///////////////////////
RHSPtr rhs = RHS::rhs();
// stress equation
rhs->addTerm( -2*u1_prev * tau11->dx() );
rhs->addTerm( -2*u1_prev * tau12->dy() );
rhs->addTerm( -2*u2_prev * tau12->dx() );
rhs->addTerm( -2*u2_prev * tau22->dy() );
// momentum equation
rhs->addTerm( u1_prev*u1_prev * v1->dx() );
rhs->addTerm( u2_prev*u1_prev * v1->dy() );
rhs->addTerm( u2_prev*u1_prev * v2->dx() );
rhs->addTerm( u2_prev*u2_prev * v2->dy() );
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
if (norm == 0)
{
ip = bf->graphNorm();
}
else if (norm == 1)
{
ip->addTerm( 0.5/nu*tau11-0.5/nu*tau22 + v1->dx() );
ip->addTerm( 1./nu*tau12 + v1->dy() );
ip->addTerm( 1./nu*tau12 + v2->dx() );
ip->addTerm( 0.5/nu*tau22-0.5/nu*tau11 + v2->dy() );
ip->addTerm( 2*tau11->dx() + 2*tau12->dy() - 2*u1_prev*v1->dx() - u2_prev*v1->dy() - u2_prev*v2->dx() );
ip->addTerm( 2*tau12->dx() + 2*tau22->dy() - 2*u2_prev*v2->dy() - u1_prev*v1->dy() - u1_prev*v2->dx() );
ip->addTerm( v1 );
ip->addTerm( v2 );
ip->addTerm( tau11 );
ip->addTerm( tau12 );
ip->addTerm( tau12 );
ip->addTerm( tau22 );
}
else if (norm == 2)
{
// ip->addTerm( 0.5/sqrt(nu)*tau11-0.5/nu*tau22 );
// ip->addTerm( 1./sqrt(nu)*tau12 );
// ip->addTerm( 1./sqrt(nu)*tau12 );
// ip->addTerm( 0.5/sqrt(nu)*tau22-0.5/nu*tau11 );
ip->addTerm( tau11 );
ip->addTerm( tau12 );
ip->addTerm( tau12 );
ip->addTerm( tau22 );
ip->addTerm( 2*tau11->dx() + 2*tau12->dy() - 2*u1_prev*v1->dx() - u2_prev*v1->dy() - u2_prev*v2->dx() );
ip->addTerm( 2*tau12->dx() + 2*tau22->dy() - 2*u2_prev*v2->dy() - u1_prev*v1->dy() - u1_prev*v2->dx() );
ip->addTerm( 2*u1_prev*v1->dx() + u2_prev*v1->dy() + u2_prev*v2->dx() );
ip->addTerm( 2*u2_prev*v2->dy() + u1_prev*v1->dy() + u1_prev*v2->dx() );
ip->addTerm( sqrt(nu)*v1->grad() );
ip->addTerm( sqrt(nu)*v2->grad() );
ip->addTerm( v1 );
ip->addTerm( v2 );
}
//////////////////// CREATE BCs ///////////////////////
BCPtr bc = BC::bc();
// Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );
SpatialFilterPtr left = Teuchos::rcp( new ConstantXBoundary(-0.5) );
SpatialFilterPtr right = Teuchos::rcp( new ConstantXBoundary(1) );
SpatialFilterPtr top = Teuchos::rcp( new ConstantYBoundary(-0.5) );
SpatialFilterPtr bottom = Teuchos::rcp( new ConstantYBoundary(1.5) );
bc->addDirichlet(u1hat, left, u1Exact);
bc->addDirichlet(u2hat, left, u2Exact);
bc->addDirichlet(u1hat, right, u1Exact);
bc->addDirichlet(u2hat, right, u2Exact);
bc->addDirichlet(u1hat, top, u1Exact);
bc->addDirichlet(u2hat, top, u2Exact);
bc->addDirichlet(u1hat, bottom, u1Exact);
bc->addDirichlet(u2hat, bottom, u2Exact);
// bc->addDirichlet(u1hat, left, zero);
// bc->addDirichlet(u2hat, left, zero);
// bc->addDirichlet(u1hat, right, zero);
// 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);
// pc->addConstraint(u1hat*u2hat-t1hat == zero, top);
// pc->addConstraint(u2hat*u2hat-t2hat == zero, top);
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
// solution->setFilter(pc);
// 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 );
HDF5Exporter exporter(mesh, "Kovasznay_np");
ofstream convOut;
stringstream convOutFile;
convOutFile << "Kovasznay_conv_" << Re <<".txt";
if (commRank == 0)
convOut.open(convOutFile.str().c_str());
set<int> nonlinearVars;
nonlinearVars.insert(u1->ID());
nonlinearVars.insert(u2->ID());
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);
// Check local conservation
if (commRank == 0)
{
cout << "L2 Norm of Update = " << L2Update << 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;
backgroundFlow->addSolution(solution, alpha, nonlinearVars);
iterCount++;
}
exporter.exportSolution(backgroundFlow, varFactory, refIndex, 2, cellIDToSubdivision(mesh, 4));
FunctionPtr u1Soln = Function::solution(u1, backgroundFlow);
FunctionPtr u2Soln = Function::solution(u2, backgroundFlow);
FunctionPtr u1Sqr = (u1Soln-u1Exact)*(u1Soln-u1Exact);
FunctionPtr u2Sqr = (u2Soln-u2Exact)*(u2Soln-u2Exact);
double u1L2Error = u1Sqr->integrate(mesh, 1e-5);
double u2L2Error = u2Sqr->integrate(mesh, 1e-5);
double l2Error = sqrt(u1L2Error+u2L2Error);
double energyError = solution->energyErrorTotal();
cout << "L2 Error: " << l2Error << " Energy Error: " << energyError << endl;
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
return 0;
}
