/** * This example program sets up and solves the Laplace * equation \f$-\nabla^2 u=0\f$. See the * document GettingStarted.pdf for more information. */ int main(int argc, char** argv) { try { /* command-line options */ std::string meshFile="plateWithHole3D-1"; std::string solverFile = "aztec-ml.xml"; Sundance::setOption("meshFile", meshFile, "mesh file"); Sundance::setOption("solver", solverFile, "name of XML file for solver"); /* Initialize */ Sundance::init(&argc, &argv); /* --- Specify vector representation to be used --- */ VectorType<double> vecType = new EpetraVectorType(); /* --- Read mesh --- */ MeshType meshType = new BasicSimplicialMeshType(); MeshSource meshSrc = new ExodusMeshReader(meshFile, meshType); Mesh mesh = meshSrc.getMesh(); /* --- Specification of geometric regions --- */ /* Region "interior" consists of all maximal-dimension cells */ CellFilter interior = new MaximalCellFilter(); /* Identify boundary regions via labels in mesh */ CellFilter edges = new DimensionalCellFilter(2); CellFilter south = edges.labeledSubset(1); CellFilter east = edges.labeledSubset(2); CellFilter north = edges.labeledSubset(3); CellFilter west = edges.labeledSubset(4); CellFilter hole = edges.labeledSubset(5); CellFilter down = edges.labeledSubset(6); CellFilter up = edges.labeledSubset(7); /* --- Symbolic equation definition --- */ /* Test and unknown function */ BasisFamily basis = new Lagrange(1); Expr u = new UnknownFunction(basis, "u"); Expr v = new TestFunction(basis, "v"); /* Gradient operator */ Expr dx = new Derivative(0); Expr dy = new Derivative(1); Expr dz = new Derivative(2); Expr grad = List(dx, dy, dz); /* We need a quadrature rule for doing the integrations */ QuadratureFamily quad1 = new GaussianQuadrature(1); QuadratureFamily quad2 = new GaussianQuadrature(2); /** Write the weak form */ Expr eqn = Integral(interior, (grad*u)*(grad*v), quad1) + Integral(east, v, quad1); /* Write the essential boundary conditions */ Expr h = new CellDiameterExpr(); Expr bc = EssentialBC(west, v*u/h, quad2); /* Set up linear problem */ LinearProblem prob(mesh, eqn, bc, v, u, vecType); /* --- solve the problem --- */ /* Create the solver as specified by parameters in * an XML file */ LinearSolver<double> solver = LinearSolverBuilder::createSolver(solverFile); /* Solve! The solution is returned as an Expr containing a * DiscreteFunction */ Expr soln = prob.solve(solver); /* --- Postprocessing --- */ /* Project the derivative onto the P1 basis */ DiscreteSpace discSpace(mesh, List(basis, basis, basis), vecType); L2Projector proj(discSpace, grad*soln); Expr gradU = proj.project(); /* Write the solution and its projected gradient to a VTK file */ FieldWriter w = new VTKWriter("LaplaceDemo3D"); w.addMesh(mesh); w.addField("soln", new ExprFieldWrapper(soln[0])); w.addField("du_dx", new ExprFieldWrapper(gradU[0])); w.addField("du_dy", new ExprFieldWrapper(gradU[1])); w.addField("du_dz", new ExprFieldWrapper(gradU[2])); w.write(); /* Check flux balance */ Expr n = CellNormalExpr(3, "n"); CellFilter wholeBdry = east+west+north+south+up+down+hole; Expr fluxExpr = Integral(wholeBdry, (n*grad)*soln, quad1); double flux = evaluateIntegral(mesh, fluxExpr); Out::root() << "numerical flux = " << flux << std::endl; /* --- Let's compute a few other quantities, such as the centroid of * the mesh:*/ /* Coordinate functions let us build up functions of position */ Expr x = new CoordExpr(0); Expr y = new CoordExpr(1); Expr z = new CoordExpr(2); Expr xCMExpr = Integral(interior, x, quad1); Expr yCMExpr = Integral(interior, y, quad1); Expr zCMExpr = Integral(interior, z, quad1); Expr volExpr = Integral(interior, 1.0, quad1); double vol = evaluateIntegral(mesh, volExpr); double xCM = evaluateIntegral(mesh, xCMExpr)/vol; double yCM = evaluateIntegral(mesh, yCMExpr)/vol; double zCM = evaluateIntegral(mesh, zCMExpr)/vol; Out::root() << "centroid = (" << xCM << ", " << yCM << ", " << zCM << ")" << std::endl; /* Next, compute the first Fourier sine coefficient of the solution on the * surface of the hole.*/ Expr r = sqrt(x*x + y*y); Expr sinPhi = y/r; /* Use a higher-order quadrature rule for these integrals */ QuadratureFamily quad4 = new GaussianQuadrature(4); Expr fourierSin1Expr = Integral(hole, sinPhi*soln, quad4); Expr fourierDenomExpr = Integral(hole, sinPhi*sinPhi, quad2); double fourierSin1 = evaluateIntegral(mesh, fourierSin1Expr); double fourierDenom = evaluateIntegral(mesh, fourierDenomExpr); Out::root() << "fourier sin m=1 = " << fourierSin1/fourierDenom << std::endl; /* Compute the L2 norm of the solution */ Expr L2NormExpr = Integral(interior, soln*soln, quad2); double l2Norm_method1 = sqrt(evaluateIntegral(mesh, L2NormExpr)); Out::os() << "method #1: ||soln|| = " << l2Norm_method1 << endl; /* Use the L2Norm() function to do the same calculation */ double l2Norm_method2 = L2Norm(mesh, interior, soln, quad2); Out::os() << "method #2: ||soln|| = " << l2Norm_method2 << endl; /* * Check that the flux is acceptably close to zero. The flux calculation * is only O(h) so keep the tolerance loose. This * is just a sanity check to ensure the code doesn't get completely * broken after a change to the library. */ Sundance::passFailTest(fabs(flux), 1.0e-2); } catch(std::exception& e) { Sundance::handleException(e); } Sundance::finalize(); return Sundance::testStatus(); }
int main(int argc, char** argv) { try { int nx = 32; double convTol = 1.0e-8; double lambda = 0.5; Sundance::setOption("nx", nx, "Number of elements"); Sundance::setOption("tol", convTol, "Convergence tolerance"); Sundance::setOption("lambda", lambda, "Lambda (parameter in Bratu's equation)"); Sundance::init(&argc, &argv); Out::root() << "Bratu problem (lambda=" << lambda << ")" << endl; Out::root() << "Newton's method, linearized by hand" << endl << endl; VectorType<double> vecType = new EpetraVectorType(); MeshType meshType = new BasicSimplicialMeshType(); MeshSource mesher = new PartitionedLineMesher(0.0, 1.0, nx, meshType); Mesh mesh = mesher.getMesh(); CellFilter interior = new MaximalCellFilter(); CellFilter sides = new DimensionalCellFilter(mesh.spatialDim()-1); CellFilter left = sides.subset(new CoordinateValueCellPredicate(0, 0.0)); CellFilter right = sides.subset(new CoordinateValueCellPredicate(0, 1.0)); BasisFamily basis = new Lagrange(1); Expr w = new UnknownFunction(basis, "w"); Expr v = new TestFunction(basis, "v"); Expr grad = gradient(1); Expr x = new CoordExpr(0); const double pi = 4.0*atan(1.0); Expr uExact = sin(pi*x); Expr R = pi*pi*uExact - lambda*exp(uExact); QuadratureFamily quad4 = new GaussianQuadrature(4); QuadratureFamily quad2 = new GaussianQuadrature(2); DiscreteSpace discSpace(mesh, basis, vecType); Expr uPrev = new DiscreteFunction(discSpace, 0.5); Expr stepVal = copyDiscreteFunction(uPrev); Expr eqn = Integral(interior, (grad*v)*(grad*w) + (grad*v)*(grad*uPrev) - v*lambda*exp(uPrev)*(1.0+w) - v*R, quad4); Expr h = new CellDiameterExpr(); Expr bc = EssentialBC(left+right, v*(uPrev+w)/h, quad2); LinearProblem prob(mesh, eqn, bc, v, w, vecType); LinearSolver<double> linSolver = LinearSolverBuilder::createSolver("amesos.xml"); Out::root() << "Newton iteration" << endl; int maxIters = 20; Expr soln ; bool converged = false; for (int i=0; i<maxIters; i++) { /* solve for the next u */ prob.solve(linSolver, stepVal); Vector<double> stepVec = getDiscreteFunctionVector(stepVal); double deltaU = stepVec.norm2(); Out::root() << "Iter=" << setw(3) << i << " ||Delta u||=" << setw(20) << deltaU << endl; addVecToDiscreteFunction(uPrev, stepVec); if (deltaU < convTol) { soln = uPrev; converged = true; break; } } TEUCHOS_TEST_FOR_EXCEPTION(!converged, std::runtime_error, "Newton iteration did not converge after " << maxIters << " iterations"); FieldWriter writer = new DSVWriter("HandCodedBratu.dat"); writer.addMesh(mesh); writer.addField("soln", new ExprFieldWrapper(soln[0])); writer.write(); Out::root() << "Converged!" << endl << endl; double L2Err = L2Norm(mesh, interior, soln-uExact, quad4); Out::root() << "L2 Norm of error: " << L2Err << endl; Sundance::passFailTest(L2Err, 1.5/((double) nx*nx)); } catch(std::exception& e) { Sundance::handleException(e); } Sundance::finalize(); }
int main(int argc, char** argv) { try { Sundance::init(&argc, &argv); int np = MPIComm::world().getNProc(); int nx = 64; const double pi = 4.0*atan(1.0); MeshType meshType = new BasicSimplicialMeshType(); MeshSource mesher = new PartitionedLineMesher(0.0, pi, nx, meshType); Mesh mesh = mesher.getMesh(); CellFilter interior = new MaximalCellFilter(); CellFilter bdry = new BoundaryCellFilter(); /* Create a vector space factory, used to * specify the low-level linear algebra representation */ VectorType<double> vecType = new EpetraVectorType(); /* create symbolic coordinate functions */ Expr x = new CoordExpr(0); /* create target function */ double R = 0.01; Expr sx = sin(x); Expr cx = cos(x); Expr ssx = sin(sx); Expr sx2 = sx*sx; Expr cx2 = cx*cx; Expr f = sx2 - sx - ssx; Expr uStar = 2.0*R*(sx2-cx2) + R*sx2*ssx + sx; /* Form exact solution */ Expr uEx = sx; Expr lambdaEx = R*sx2; Expr alphaEx = -lambdaEx/R; /* create a discrete space on the mesh */ BasisFamily bas = new Lagrange(1); DiscreteSpace discreteSpace(mesh, bas, vecType); /* initialize the design, state, and multiplier vectors to constants */ Expr alpha0 = new DiscreteFunction(discreteSpace, 0.25, "alpha0"); Expr u0 = new DiscreteFunction(discreteSpace, 0.5, "u0"); Expr lambda0 = new DiscreteFunction(discreteSpace, 0.25, "lambda0"); /* create symbolic objects for test and unknown functions */ Expr u = new UnknownFunction(bas, "u"); Expr lambda = new UnknownFunction(bas, "lambda"); Expr alpha = new UnknownFunction(bas, "alpha"); /* create symbolic differential operators */ Expr dx = new Derivative(0); Expr grad = dx; /* create quadrature rules of different orders */ QuadratureFamily q1 = new GaussianQuadrature(1); QuadratureFamily q2 = new GaussianQuadrature(2); QuadratureFamily q4 = new GaussianQuadrature(4); /* Form objective function */ Expr reg = Integral(interior, 0.5 * R * alpha*alpha, q2); Expr fit = Integral(interior, 0.5 * pow(u-uStar, 2.0), q4); Expr constraintEqn = Integral(interior, (grad*lambda)*(grad*u) + lambda*(alpha + sin(u) + f), q4); Expr L = reg + fit + constraintEqn; Expr constraintBC = EssentialBC(bdry, lambda*u, q2); Functional Lagrangian(mesh, L, constraintBC, vecType); LinearSolver<double> adjSolver = LinearSolverBuilder::createSolver("amesos.xml"); ParameterXMLFileReader reader("nox-amesos.xml"); ParameterList noxParams = reader.getParameters(); NOXSolver nonlinSolver(noxParams); RCP<PDEConstrainedObjBase> obj = rcp(new NonlinearPDEConstrainedObj( Lagrangian, u, u0, lambda, lambda0, alpha, alpha0, nonlinSolver, adjSolver)); Vector<double> xInit = obj->getInit(); bool doFDCheck = true; if (doFDCheck) { Out::root() << "Doing FD check of gradient..." << endl; bool fdOK = obj->fdCheck(xInit, 1.0e-6, 0); if (fdOK) { Out::root() << "FD check OK" << endl; } else { Out::root() << "FD check FAILED" << endl; TEUCHOS_TEST_FOR_EXCEPT(!fdOK); } } RCP<UnconstrainedOptimizerBase> opt = OptBuilder::createOptimizer("basicLMBFGS.xml"); opt->setVerb(3); OptState state = opt->run(obj, xInit); if (state.status() != Opt_Converged) { Out::root()<< "optimization failed: " << state.status() << endl; TEUCHOS_TEST_FOR_EXCEPT(state.status() != Opt_Converged); } else { Out::root() << "opt converged: " << state.iter() << " iterations" << endl; } FieldWriter w = new MatlabWriter("NonlinControl1D"); w.addMesh(mesh); w.addField("u", new ExprFieldWrapper(u0)); w.addField("alpha", new ExprFieldWrapper(alpha0)); w.addField("lambda", new ExprFieldWrapper(lambda0)); w.write(); double uErr = L2Norm(mesh, interior, u0-uEx, q4); double lamErr = L2Norm(mesh, interior, lambda0-lambdaEx, q4); double aErr = L2Norm(mesh, interior, alpha0-alphaEx, q4); Out::root() << "error in u = " << uErr << endl; Out::root() << "error in lambda = " << lamErr << endl; Out::root() << "error in alpha = " << aErr << endl; double tol = 0.05; Sundance::passFailTest(uErr + lamErr + aErr, tol); } catch(exception& e) { cerr << "main() caught exception: " << e.what() << endl; } Sundance::finalize(); return Sundance::testStatus(); }
int main(int argc, char** argv) { try { const double pi = 4.0*atan(1.0); double lambda = 1.25*pi*pi; int nx = 32; int nt = 10; double tFinal = 1.0/lambda; Sundance::setOption("nx", nx, "Number of elements"); Sundance::setOption("nt", nt, "Number of timesteps"); Sundance::setOption("tFinal", tFinal, "Final time"); Sundance::init(&argc, &argv); /* Creation of vector type */ VectorType<double> vecType = new EpetraVectorType(); /* Set up mesh */ MeshType meshType = new BasicSimplicialMeshType(); MeshSource meshSrc = new PartitionedRectangleMesher( 0.0, 1.0, nx, 0.0, 1.0, nx, meshType); Mesh mesh = meshSrc.getMesh(); /* * Specification of cell filters */ CellFilter interior = new MaximalCellFilter(); CellFilter edges = new DimensionalCellFilter(1); CellFilter west = edges.coordSubset(0, 0.0); CellFilter east = edges.coordSubset(0, 1.0); CellFilter south = edges.coordSubset(1, 0.0); CellFilter north = edges.coordSubset(1, 1.0); /* set up test and unknown functions */ BasisFamily basis = new Lagrange(1); Expr u = new UnknownFunction(basis, "u"); Expr v = new TestFunction(basis, "v"); /* set up differential operators */ Expr grad = gradient(2); Expr x = new CoordExpr(0); Expr y = new CoordExpr(1); Expr t = new Sundance::Parameter(0.0); Expr tPrev = new Sundance::Parameter(0.0); DiscreteSpace discSpace(mesh, basis, vecType); Expr uExact = cos(0.5*pi*y)*sin(pi*x)*exp(-lambda*t); L2Projector proj(discSpace, uExact); Expr uPrev = proj.project(); /* * We need a quadrature rule for doing the integrations */ QuadratureFamily quad = new GaussianQuadrature(2); double deltaT = tFinal/nt; Expr gWest = -pi*exp(-lambda*t)*cos(0.5*pi*y); Expr gWestPrev = -pi*exp(-lambda*tPrev)*cos(0.5*pi*y); /* Create the weak form */ Expr eqn = Integral(interior, v*(u-uPrev)/deltaT + 0.5*(grad*v)*(grad*u + grad*uPrev), quad) + Integral(west, -0.5*v*(gWest+gWestPrev), quad); Expr bc = EssentialBC(east + north, v*u, quad); LinearProblem prob(mesh, eqn, bc, v, u, vecType); LinearSolver<double> solver = LinearSolverBuilder::createSolver("amesos.xml"); FieldWriter w0 = new VTKWriter("TransientHeat2D-0"); w0.addMesh(mesh); w0.addField("T", new ExprFieldWrapper(uPrev[0])); w0.write(); for (int i=0; i<nt; i++) { t.setParameterValue((i+1)*deltaT); tPrev.setParameterValue(i*deltaT); Out::root() << "t=" << (i+1)*deltaT << endl; Expr uNext = prob.solve(solver); ostringstream oss; oss << "TransientHeat2D-" << i+1; FieldWriter w = new VTKWriter(oss.str()); w.addMesh(mesh); w.addField("T", new ExprFieldWrapper(uNext[0])); w.write(); updateDiscreteFunction(uNext, uPrev); } double err = L2Norm(mesh, interior, uExact-uPrev, quad); Out::root() << "error norm=" << err << endl; double h = 1.0/(nx-1.0); double tol = 0.1*(pow(h,2.0) + pow(lambda*deltaT, 2.0)); Out::root() << "tol=" << tol << endl; Sundance::passFailTest(err, tol); } catch(std::exception& e) { Sundance::handleException(e); } Sundance::finalize(); return Sundance::testStatus(); }
int main(int argc, char** argv) { try { int depth = 0; bool useCCode = false; Sundance::ElementIntegral::alwaysUseCofacets() = true; Sundance::clp().setOption("depth", &depth, "expression depth"); Sundance::clp().setOption("C", "symb", &useCCode, "Code type (C or symbolic)"); Sundance::init(&argc, &argv); /* We will do our linear algebra using Epetra */ VectorType<double> vecType = new EpetraVectorType(); /* Read the mesh */ MeshType meshType = new BasicSimplicialMeshType(); MeshSource mesher = new ExodusMeshReader("cube-0.1", meshType); Mesh mesh = mesher.getMesh(); /* Create a cell filter that will identify the maximal cells * in the interior of the domain */ CellFilter interior = new MaximalCellFilter(); CellFilter faces = new DimensionalCellFilter(2); CellFilter side1 = faces.labeledSubset(1); CellFilter side2 = faces.labeledSubset(2); CellFilter side3 = faces.labeledSubset(3); CellFilter side4 = faces.labeledSubset(4); CellFilter side5 = faces.labeledSubset(5); CellFilter side6 = faces.labeledSubset(6); /* Create unknown and test functions, discretized using second-order * Lagrange interpolants */ Expr u = new UnknownFunction(new Lagrange(1), "u"); Expr v = new TestFunction(new Lagrange(1), "v"); /* Create differential operator and coordinate functions */ Expr dx = new Derivative(0); Expr dy = new Derivative(1); Expr dz = new Derivative(2); Expr grad = List(dx, dy, dz); Expr x = new CoordExpr(0); Expr y = new CoordExpr(1); Expr z = new CoordExpr(2); /* We need a quadrature rule for doing the integrations */ QuadratureFamily quad2 = new GaussianQuadrature(2); QuadratureFamily quad4 = new GaussianQuadrature(4); /* Define the weak form */ //Expr eqn = Integral(interior, (grad*v)*(grad*u) + v, quad); Expr coeff = 1.0; #ifdef FOR_TIMING if (useCCode) { coeff = Poly(depth, x); } else { for (int i=0; i<depth; i++) { Expr t = 1.0; for (int j=0; j<depth; j++) t = t*x; coeff = coeff + 2.0*t - t - t; } } #endif Expr eqn = Integral(interior, coeff*(grad*v)*(grad*u) /*+ 2.0*v*/, quad2); /* Define the Dirichlet BC */ Expr exactSoln = x;//(x + 1.0)*x - 1.0/4.0; Expr h = new CellDiameterExpr(); WatchFlag watchBC("watch BCs"); watchBC.setParam("integration setup", 6); watchBC.setParam("integration", 6); watchBC.setParam("fill", 6); watchBC.setParam("evaluation", 6); watchBC.deactivate(); Expr bc = EssentialBC(side4, v*(u-exactSoln), quad4) + EssentialBC(side6, v*(u-exactSoln), quad4, watchBC); /* We can now set up the linear problem! */ LinearProblem prob(mesh, eqn, bc, v, u, vecType); #ifdef HAVE_CONFIG_H ParameterXMLFileReader reader(searchForFile("SolverParameters/aztec-ml.xml")); #else ParameterXMLFileReader reader("aztec-ml.xml"); #endif ParameterList solverParams = reader.getParameters(); std::cerr << "params = " << solverParams << std::endl; LinearSolver<double> solver = LinearSolverBuilder::createSolver(solverParams); Expr soln = prob.solve(solver); #ifndef FOR_TIMING DiscreteSpace discSpace(mesh, new Lagrange(1), vecType); L2Projector proj1(discSpace, exactSoln); L2Projector proj2(discSpace, soln-exactSoln); L2Projector proj3(discSpace, pow(soln-exactSoln, 2.0)); Expr exactDisc = proj1.project(); Expr errorDisc = proj2.project(); // Expr errorSqDisc = proj3.project(); std::cerr << "writing fields" << std::endl; /* Write the field in VTK format */ FieldWriter w = new VTKWriter("Poisson3d"); w.addMesh(mesh); w.addField("soln", new ExprFieldWrapper(soln[0])); w.addField("exact soln", new ExprFieldWrapper(exactDisc)); w.addField("error", new ExprFieldWrapper(errorDisc)); // w.addField("errorSq", new ExprFieldWrapper(errorSqDisc)); w.write(); std::cerr << "computing error" << std::endl; Expr errExpr = Integral(interior, pow(soln-exactSoln, 2.0), new GaussianQuadrature(4)); double errorSq = evaluateIntegral(mesh, errExpr); std::cerr << "error norm = " << sqrt(errorSq) << std::endl << std::endl; #else double errorSq = 1.0; #endif double tol = 1.0e-10; Sundance::passFailTest(sqrt(errorSq), tol); } catch(std::exception& e) { Sundance::handleException(e); } Sundance::finalize(); return Sundance::testStatus(); }
int main(int argc, char** argv) { try { /* * Initialization code */ std::string meshFile="plateWithHole2D-1"; std::string solverFile = "nox-aztec.xml"; Sundance::setOption("meshFile", meshFile, "mesh file"); Sundance::setOption("solver", solverFile, "name of XML file for solver"); Sundance::init(&argc, &argv); // This next line is just a hack to deal with some // transitional code in the // element integration logic. Sundance::ElementIntegral::alwaysUseCofacets() = false; /* * Creation of vector type */ VectorType<double> vecType = new EpetraVectorType(); /* * Creation of mesh */ MeshType meshType = new BasicSimplicialMeshType(); MeshSource meshSrc = new ExodusMeshReader(meshFile, meshType); Mesh mesh = meshSrc.getMesh(); /* * Specification of cell filters */ CellFilter interior = new MaximalCellFilter(); CellFilter edges = new DimensionalCellFilter(1); CellFilter south = edges.labeledSubset(1); CellFilter east = edges.labeledSubset(2); CellFilter north = edges.labeledSubset(3); CellFilter west = edges.labeledSubset(4); /* * <Header level="subsubsection" name="symb_setup"> * Setup of symbolic problem description * </Header> * * Create unknown and test functions discretized on the space * first-order Lagrange polynomials. */ BasisFamily basis = new Lagrange(2); Expr u = new UnknownFunction(basis, "u"); Expr v = new TestFunction(basis, "v"); /* * Create differential operators and coordinate functions. Directions * are indexed starting from zero. The \verb+List()+ function can * collect expressions into a vector. */ Expr dx = new Derivative(0); Expr dy = new Derivative(1); Expr grad = List(dx, dy); Expr x = new CoordExpr(0); Expr y = new CoordExpr(1); /* * We need a quadrature rule for doing the integrations */ QuadratureFamily quad2 = new GaussianQuadrature(2); QuadratureFamily quad4 = new GaussianQuadrature(4); /* * Create the weak form and the BCs */ Expr source=exp(u); Expr eqn = Integral(interior, (grad*u)*(grad*v)+v*source, quad4); Expr h = new CellDiameterExpr(); Expr bc = EssentialBC(west+east, v*(u-1.0)/h, quad2); /* * <Header level="subsubsection" name="lin_prob"> * Creation of initial guess * </Header> * * So far the setup has been almost identical to that for the linear * problem, the only difference being the nonlinear term in the * equation set. */ DiscreteSpace discSpace(mesh, basis, vecType); L2Projector proj(discSpace, 1.0); Expr u0 = proj.project(); /* * <Header level="subsubsection" name="lin_prob"> * Creation of nonlinear problem * </Header> * * Similar to the setup of a \verb+LinearProblem+, the equation, BCs, * and mesh are put into a \verb+NonlinearProblem+ object which * controls the construction of the \verb+Assembler+ and its use * in building Jacobians and residuals during a nonlinear solve. */ NonlinearProblem prob(mesh, eqn, bc, v, u, u0, vecType); /* * */ ParameterXMLFileReader reader(solverFile); ParameterList solverParams = reader.getParameters(); NOXSolver solver(solverParams); prob.solve(solver); /* * Visualization output */ FieldWriter w = new VTKWriter("PoissonBoltzmannDemo2D"); w.addMesh(mesh); w.addField("soln", new ExprFieldWrapper(u0)); w.write(); /* * <Header level="subsubsection" name="postproc"> * Postprocessing * </Header> * * Postprocessing can be done using the same symbolic language * as was used for the problem specification. Here, we define * an integral giving the flux, then evaluate it on the mesh. */ Expr n = CellNormalExpr(2, "n"); Expr fluxExpr = Integral(east + west, (n*grad)*u0, quad2); double flux = evaluateIntegral(mesh, fluxExpr); Out::os() << "numerical flux = " << flux << std::endl; Expr sourceExpr = Integral(interior, exp(u0), quad4); double src = evaluateIntegral(mesh, sourceExpr); Out::os() << "numerical integrated source = " << src << std::endl; /* * Check that the flux is acceptably close to zero. This * is just a sanity check to ensure the code doesn't get completely * broken after a change to the library. */ Sundance::passFailTest(fabs(flux-src), 1.0e-3); /* * <Header level="subsubsection" name="finalize"> * Finalization boilerplate * </Header> * Finally, we have boilerplate code for exception handling * and finalization. */ } catch(std::exception& e) { Sundance::handleException(e); } Sundance::finalize(); return Sundance::testStatus(); return Sundance::testStatus(); }
void LinearPDEConstrainedObj ::solveStateAndAdjoint(const Vector<double>& x) const { Tabs tab(0); PLAYA_MSG2(verb(), tab << "solving state and adjoint"); PLAYA_MSG3(verb(), tab << "|x|=" << x.norm2()); PLAYA_MSG5(verb(), tab << "x=" << endl << tab << x.norm2()); Tabs tab1; setDiscreteFunctionVector(designVarVal(), x); PLAYA_MSG3(verb(), tab1 << "solving state eqns"); /* solve the state equations in order */ for (int i=0; i<stateProbs_.size(); i++) { SolverState<double> status = stateProbs_[i].solve(solvers_[i], stateVarVals(i)); /* if the solve failed, write out the design var and known state * variables */ if (status.finalState() != SolveConverged) { FieldWriter w = new VTKWriter("badSolve"); w.addMesh(Lagrangian().mesh()); w.addField("designVar", new ExprFieldWrapper(designVarVal())); for (int j=0; j<i; j++) { Expr tmp = stateVarVals(j).flatten(); for (int k=0; k<tmp.size(); k++) { w.addField("stateVar-"+Teuchos::toString(j)+"-"+Teuchos::toString(k), new ExprFieldWrapper(tmp[k])); } } w.write(); } TEUCHOS_TEST_FOR_EXCEPTION(status.finalState() != SolveConverged, std::runtime_error, "state equation " << i << " could not be solved: status=" << status.stateDescription()); } PLAYA_MSG3(verb(), tab1 << "done solving state eqns"); /* do postprocessing */ statePostprocCallback(); PLAYA_MSG3(verb(), tab1 << "solving adjoint eqns"); /* solve the adjoint equations in reverse order */ for (int i=adjointProbs_.size()-1; i>=0; i--) { SolverState<double> status = adjointProbs_[i].solve(solvers_[i], adjointVarVals(i)); /* if the solve failed, write out the design var and known state * and adjoint variables */ if (status.finalState() != SolveConverged) { FieldWriter w = new VTKWriter("badSolve"); w.addMesh(Lagrangian().mesh()); w.addField("designVar", new ExprFieldWrapper(designVarVal())); for (int j=0; j<stateProbs_.size(); j++) { Expr tmp = stateVarVals(j).flatten(); for (int k=0; k<tmp.size(); k++) { w.addField("stateVar-"+Teuchos::toString(j)+"-"+Teuchos::toString(k), new ExprFieldWrapper(tmp[k])); } } for (int j=adjointProbs_.size()-1; j>i; j--) { Expr tmp = adjointVarVals(j).flatten(); for (int k=0; k<tmp.size(); k++) { w.addField("adjointVar-"+Teuchos::toString(j)+"-"+Teuchos::toString(k), new ExprFieldWrapper(tmp[k])); } } w.write(); } TEUCHOS_TEST_FOR_EXCEPTION(status.finalState() != SolveConverged, std::runtime_error, "adjoint equation " << i << " could not be solved: status=" << status.stateDescription()); } PLAYA_MSG3(verb(), tab1 << "done solving adjoint eqns"); PLAYA_MSG2(verb(), tab1 << "done solving state and adjoint eqns"); }
bool BlockStochPoissonTest1D() { /* We will do our linear algebra using Epetra */ VectorType<double> vecType = new EpetraVectorType(); /* Read a mesh */ MeshType meshType = new BasicSimplicialMeshType(); int nx = 32; MeshSource mesher = new PartitionedLineMesher(0.0, 1.0, nx, meshType); Mesh mesh = mesher.getMesh(); /* Create a cell filter that will identify the maximal cells * in the interior of the domain */ CellFilter interior = new MaximalCellFilter(); CellFilter pts = new DimensionalCellFilter(0); CellFilter left = pts.subset(new CoordinateValueCellPredicate(0,0.0)); CellFilter right = pts.subset(new CoordinateValueCellPredicate(0,1.0)); Expr x = new CoordExpr(0); /* Create the stochastic coefficients */ int nDim = 1; int order = 6; #ifdef HAVE_SUNDANCE_STOKHOS Out::root() << "using Stokhos hermite basis" << std::endl; SpectralBasis pcBasis = new Stokhos::HermiteBasis<int,double>(order); #else Out::root() << "using George's hermite basis" << std::endl; SpectralBasis pcBasis = new HermiteSpectralBasis(nDim, order); #endif Array<Expr> q(pcBasis.nterms()); Array<Expr> kappa(pcBasis.nterms()); Array<Expr> uEx(pcBasis.nterms()); double a = 0.1; q[0] = -2 + pow(a,2)*(4 - 9*x)*x - 2*pow(a,3)*(-1 + x)*(1 + 3*x*(-3 + 4*x)); q[1] = -(a*(-3 + 10*x + 2*a*(-1 + x*(8 - 9*x + a*(-4 + 3*(5 - 4*x)*x + 12*a*(-1 + x)*(1 + 5*(-1 + x)*x)))))); q[2] = a*(-4 + 6*x + a*(1 - x*(2 + 3*x) + a*(4 - 28*x + 30*pow(x,2)))); q[3] = -(pow(a,2)*(-3 + x*(20 - 21*x + a*(-4 + 3*(5 - 4*x)*x + 24*a*(-1 + x)*(1 + 5*(-1 + x)*x))))); q[4] = pow(a,3)*(1 + x*(-6 + x*(3 + 4*x))); q[5] = -4*pow(a,4)*(-1 + x)*x*(1 + 5*(-1 + x)*x); q[6] = 0.0; uEx[0] = -((-1 + x)*x); uEx[1] = -(a*(-1 + x)*pow(x,2)); uEx[2] = a*pow(-1 + x,2)*x; uEx[3] = pow(a,2)*pow(-1 + x,2)*pow(x,2); uEx[4] = 0.0; uEx[5] = 0.0; uEx[6] = 0.0; kappa[0] = 1.0; kappa[1] = a*x; kappa[2] = -(pow(a,2)*(-1 + x)*x); kappa[3] = 1.0; // unused kappa[4] = 1.0; // unused kappa[5] = 1.0; // unused kappa[6] = 1.0; // unused Array<Expr> uBC(pcBasis.nterms()); for (int i=0; i<pcBasis.nterms(); i++) uBC[i] = 0.0; int L = nDim+2; int P = pcBasis.nterms(); Out::os() << "L = " << L << std::endl; Out::os() << "P = " << P << std::endl; /* Create the unknown and test functions. Do NOT use the spectral * basis here */ Expr u = new UnknownFunction(new Lagrange(4), "u"); Expr v = new TestFunction(new Lagrange(4), "v"); /* Create differential operator and coordinate function */ Expr dx = new Derivative(0); Expr grad = dx; /* We need a quadrature rule for doing the integrations */ QuadratureFamily quad = new GaussianQuadrature(12); /* Now we create problem objects to build each $K_j$ and $f_j$. * There will be L matrix-vector pairs */ Array<Expr> eqn(P); Array<Expr> bc(P); Array<LinearProblem> prob(P); Array<LinearOperator<double> > KBlock(L); Array<Vector<double> > fBlock(P); Array<Vector<double> > solnBlock; for (int j=0; j<P; j++) { eqn[j] = Integral(interior, kappa[j]*(grad*v)*(grad*u) + v*q[j], quad); bc[j] = EssentialBC(left+right, v*(u-uBC[j]), quad); prob[j] = LinearProblem(mesh, eqn[j], bc[j], v, u, vecType); if (j<L) KBlock[j] = prob[j].getOperator(); fBlock[j] = -1.0*prob[j].getSingleRHS(); } /* Read the solver to be used on the diagonal blocks */ LinearSolver<double> diagSolver = LinearSolverBuilder::createSolver("amesos.xml"); double convTol = 1.0e-12; int maxIters = 30; int verb = 1; StochBlockJacobiSolver solver(diagSolver, pcBasis, convTol, maxIters, verb); solver.solve(KBlock, fBlock, solnBlock); /* write the solution */ FieldWriter w = new MatlabWriter("Stoch1D"); w.addMesh(mesh); DiscreteSpace discSpace(mesh, new Lagrange(4), vecType); for (int i=0; i<P; i++) { L2Projector proj(discSpace, uEx[i]); Expr ue_i = proj.project(); Expr df = new DiscreteFunction(discSpace, solnBlock[i]); w.addField("u["+ Teuchos::toString(i)+"]", new ExprFieldWrapper(df)); w.addField("uEx["+ Teuchos::toString(i)+"]", new ExprFieldWrapper(ue_i)); } w.write(); double totalErr2 = 0.0; DiscreteSpace discSpace4(mesh, new Lagrange(4), vecType); for (int i=0; i<P; i++) { Expr df = new DiscreteFunction(discSpace4, solnBlock[i]); Expr errExpr = Integral(interior, pow(uEx[i]-df, 2.0), quad); Expr scaleExpr = Integral(interior, pow(uEx[i], 2.0), quad); double errSq = evaluateIntegral(mesh, errExpr); double scale = evaluateIntegral(mesh, scaleExpr); if (scale > 0.0) Out::os() << "mode i=" << i << " error=" << sqrt(errSq/scale) << std::endl; else Out::os() << "mode i=" << i << " error=" << sqrt(errSq) << std::endl; } double tol = 1.0e-12; return SundanceGlobal::checkTest(sqrt(totalErr2), tol); }
bool DuffingFloquet() { int np = MPIComm::world().getNProc(); TEUCHOS_TEST_FOR_EXCEPT(np != 1); const double pi = 4.0*atan(1.0); /* We will do our linear algebra using Epetra */ VectorType<double> vecType = new EpetraVectorType(); /* Create a periodic mesh */ int nx = 128; MeshType meshType = new PeriodicMeshType1D(); MeshSource mesher = new PeriodicLineMesher(0.0, 2.0*pi, nx, meshType); Mesh mesh = mesher.getMesh(); /* Create a cell filter that will identify the maximal cells * in the interior of the domain */ CellFilter interior = new MaximalCellFilter(); CellFilter pts = new DimensionalCellFilter(0); CellFilter left = pts.subset(new CoordinateValueCellPredicate(0,0.0)); CellFilter right = pts.subset(new CoordinateValueCellPredicate(0,2.0*pi)); /* Create unknown and test functions, discretized using first-order * Lagrange interpolants */ Expr u1 = new UnknownFunction(new Lagrange(1), "u1"); Expr u2 = new UnknownFunction(new Lagrange(1), "u2"); Expr v1 = new TestFunction(new Lagrange(1), "v1"); Expr v2 = new TestFunction(new Lagrange(1), "v2"); /* Create differential operator and coordinate function */ Expr dx = new Derivative(0); Expr x = new CoordExpr(0); /* We need a quadrature rule for doing the integrations */ QuadratureFamily quad = new GaussianQuadrature(4); double F0 = 0.5; double gamma = 2.0/3.0; double a0 = 1.0; double w0 = 1.0; double eps = 0.5; Expr u1Guess = -0.75*cos(x) + 0.237*sin(x); Expr u2Guess = 0.237*cos(x) + 0.75*sin(x); DiscreteSpace discSpace(mesh, List(new Lagrange(1), new Lagrange(1)), vecType); L2Projector proj(discSpace, List(u1Guess, u2Guess)); Expr u0 = proj.project(); Expr rhs1 = u2; Expr rhs2 = -w0*w0*u1 - gamma*u2 - eps*w0*w0*pow(u1,3.0)/a0/a0 + F0*w0*w0*sin(x); /* Define the weak form */ Expr eqn = Integral(interior, v1*(dx*u1 - rhs1) + v2*(dx*u2 - rhs2), quad); Expr dummyBC ; NonlinearProblem prob(mesh, eqn, dummyBC, List(v1,v2), List(u1,u2), u0, vecType); ParameterXMLFileReader reader("nox.xml"); ParameterList solverParams = reader.getParameters(); Out::root() << "finding periodic solution" << endl; NOXSolver solver(solverParams); prob.solve(solver); /* unfold the solution onto a non-periodic mesh */ Expr uP = unfoldPeriodicDiscreteFunction(u0, "u_p"); Out::root() << "uP=" << uP << endl; Mesh unfoldedMesh = DiscreteFunction::discFunc(uP)->mesh(); DiscreteSpace unfDiscSpace = DiscreteFunction::discFunc(uP)->discreteSpace(); FieldWriter writer = new MatlabWriter("Floquet.dat"); writer.addMesh(unfoldedMesh); writer.addField("u_p[0]", new ExprFieldWrapper(uP[0])); writer.addField("u_p[1]", new ExprFieldWrapper(uP[1])); Array<Expr> a(2); a[0] = new Sundance::Parameter(0.0, "a1"); a[1] = new Sundance::Parameter(0.0, "a2"); Expr bc = EssentialBC(left, v1*(u1-uP[0]-a[0]) + v2*(u2-uP[1]-a[1]), quad); NonlinearProblem unfProb(unfoldedMesh, eqn, bc, List(v1,v2), List(u1,u2), uP, vecType); unfProb.setEvalPoint(uP); LinearOperator<double> J = unfProb.allocateJacobian(); Vector<double> b = J.domain().createMember(); LinearSolver<double> linSolver = LinearSolverBuilder::createSolver("amesos.xml"); SerialDenseMatrix<int, double> F(a.size(), a.size()); for (int i=0; i<a.size(); i++) { Out::root() << "doing perturbed orbit #" << i << endl; for (int j=0; j<a.size(); j++) { if (i==j) a[j].setParameterValue(1.0); else a[j].setParameterValue(0.0); } unfProb.computeJacobianAndFunction(J, b); Vector<double> w = b.copy(); linSolver.solve(J, b, w); Expr w_i = new DiscreteFunction(unfDiscSpace, w); for (int j=0; j<a.size(); j++) { Out::root() << "postprocessing" << i << endl; writer.addField("w[" + Teuchos::toString(i) + ", " + Teuchos::toString(j) + "]", new ExprFieldWrapper(w_i[j])); Expr g = Integral(right, w_i[j], quad); F(j,i) = evaluateIntegral(unfoldedMesh, g); } } writer.write(); Out::root() << "Floquet matrix = " << endl << F << endl; Out::root() << "doing eigenvalue analysis" << endl; Array<double> ew_r(a.size()); Array<double> ew_i(a.size()); int lWork = 6*a.size(); Array<double> work(lWork); int info = 0; LAPACK<int, double> lapack; lapack.GEEV('N','N', a.size(), F.values(), a.size(), &(ew_r[0]), &(ew_i[0]), 0, 1, 0, 1, &(work[0]), lWork, &info); TEUCHOS_TEST_FOR_EXCEPTION(info != 0, std::runtime_error, "LAPACK GEEV returned error code =" << info); Array<double> ew(a.size()); for (int i=0; i<a.size(); i++) { ew[i] = sqrt(ew_r[i]*ew_r[i]+ew_i[i]*ew_i[i]); Out::root() << setw(5) << i << setw(16) << ew_r[i] << setw(16) << ew_i[i] << setw(16) << ew[i] << endl; } double err = ::fabs(ew[0] - 0.123); return SundanceGlobal::checkTest(err, 0.001); }
int main( int argc , char **argv ) { try { int nx = 128; double C = 4.0; std::string solverFile = "aztec-ml.xml"; Sundance::setOption("nx", nx, "number of elements in x"); Sundance::setOption("C", C, "Nitsche penalty"); Sundance::setOption("solver", solverFile, "name of XML file for solver"); Sundance::init( &argc , &argv ); int np = MPIComm::world().getNProc(); int npx = -1; int npy = -1; balanceXY(np, &npx, &npy); TEST_FOR_EXCEPT(npx < 1); TEST_FOR_EXCEPT(npy < 1); TEST_FOR_EXCEPT(npx * npy != np); VectorType<double> vecType = new EpetraVectorType(); const int k = 1; const int splitBC = 1; MeshType meshType = new BasicSimplicialMeshType(); MeshSource mesher = new PartitionedRectangleMesher( 0.0 , 1.0 , nx , npx , 0.0 , 1.0 , nx , npy, meshType ); Mesh mesh = mesher.getMesh(); BasisFamily L = new Lagrange( k ); Expr u = new UnknownFunction( L , "u" ); Expr v = new TestFunction( L , "v" ); QuadratureFamily quad = new GaussianQuadrature( 2 * k ); Expr h = new CellDiameterExpr(); Expr alpha = C / h; Expr eqn = poissonEquationNitsche( splitBC, u , v , alpha , quad ); Expr bc; LinearProblem prob( mesh , eqn , bc , v , u , vecType); #ifdef HAVE_CONFIG_H ParameterXMLFileReader reader(searchForFile("SolverParameters/" + solverFile)); #else ParameterXMLFileReader reader(solverFile); #endif ParameterList solverParams = reader.getParameters(); LinearSolver<double> solver = LinearSolverBuilder::createSolver(solverParams); Expr soln = prob.solve( solver ); FieldWriter w = new VTKWriter( "NitschePoisson2D" ); w.addMesh( mesh ); w.addField( "u" , new ExprFieldWrapper( soln ) ); w.write(); Expr x = new CoordExpr(0); Expr y = new CoordExpr(1); QuadratureFamily quad4 = new GaussianQuadrature(4); CellFilter interior = new MaximalCellFilter(); const double pi = 4.0*atan(1.0); Expr exactSoln = sin(pi*x)*sin(pi*y); Expr err = exactSoln - soln; Expr errExpr = Integral(interior, err*err, quad4); FunctionalEvaluator errInt(mesh, errExpr); double errorSq = errInt.evaluate(); cout << "error norm = " << sqrt(errorSq) << std::endl << std::endl; Sundance::passFailTest(sqrt(errorSq), 1.0e-4); } catch (std::exception &e) { Sundance::handleException(e); } Sundance::finalize(); return Sundance::testStatus(); }
int main(int argc, char** argv) { try { int nx = 32; double convTol = 1.0e-8; double lambda = 0.5; Sundance::setOption("nx", nx, "Number of elements"); Sundance::setOption("tol", convTol, "Convergence tolerance"); Sundance::setOption("lambda", lambda, "Lambda (parameter in Bratu's equation)"); Sundance::init(&argc, &argv); Out::root() << "Bratu problem (lambda=" << lambda << ")" << endl; Out::root() << "Fixed-point iteration" << endl << endl; VectorType<double> vecType = new EpetraVectorType(); MeshType meshType = new BasicSimplicialMeshType(); MeshSource mesher = new PartitionedLineMesher(0.0, 1.0, nx, meshType); Mesh mesh = mesher.getMesh(); CellFilter interior = new MaximalCellFilter(); CellFilter sides = new DimensionalCellFilter(mesh.spatialDim()-1); CellFilter left = sides.subset(new CoordinateValueCellPredicate(0, 0.0)); CellFilter right = sides.subset(new CoordinateValueCellPredicate(0, 1.0)); BasisFamily basis = new Lagrange(1); Expr u = new UnknownFunction(basis, "u"); Expr v = new TestFunction(basis, "v"); Expr grad = gradient(1); Expr x = new CoordExpr(0); const double pi = 4.0*atan(1.0); Expr uExact = sin(pi*x); Expr R = pi*pi*uExact - lambda*exp(uExact); QuadratureFamily quad4 = new GaussianQuadrature(4); QuadratureFamily quad2 = new GaussianQuadrature(2); DiscreteSpace discSpace(mesh, basis, vecType); Expr uPrev = new DiscreteFunction(discSpace, 0.5); Expr uCur = copyDiscreteFunction(uPrev); Expr eqn = Integral(interior, (grad*u)*(grad*v) - v*lambda*exp(uPrev) - v*R, quad4); Expr h = new CellDiameterExpr(); Expr bc = EssentialBC(left+right, v*u/h, quad4); LinearProblem prob(mesh, eqn, bc, v, u, vecType); Expr normSqExpr = Integral(interior, pow(u-uPrev, 2.0), quad2); Functional normSqFunc(mesh, normSqExpr, vecType); FunctionalEvaluator normSqEval = normSqFunc.evaluator(u, uCur); LinearSolver<double> linSolver = LinearSolverBuilder::createSolver("amesos.xml"); Out::root() << "Fixed-point iteration" << endl; int maxIters = 20; Expr soln ; bool converged = false; for (int i=0; i<maxIters; i++) { /* solve for the next u */ prob.solve(linSolver, uCur); /* evaluate the norm of (uCur-uPrev) using * the FunctionalEvaluator defined above */ double deltaU = sqrt(normSqEval.evaluate()); Out::root() << "Iter=" << setw(3) << i << " ||Delta u||=" << setw(20) << deltaU << endl; /* check for convergence */ if (deltaU < convTol) { soln = uCur; converged = true; break; } /* get the vector from the current discrete function */ Vector<double> uVec = getDiscreteFunctionVector(uCur); /* copy the vector into the previous discrete function */ setDiscreteFunctionVector(uPrev, uVec); } TEUCHOS_TEST_FOR_EXCEPTION(!converged, std::runtime_error, "Fixed point iteration did not converge after " << maxIters << " iterations"); FieldWriter writer = new DSVWriter("FixedPointBratu.dat"); writer.addMesh(mesh); writer.addField("soln", new ExprFieldWrapper(soln[0])); writer.write(); Out::root() << "Converged!" << endl << endl; double L2Err = L2Norm(mesh, interior, soln-uExact, quad4); Out::root() << "L2 Norm of error: " << L2Err << endl; Sundance::passFailTest(L2Err, 1.5/((double) nx*nx)); } catch(exception& e) { Sundance::handleException(e); } Sundance::finalize(); }
int main(int argc, char** argv) { try { int nx = 32; double convTol = 1.0e-8; double lambda = 0.5; Sundance::setOption("nx", nx, "Number of elements"); Sundance::setOption("tol", convTol, "Convergence tolerance"); Sundance::setOption("lambda", lambda, "Lambda (parameter in Bratu's equation)"); Sundance::init(&argc, &argv); Out::root() << "Bratu problem (lambda=" << lambda << ")" << endl; Out::root() << "Newton's method with automated linearization" << endl << endl; VectorType<double> vecType = new EpetraVectorType(); MeshType meshType = new BasicSimplicialMeshType(); MeshSource mesher = new PartitionedLineMesher(0.0, 1.0, nx, meshType); Mesh mesh = mesher.getMesh(); CellFilter interior = new MaximalCellFilter(); CellFilter sides = new DimensionalCellFilter(mesh.spatialDim()-1); CellFilter left = sides.subset(new CoordinateValueCellPredicate(0, 0.0)); CellFilter right = sides.subset(new CoordinateValueCellPredicate(0, 1.0)); BasisFamily basis = new Lagrange(1); Expr u = new UnknownFunction(basis, "w"); Expr v = new TestFunction(basis, "v"); Expr grad = gradient(1); Expr x = new CoordExpr(0); const double pi = 4.0*atan(1.0); Expr uExact = sin(pi*x); Expr R = pi*pi*uExact - lambda*exp(uExact); QuadratureFamily quad4 = new GaussianQuadrature(4); QuadratureFamily quad2 = new GaussianQuadrature(2); DiscreteSpace discSpace(mesh, basis, vecType); Expr uPrev = new DiscreteFunction(discSpace, 0.5); Expr eqn = Integral(interior, (grad*v)*(grad*u) - v*lambda*exp(u) - v*R, quad4); Expr h = new CellDiameterExpr(); Expr bc = EssentialBC(left+right, v*u/h, quad2); NonlinearProblem prob(mesh, eqn, bc, v, u, uPrev, vecType); NonlinearSolver<double> solver = NonlinearSolverBuilder::createSolver("playa-newton-amesos.xml"); Out::root() << "Newton solve" << endl; SolverState<double> state = prob.solve(solver); TEUCHOS_TEST_FOR_EXCEPTION(state.finalState() != SolveConverged, std::runtime_error, "Nonlinear solve failed to converge: message=" << state.finalMsg()); Expr soln = uPrev; FieldWriter writer = new DSVWriter("AutoLinearizedBratu.dat"); writer.addMesh(mesh); writer.addField("soln", new ExprFieldWrapper(soln[0])); writer.write(); Out::root() << "Converged!" << endl << endl; double L2Err = L2Norm(mesh, interior, soln-uExact, quad4); Out::root() << "L2 Norm of error: " << L2Err << endl; Sundance::passFailTest(L2Err, 1.5/((double) nx*nx)); } catch(std::exception& e) { Sundance::handleException(e); } Sundance::finalize(); return Sundance::testStatus(); }
bool AToCDensitySample() { /* We will do our linear algebra using Epetra */ VectorType<double> vecType = new EpetraVectorType(); /* Create a mesh. It will be of type BasisSimplicialMesh, and will * be built using a PartitionedLineMesher. */ MeshType meshType = new BasicSimplicialMeshType(); MeshSource mesher = new PartitionedRectangleMesher(-1.0, 1.0, 32, 1, -1.0, 1.0, 32, 1, meshType); Mesh mesh = mesher.getMesh(); /* Create a cell filter that will identify the maximal cells * in the interior of the domain */ CellFilter interior = new MaximalCellFilter(); Expr x = new CoordExpr(0); Expr y = new CoordExpr(1); BasisFamily L1 = new Lagrange(1); DiscreteSpace discSpace(mesh, List(L1, L1), vecType); /* Discretize some expression for the force. We'll pick a linear function * so that it can be interpolated exactly, letting us check the * validity of our interpolations. */ L2Projector proj(discSpace, List(x, y)); Expr F = proj.project(); /* create a sampler */ cout << "making grid" << std::endl; AToCPointLocator locator(mesh, interior, createVector(tuple(200, 200))); AToCDensitySampler sampler(locator, vecType); CToAInterpolator forceInterpolator(locator, F); cout << "making points" << std::endl; /* create a bunch of particles */ int nCells = mesh.numCells(2); int nPts = 15000; Array<double> pos(2*nPts); Array<double> f(F.size() * nPts); Array<Point> physPts; /* We'll generate random sample points in a way that lets us make an exact check * of the density recovery. We pick random cells, then random local coordinates * within each cell. This way, we can compute the density exactly as we * go, giving us something to check the recovered density against. */ Array<int> counts(nCells); for (int i=0; i<nPts; i++) { /* pick a random cell */ int cell = (int) floor(nCells * drand48()); counts[cell]++; /* generate a point in local coordinates */ double s = drand48(); double t = drand48() * (1.0-s); Point refPt(s, t); /* map to physical coordinates */ mesh.pushForward(2, tuple(cell), tuple(refPt), physPts); Point X = physPts[0]; pos[2*i] = X[0]; pos[2*i+1] = X[1]; } cout << "sampling..." << std::endl; Expr density = sampler.sample(createVector(pos), 1.0); cout << "computing forces..." << std::endl; forceInterpolator.interpolate(pos, f); double maxForceErr = 0.0; for (int i=0; i<nPts; i++) { double x0 = pos[2*i]; double y0 = pos[2*i+1]; double fx = x0; double fy = y0; double df = ::fabs(fx - f[2*i]) + ::fabs(fy - f[2*i+1]); maxForceErr = max(maxForceErr, df); } cout << "max force error = " << maxForceErr << std::endl; cout << "writing..." << std::endl; /* Write the field in VTK format */ FieldWriter w = new VTKWriter("Density2d"); w.addMesh(mesh); w.addField("rho", new ExprFieldWrapper(density)); w.write(); double errorSq = 0.0; double tol = 1.0e-6; return SundanceGlobal::passFailTest(::sqrt(errorSq), tol); }
bool PoissonOnDisk() { #ifdef HAVE_SUNDANCE_EXODUS /* We will do our linear algebra using Epetra */ VectorType<double> vecType = new EpetraVectorType(); /* Get a mesh */ MeshType meshType = new BasicSimplicialMeshType(); MeshSource meshReader = new ExodusNetCDFMeshReader("disk.ncdf", meshType); Mesh mesh = meshReader.getMesh(); /* Create a cell filter that will identify the maximal cells * in the interior of the domain */ CellFilter interior = new MaximalCellFilter(); CellFilter bdry = new BoundaryCellFilter(); /* Create unknown and test functions, discretized using first-order * Lagrange interpolants */ Expr u = new UnknownFunction(new Lagrange(1), "u"); Expr v = new TestFunction(new Lagrange(1), "v"); /* Create differential operator and coordinate functions */ Expr dx = new Derivative(0); Expr dy = new Derivative(1); Expr grad = List(dx, dy); Expr x = new CoordExpr(0); Expr y = new CoordExpr(1); /* We need a quadrature rule for doing the integrations */ QuadratureFamily quad2 = new GaussianQuadrature(2); QuadratureFamily quad4 = new GaussianQuadrature(4); /* Define the weak form */ Expr eqn = Integral(interior, (grad*v)*(grad*u) + v, quad2); /* Define the Dirichlet BC */ Expr bc = EssentialBC(bdry, v*u, quad4); /* We can now set up the linear problem! */ LinearProblem prob(mesh, eqn, bc, v, u, vecType); LinearSolver<double> solver = LinearSolverBuilder::createSolver("amesos.xml"); Expr soln = prob.solve(solver); double R = 1.0; Expr exactSoln = 0.25*(x*x + y*y - R*R); DiscreteSpace discSpace(mesh, new Lagrange(1), vecType); Expr du = L2Projector(discSpace, exactSoln-soln).project(); /* Write the field in VTK format */ FieldWriter w = new VTKWriter("PoissonOnDisk"); w.addMesh(mesh); w.addField("soln", new ExprFieldWrapper(soln[0])); w.addField("error", new ExprFieldWrapper(du)); w.write(); Expr errExpr = Integral(interior, pow(soln-exactSoln, 2), new GaussianQuadrature(4)); double errorSq = evaluateIntegral(mesh, errExpr); std::cerr << "soln error norm = " << sqrt(errorSq) << std::endl << std::endl; /* Check error in automatically-computed cell normals */ /* Create a cell normal expression. Note that this is NOT a constructor * call, hence no "new" before the CellNormalExpr() function. The * argument "2" is the spatial dimension (mandatory), and * the "n" is the name of the expression (optional). */ Expr n = CellNormalExpr(2, "n"); Expr nExact = List(x, y)/sqrt(x*x + y*y); Expr nErrExpr = Integral(bdry, pow(n-nExact, 2.0), new GaussianQuadrature(1)); double nErrorSq = evaluateIntegral(mesh, nErrExpr); Out::root() << "normalVector error norm = " << sqrt(nErrorSq) << std::endl << std::endl; double tol = 1.0e-4; return SundanceGlobal::checkTest(sqrt(errorSq + nErrorSq), tol); #else std::cout << "dummy PoissonOnDisk PASSED. Enable Exodus to run the actual test" << std::endl; return true; #endif }
int main(int argc, char** argv) { try { Sundance::init(&argc, &argv); /* We will do our linear algebra using Epetra */ VectorType<double> vecType = new EpetraVectorType(); /* Create a mesh. It will be of type BasisSimplicialMesh, and will * be built using a PartitionedLineMesher. */ MeshType meshType = new BasicSimplicialMeshType(); int nx = 32; MeshSource mesher = new PartitionedRectangleMesher( 0.0, 1.0, nx, 0.0, 1.0, nx, meshType); Mesh mesh = mesher.getMesh(); /* Create a cell filter that will identify the maximal cells * in the interior of the domain */ CellFilter interior = new MaximalCellFilter(); /* Make cell filters for the east and west boundaries */ CellFilter edges = new DimensionalCellFilter(1); CellFilter west = edges.coordSubset(0, 0.0); CellFilter east = edges.coordSubset(0, 1.0); /* Create unknown and test functions */ Expr u = new UnknownFunction(new Lagrange(1), "u"); Expr v = new TestFunction(new Lagrange(1), "v"); /* Create differential operator and coordinate function */ Expr x = new CoordExpr(0); Expr grad = gradient(1); /* We need a quadrature rule for doing the integrations */ QuadratureFamily quad = new GaussianQuadrature(4); /* Define the parameter */ Expr xi = new Sundance::Parameter(0.0); /* Construct a forcing term to provide an exact solution for * validation purposes. This will involve the parameter. */ Expr uEx = x*(1.0-x)*(1.0+xi*exp(x)); Expr f = -(-20 - exp(x)*xi*(1 + 32*x + 10*x*x + exp(x)*(-1 + 2*x*(2 + x))*xi))/10.0; /* Define the weak form, using the parameter expression. This weak form * can be used for all parameter values. */ Expr eqn = Integral(interior, (1.0 + 0.1*xi*exp(x))*(grad*v)*(grad*u) - f*v, quad); /* Define the Dirichlet BC */ Expr h = new CellDiameterExpr(); Expr bc = EssentialBC(east + west, v*u/h, quad); /* We can now set up the linear problem. This can be reused * for different parameter values. */ LinearProblem prob(mesh, eqn, bc, v, u, vecType); /* make a projector for the exact solution. Just like the * problem, this can be reused for different parameter values. */ DiscreteSpace ds(mesh, new Lagrange(1), vecType); L2Projector proj(ds, uEx); /* Get the solver and declare variables for the results */ LinearSolver<double> solver = LinearSolverBuilder::createSolver("aztec-ml.xml"); Expr soln; SolverState<double> state; /* Set up the sweep from xi=0 to xi=xiMax in nSteps steps. */ int nSteps = 10; double xiMax = 2.0; /* Make an array in which to keep the observed errors */ Array<double> err(nSteps); /* Do the sweep */ for (int n=0; n<nSteps; n++) { /* Update the parameter value */ double xiVal = xiMax*n/(nSteps - 1.0); xi.setParameterValue(xiVal); Out::root() << "step n=" << n << " of " << nSteps << " xi=" << xiVal; /* Solve the problem. The updated parameter value is automatically used. */ state = prob.solve(solver, soln); TEUCHOS_TEST_FOR_EXCEPTION(state.finalState() != SolveConverged, std::runtime_error, "solve failed!"); /* Project the exact solution onto a discrrete space for viz. The updated * parameter value is automatically used. */ Expr uEx0 = proj.project(); /* Write the approximate and exact solutions for viz */ FieldWriter w = new VTKWriter("ParameterSweep-" + Teuchos::toString(n)); w.addMesh(mesh); w.addField("u", new ExprFieldWrapper(soln[0])); w.addField("uEx", new ExprFieldWrapper(uEx0[0])); w.write(); /* Compute the L2 norm of the error */ err[n] = L2Norm(mesh, interior, soln-uEx, quad); Out::root() << " L2 error = " << err[n] << endl; } /* The errors are O(h^2), so use that to set a tolerance */ double hVal = 1.0/(nx-1.0); double fudge = 2.0; double tol = fudge*hVal*hVal; /* Find the max error over all parameter values */ double maxErr = *std::max_element(err.begin(), err.end()); /* Check the error */ Sundance::passFailTest(maxErr, tol); } catch(std::exception& e) { Sundance::handleException(e); } Sundance::finalize(); return Sundance::testStatus(); }
int main(int argc, char** argv) { try { Sundance::init(&argc, &argv); int np = MPIComm::world().getNProc(); int nx = 48; int ny = 48; int npx = -1; int npy = -1; PartitionedRectangleMesher::balanceXY(np, &npx, &npy); TEUCHOS_TEST_FOR_EXCEPT(npx < 1); TEUCHOS_TEST_FOR_EXCEPT(npy < 1); TEUCHOS_TEST_FOR_EXCEPT(npx * npy != np); MeshType meshType = new BasicSimplicialMeshType(); MeshSource mesher = new PartitionedRectangleMesher(0.0, 1.0, nx, npx, 0.0, 1.0, ny, npy, meshType); Mesh mesh = mesher.getMesh(); CellFilter interior = new MaximalCellFilter(); CellFilter bdry = new BoundaryCellFilter(); /* Create a vector space factory, used to * specify the low-level linear algebra representation */ VectorType<double> vecType = new EpetraVectorType(); /* create a discrete space on the mesh */ DiscreteSpace discreteSpace(mesh, new Lagrange(1), vecType); /* initialize the design, state, and multiplier vectors */ Expr alpha0 = new DiscreteFunction(discreteSpace, 1.0, "alpha0"); Expr u0 = new DiscreteFunction(discreteSpace, 1.0, "u0"); Expr lambda0 = new DiscreteFunction(discreteSpace, 1.0, "lambda0"); /* create symbolic objects for test and unknown functions */ Expr u = new UnknownFunction(new Lagrange(1), "u"); Expr lambda = new UnknownFunction(new Lagrange(1), "lambda"); Expr alpha = new UnknownFunction(new Lagrange(1), "alpha"); /* create symbolic differential operators */ Expr dx = new Derivative(0); Expr dy = new Derivative(1); Expr grad = List(dx, dy); /* create symbolic coordinate functions */ Expr x = new CoordExpr(0); Expr y = new CoordExpr(1); /* create target function */ const double pi = 4.0*atan(1.0); Expr uStar = sin(pi*x)*sin(pi*y); /* create quadrature rules of different orders */ QuadratureFamily q1 = new GaussianQuadrature(1); QuadratureFamily q2 = new GaussianQuadrature(2); QuadratureFamily q4 = new GaussianQuadrature(4); /* Regularization weight */ double R = 0.001; double U0 = 1.0/(1.0 + 4.0*pow(pi,4.0)*R); double A0 = -2.0*pi*pi*U0; /* Form objective function */ Expr reg = Integral(interior, 0.5 * R * alpha*alpha, q2); Expr fit = Integral(interior, 0.5 * pow(u-uStar, 2.0), q4); Expr constraintEqn = Integral(interior, (grad*lambda)*(grad*u) + lambda*alpha, q2); Expr L = reg + fit + constraintEqn; Expr constraintBC = EssentialBC(bdry, lambda*u, q2); Functional Lagrangian(mesh, L, constraintBC, vecType); LinearSolver<double> solver = LinearSolverBuilder::createSolver("amesos.xml"); RCP<ObjectiveBase> obj = rcp(new LinearPDEConstrainedObj( Lagrangian, u, u0, lambda, lambda0, alpha, alpha0, solver)); Vector<double> xInit = obj->getInit(); bool doFDCheck = false; if (doFDCheck) { Out::root() << "Doing FD check of gradient..." << endl; bool fdOK = obj->fdCheck(xInit, 1.0e-6, 2); if (fdOK) { Out::root() << "FD check OK" << endl; } else { Out::root() << "FD check FAILED" << endl; } } RCP<UnconstrainedOptimizerBase> opt = OptBuilder::createOptimizer("basicLMBFGS.xml"); opt->setVerb(2); OptState state = opt->run(obj, xInit); bool ok = true; if (state.status() != Opt_Converged) { Out::root()<< "optimization failed: " << state.status() << endl; TEUCHOS_TEST_FOR_EXCEPT(state.status() != Opt_Converged); } Out::root() << "opt converged: " << state.iter() << " iterations" << endl; Out::root() << "exact solution: U0=" << U0 << " A0=" << A0 << endl; FieldWriter w = new VTKWriter("PoissonSourceInversion"); w.addMesh(mesh); w.addField("u", new ExprFieldWrapper(u0)); w.addField("alpha", new ExprFieldWrapper(alpha0)); w.addField("lambda", new ExprFieldWrapper(lambda0)); w.write(); double uErr = L2Norm(mesh, interior, u0-U0*uStar, q4); double aErr = L2Norm(mesh, interior, alpha0-A0*uStar, q4); Out::root() << "error in u = " << uErr << endl; Out::root() << "error in alpha = " << aErr << endl; double tol = 0.01; Sundance::passFailTest(uErr + aErr, tol); } catch(std::exception& e) { cerr << "main() caught exception: " << e.what() << endl; } Sundance::finalize(); return Sundance::testStatus(); }
bool NonlinReducedIntegration() { int np = MPIComm::world().getNProc(); int n = 4; bool increaseProbSize = true; if ( (np % 4)==0 ) increaseProbSize = false; Array<double> h; Array<double> errQuad; Array<double> errReduced; for (int i=0; i<4; i++) { n *= 2; int nx = n; int ny = n; VectorType<double> vecType = new EpetraVectorType(); MeshType meshType = new BasicSimplicialMeshType(); int npx = -1; int npy = -1; PartitionedRectangleMesher::balanceXY(np, &npx, &npy); TEUCHOS_TEST_FOR_EXCEPT(npx < 1); TEUCHOS_TEST_FOR_EXCEPT(npy < 1); TEUCHOS_TEST_FOR_EXCEPT(npx * npy != np); if (increaseProbSize) { nx = nx*npx; ny = ny*npy; } MeshSource mesher = new PartitionedRectangleMesher(0.0, 1.0, nx, npx, 0.0, 1.0, ny, npy, meshType); Mesh mesh = mesher.getMesh(); WatchFlag watchMe("watch eqn"); watchMe.setParam("integration setup", 0); watchMe.setParam("integration", 0); watchMe.setParam("fill", 0); watchMe.setParam("evaluation", 0); watchMe.deactivate(); WatchFlag watchBC("watch BCs"); watchBC.setParam("integration setup", 0); watchBC.setParam("integration", 0); watchBC.setParam("fill", 0); watchBC.setParam("evaluation", 0); watchBC.deactivate(); CellFilter interior = new MaximalCellFilter(); CellFilter edges = new DimensionalCellFilter(1); CellFilter left = edges.subset(new CoordinateValueCellPredicate(0,0.0)); CellFilter right = edges.subset(new CoordinateValueCellPredicate(0,1.0)); CellFilter top = edges.subset(new CoordinateValueCellPredicate(1,1.0)); CellFilter bottom = edges.subset(new CoordinateValueCellPredicate(1,0.0)); BasisFamily basis = new Lagrange(1); Expr u = new UnknownFunction(basis, "u"); Expr v = new TestFunction(basis, "v"); Expr dx = new Derivative(0); Expr dy = new Derivative(1); Expr grad = List(dx, dy); Expr x = new CoordExpr(0); Expr y = new CoordExpr(1); QuadratureFamily quad = new ReducedQuadrature(); QuadratureFamily quad2 = new GaussianQuadrature(2); /* Define the weak form */ const double pi = 4.0*atan(1.0); Expr c = cos(pi*x); Expr s = sin(pi*x); Expr ch = cosh(y); Expr sh = sinh(y); Expr s2 = s*s; Expr c2 = c*c; Expr sh2 = sh*sh; Expr ch2 = ch*ch; Expr pi2 = pi*pi; Expr uEx = s*ch; Expr eu = exp(uEx); Expr f = -(ch*eu*(-1 + pi2)*s) + ch2*(c2*eu*pi2 - s2) + eu*s2*sh2; Expr eqn = Integral(interior, exp(u)*(grad*u)*(grad*v) + v*f + v*u*u, quad, watchMe) + Integral(right, v*exp(u)*pi*cosh(y), quad,watchBC); /* Define the Dirichlet BC */ Expr bc = EssentialBC(left+top, v*(u-uEx), quad, watchBC); Expr eqn2 = Integral(interior, exp(u)*(grad*u)*(grad*v) + v*f + v*u*u, quad2, watchMe) + Integral(right, v*exp(u)*pi*cosh(y), quad2,watchBC); /* Define the Dirichlet BC */ Expr bc2 = EssentialBC(left+top, v*(u-uEx), quad2, watchBC); DiscreteSpace discSpace(mesh, new Lagrange(1), vecType); Expr soln1 = new DiscreteFunction(discSpace, 0.0, "u0"); Expr soln2 = new DiscreteFunction(discSpace, 0.0, "u0"); L2Projector proj(discSpace, uEx); Expr uEx0 = proj.project(); NonlinearProblem nlp(mesh, eqn, bc, v, u, soln1, vecType); NonlinearProblem nlp2(mesh, eqn2, bc2, v, u, soln2, vecType); ParameterXMLFileReader reader("nox-aztec.xml"); ParameterList noxParams = reader.getParameters(); NOXSolver solver(noxParams); nlp.solve(solver); nlp2.solve(solver); FieldWriter w = new VTKWriter("NonlinReduced-n" + Teuchos::toString(n)); w.addMesh(mesh); w.addField("soln1", new ExprFieldWrapper(soln1[0])); w.addField("soln2", new ExprFieldWrapper(soln2[0])); w.addField("exact", new ExprFieldWrapper(uEx0[0])); w.write(); Expr err1 = uEx - soln1; Expr errExpr1 = Integral(interior, err1*err1, new GaussianQuadrature(4)); Expr err2 = uEx - soln2; Expr errExpr2 = Integral(interior, err2*err2, new GaussianQuadrature(4)); Expr err12 = soln2 - soln1; Expr errExpr12 = Integral(interior, err12*err12, new GaussianQuadrature(4)); double error1 = ::sqrt(evaluateIntegral(mesh, errExpr1)); double error2 = ::sqrt(evaluateIntegral(mesh, errExpr2)); double error12 = ::sqrt(evaluateIntegral(mesh, errExpr12)); Out::root() << "final result: " << n << " " << error1 << " " << error2 << " " << error12 << endl; h.append(1.0/((double) n)); errQuad.append(error2); errReduced.append(error1); } double pQuad = fitPower(h, errQuad); double pRed = fitPower(h, errReduced); Out::root() << "exponent (reduced integration) " << pRed << endl; Out::root() << "exponent (full integration) " << pQuad << endl; return SundanceGlobal::checkTest(::fabs(pRed-2.0), 0.1); }