BOOST_AUTO_TEST_CASE_TEMPLATE(symmetric_matches_nonsymmetric_in_aca_mode, ValueType, result_types) { typedef ValueType RT; typedef typename Fiber::ScalarTraits<ValueType>::RealType RealType; typedef RealType BFT; if (boost::is_same<RT, std::complex<float> >::value) { // The AHMED support for single-precision complex symmetric matrices // is broken BOOST_CHECK(true); return; } GridParameters params; params.topology = GridParameters::TRIANGULAR; shared_ptr<Grid> grid = GridFactory::importGmshGrid( params, "../../examples/meshes/sphere-h-0.4.msh", false /* verbose */); PiecewiseLinearContinuousScalarSpace<BFT> pwiseLinears(grid); PiecewiseConstantScalarSpace<BFT> pwiseConstants(grid); AssemblyOptions assemblyOptions; assemblyOptions.setVerbosityLevel(VerbosityLevel::LOW); AcaOptions acaOptions; acaOptions.minimumBlockSize = 4; assemblyOptions.switchToAcaMode(acaOptions); AccuracyOptions accuracyOptions; accuracyOptions.doubleRegular.setRelativeQuadratureOrder(4); accuracyOptions.doubleSingular.setRelativeQuadratureOrder(2); NumericalQuadratureStrategy<BFT, RT> quadStrategy(accuracyOptions); Context<BFT, RT> context(make_shared_from_ref(quadStrategy), assemblyOptions); const RT waveNumber = initWaveNumber<RT>(); BoundaryOperator<BFT, RT> opNonsymmetric = modifiedHelmholtz3dSingleLayerBoundaryOperator<BFT, RT, RT>( make_shared_from_ref(context), make_shared_from_ref(pwiseLinears), make_shared_from_ref(pwiseConstants), make_shared_from_ref(pwiseLinears), waveNumber, "", NO_SYMMETRY); BoundaryOperator<BFT, RT> opSymmetric = modifiedHelmholtz3dSingleLayerBoundaryOperator<BFT, RT, RT>( make_shared_from_ref(context), make_shared_from_ref(pwiseLinears), make_shared_from_ref(pwiseConstants), make_shared_from_ref(pwiseLinears), waveNumber, "", SYMMETRIC); arma::Mat<RT> matNonsymmetric = opNonsymmetric.weakForm()->asMatrix(); arma::Mat<RT> matSymmetric = opSymmetric.weakForm()->asMatrix(); BOOST_CHECK(check_arrays_are_close<RT>( matNonsymmetric, matSymmetric, 2 * acaOptions.eps)); }
BOOST_AUTO_TEST_CASE_TEMPLATE(aca_of_synthetic_maxwell_single_layer_operator_agrees_with_dense_assembly_in_asymmetric_case, ValueType, complex_result_types) { typedef ValueType RT; typedef typename ScalarTraits<ValueType>::RealType RealType; typedef RealType BFT; GridParameters params; params.topology = GridParameters::TRIANGULAR; shared_ptr<Grid> grid = GridFactory::importGmshGrid( params, "../../meshes/sphere-h-0.4.msh", false /* verbose */); RT waveNumber = initWaveNumber<RT>(); shared_ptr<Space<BFT> > vectorPwiseLinears( new RaviartThomas0VectorSpace<BFT>(grid)); shared_ptr<Space<BFT> > vectorPwiseLinears2( new RaviartThomas0VectorSpace<BFT>(grid)); AccuracyOptions accuracyOptions; accuracyOptions.doubleRegular.setRelativeQuadratureOrder(2); accuracyOptions.singleRegular.setRelativeQuadratureOrder(2); shared_ptr<NumericalQuadratureStrategy<BFT, RT> > quadStrategy( new NumericalQuadratureStrategy<BFT, RT>(accuracyOptions)); AssemblyOptions assemblyOptionsDense; assemblyOptionsDense.setVerbosityLevel(VerbosityLevel::LOW); shared_ptr<Context<BFT, RT> > contextDense( new Context<BFT, RT>(quadStrategy, assemblyOptionsDense)); BoundaryOperator<BFT, RT> opDense = maxwell3dSingleLayerBoundaryOperator<BFT>( contextDense, vectorPwiseLinears, vectorPwiseLinears, vectorPwiseLinears, waveNumber); arma::Mat<RT> weakFormDense = opDense.weakForm()->asMatrix(); AssemblyOptions assemblyOptionsAca; assemblyOptionsAca.setVerbosityLevel(VerbosityLevel::LOW); AcaOptions acaOptions; acaOptions.mode = AcaOptions::LOCAL_ASSEMBLY; assemblyOptionsAca.switchToAcaMode(acaOptions); shared_ptr<Context<BFT, RT> > contextAca( new Context<BFT, RT>(quadStrategy, assemblyOptionsAca)); // Internal domain different from dualToRange BoundaryOperator<BFT, RT> opAca = maxwell3dSingleLayerBoundaryOperator<BFT>( contextAca, vectorPwiseLinears, vectorPwiseLinears, vectorPwiseLinears2, waveNumber); arma::Mat<RT> weakFormAca = opAca.weakForm()->asMatrix(); BOOST_CHECK(check_arrays_are_close<ValueType>( weakFormDense, weakFormAca, 2. * acaOptions.eps)); }
BOOST_AUTO_TEST_CASE_TEMPLATE(aca_of_synthetic_modified_helmholtz_hypersingular_operator_agrees_with_dense_assembly_in_symmetric_case, ValueType, result_types) { typedef ValueType RT; typedef typename ScalarTraits<ValueType>::RealType RealType; typedef RealType BFT; GridParameters params; params.topology = GridParameters::TRIANGULAR; shared_ptr<Grid> grid = GridFactory::importGmshGrid( params, "../../meshes/sphere-h-0.4.msh", false /* verbose */); RT waveNumber = initWaveNumber<RT>(); shared_ptr<Space<BFT> > pwiseConstants( new PiecewiseConstantScalarSpace<BFT>(grid)); shared_ptr<Space<BFT> > pwiseLinears( new PiecewiseLinearContinuousScalarSpace<BFT>(grid)); AccuracyOptions accuracyOptions; accuracyOptions.doubleRegular.setRelativeQuadratureOrder(2); accuracyOptions.singleRegular.setRelativeQuadratureOrder(2); shared_ptr<NumericalQuadratureStrategy<BFT, RT> > quadStrategy( new NumericalQuadratureStrategy<BFT, RT>(accuracyOptions)); AssemblyOptions assemblyOptionsDense; assemblyOptionsDense.setVerbosityLevel(VerbosityLevel::LOW); shared_ptr<Context<BFT, RT> > contextDense( new Context<BFT, RT>(quadStrategy, assemblyOptionsDense)); BoundaryOperator<BFT, RT> opDense = modifiedHelmholtz3dHypersingularBoundaryOperator<BFT, RT, RT>( contextDense, pwiseLinears, pwiseConstants, pwiseLinears, waveNumber); arma::Mat<RT> weakFormDense = opDense.weakForm()->asMatrix(); AssemblyOptions assemblyOptionsAca; assemblyOptionsAca.setVerbosityLevel(VerbosityLevel::LOW); AcaOptions acaOptions; acaOptions.mode = AcaOptions::LOCAL_ASSEMBLY; assemblyOptionsAca.switchToAcaMode(acaOptions); shared_ptr<Context<BFT, RT> > contextAca( new Context<BFT, RT>(quadStrategy, assemblyOptionsAca)); BoundaryOperator<BFT, RT> opAca = modifiedHelmholtz3dHypersingularBoundaryOperator<BFT, RT, RT>( contextAca, pwiseLinears, pwiseConstants, pwiseLinears, waveNumber); arma::Mat<RT> weakFormAca = opAca.weakForm()->asMatrix(); BOOST_CHECK(check_arrays_are_close<ValueType>( weakFormDense, weakFormAca, 2. * acaOptions.eps)); }
int main() { // Import symbols from namespace Bempp to the global namespace using namespace Bempp; // Load mesh const char* meshFile = "meshes/sphere-h-0.2.msh"; GridParameters params; params.topology = GridParameters::TRIANGULAR; shared_ptr<Grid> grid = GridFactory::importGmshGrid(params, meshFile); // Initialize the spaces PiecewiseLinearContinuousScalarSpace<BFT> pwiseLinears(grid); PiecewiseConstantScalarSpace<BFT> pwiseConstants(grid); // Define the quadrature strategy AccuracyOptions accuracyOptions; // Increase by 2 the order of quadrature rule used to approximate // integrals of regular functions on pairs on elements accuracyOptions.doubleRegular.setRelativeQuadratureOrder(2); // Increase by 2 the order of quadrature rule used to approximate // integrals of regular functions on single elements accuracyOptions.singleRegular.setRelativeQuadratureOrder(2); NumericalQuadratureStrategy<BFT, RT> quadStrategy(accuracyOptions); // Specify the assembly method. We want to use ACA AssemblyOptions assemblyOptions; AcaOptions acaOptions; // Default parameters for ACA assemblyOptions.switchToAcaMode(acaOptions); // Create the assembly context Context<BFT, RT> context(make_shared_from_ref(quadStrategy), assemblyOptions); // Construct elementary operators BoundaryOperator<BFT, RT> slpOp = laplace3dSingleLayerBoundaryOperator<BFT, RT>( make_shared_from_ref(context), make_shared_from_ref(pwiseConstants), make_shared_from_ref(pwiseLinears), make_shared_from_ref(pwiseConstants)); BoundaryOperator<BFT, RT> dlpOp = laplace3dDoubleLayerBoundaryOperator<BFT, RT>( make_shared_from_ref(context), make_shared_from_ref(pwiseLinears), make_shared_from_ref(pwiseLinears), make_shared_from_ref(pwiseConstants)); BoundaryOperator<BFT, RT> idOp = identityOperator<BFT, RT>( make_shared_from_ref(context), make_shared_from_ref(pwiseLinears), make_shared_from_ref(pwiseLinears), make_shared_from_ref(pwiseConstants)); // Form the right-hand side sum BoundaryOperator<BFT, RT> rhsOp = -0.5 * idOp + dlpOp; // Construct the grid function representing the (input) Dirichlet data GridFunction<BFT, RT> dirichletData( make_shared_from_ref(context), make_shared_from_ref(pwiseLinears), make_shared_from_ref(pwiseLinears), surfaceNormalIndependentFunction(DirichletData())); // Construct the right-hand-side grid function GridFunction<BFT, RT> rhs = rhsOp * dirichletData; // Initialize the solver DefaultIterativeSolver<BFT, RT> solver(slpOp); solver.initializeSolver(defaultGmresParameterList(1e-5)); // Solve the equation Solution<BFT, RT> solution = solver.solve(rhs); std::cout << solution.solverMessage() << std::endl; // Extract the solution in the form of a grid function // and export it in VTK format const GridFunction<BFT, RT>& solFun = solution.gridFunction(); solFun.exportToVtk(VtkWriter::CELL_DATA, "Neumann_data", "solution"); // Compare the numerical and analytical solution on the grid // GridFunction<BFT, RT> exactSolFun( // make_shared_from_ref(context), // make_shared_from_ref(pwiseConstants), // make_shared_from_ref(pwiseConstants), // surfaceNormalIndependentFunction(ExactNeumannData())); CT absoluteError, relativeError; estimateL2Error( solFun, surfaceNormalIndependentFunction(ExactNeumannData()), quadStrategy, absoluteError, relativeError); std::cout << "Relative L^2 error: " << relativeError << std::endl; // GridFunction<BFT, RT> diff = solFun - exactSolFun; // double relativeError = diff.L2Norm() / exactSolFun.L2Norm(); // std::cout << "Relative L^2 error: " << relativeError << std::endl; // Prepare to evaluate the solution on an annulus outside the sphere // Create potential operators Laplace3dSingleLayerPotentialOperator<BFT, RT> slPotOp; Laplace3dDoubleLayerPotentialOperator<BFT, RT> dlPotOp; // Construct the array 'evaluationPoints' containing the coordinates // of points where the solution should be evaluated const int rCount = 51; const int thetaCount = 361; const CT minTheta = 0., maxTheta = 2. * M_PI; const CT minR = 1., maxR = 2.; const int dimWorld = 3; arma::Mat<CT> evaluationPoints(dimWorld, rCount * thetaCount); for (int iTheta = 0; iTheta < thetaCount; ++iTheta) { CT theta = minTheta + (maxTheta - minTheta) * iTheta / (thetaCount - 1); for (int iR = 0; iR < rCount; ++iR) { CT r = minR + (maxR - minR) * iR / (rCount - 1); evaluationPoints(0, iR + iTheta * rCount) = r * cos(theta); // x evaluationPoints(1, iR + iTheta * rCount) = r * sin(theta); // y evaluationPoints(2, iR + iTheta * rCount) = 0.; // z } } // Use the Green's representation formula to evaluate the solution EvaluationOptions evaluationOptions; arma::Mat<RT> field = -slPotOp.evaluateAtPoints(solFun, evaluationPoints, quadStrategy, evaluationOptions) + dlPotOp.evaluateAtPoints(dirichletData, evaluationPoints, quadStrategy, evaluationOptions); // Export the solution into text file std::ofstream out("solution.txt"); out << "# x y z u\n"; for (int i = 0; i < rCount * thetaCount; ++i) out << evaluationPoints(0, i) << ' ' << evaluationPoints(1, i) << ' ' << evaluationPoints(2, i) << ' ' << field(0, i) << '\n'; }
int main(int argc, char* argv[]) { // Physical parameters, general const BFT c0 = 0.3; // speed of light in vacuum [mm/ps] BFT refind = 1.4; // refractive index BFT alpha = A_Keijzer(refind); // boundary term BFT c = c0/refind; // speed of light in medium [mm/ps] BFT freq = 100*1e6; // modulation frequency [Hz] BFT omega = 2.0*M_PI * freq*1e-12; // modulation frequency [cycles/ps] // Physical parameters, outer region BFT mua1 = 0.01; // absorption coefficient BFT mus1 = 1.0; // scattering coefficient BFT kappa1 = 1.0/(3.0*(mua1+mus1)); // diffusion coefficient RT waveNumber1 = sqrt (RT(mua1/kappa1, omega/(c*kappa1))); // outer region // Physical parameters, inner region BFT mua2 = 0.02; // absorption coefficient BFT mus2 = 0.5; // scattering coefficient BFT kappa2 = 1.0/(3.0*(mua2+mus2)); // diffusion coefficient RT waveNumber2 = sqrt (RT(mua2/kappa2, omega/(c*kappa2))); // outer region // Create sphere meshes on the fly shared_ptr<Grid> grid1 = CreateSphere(25.0, 1.0); shared_ptr<Grid> grid2 = CreateSphere(15.0, 1.0); // Initialize the spaces PiecewiseLinearContinuousScalarSpace<BFT> HplusHalfSpace1(grid1); PiecewiseLinearContinuousScalarSpace<BFT> HplusHalfSpace2(grid2); // Define some default options. AssemblyOptions assemblyOptions; // We want to use ACA AcaOptions acaOptions; // Default parameters for ACA acaOptions.eps = 1e-5; assemblyOptions.switchToAcaMode(acaOptions); // Define the standard integration factory AccuracyOptions accuracyOptions; accuracyOptions.doubleRegular.setRelativeQuadratureOrder(2); accuracyOptions.singleRegular.setRelativeQuadratureOrder(1); NumericalQuadratureStrategy<BFT, RT> quadStrategy(accuracyOptions); Context<BFT, RT> context(make_shared_from_ref(quadStrategy), assemblyOptions); // We need the single layer, double layer, and the identity operator // mesh1 x mesh1 BoundaryOperator<BFT, RT> slp11 = modifiedHelmholtz3dSingleLayerBoundaryOperator<BFT, RT, RT>( SHARED(context), SHARED(HplusHalfSpace1), SHARED(HplusHalfSpace1), SHARED(HplusHalfSpace1), waveNumber1); BoundaryOperator<BFT, RT> dlp11 = modifiedHelmholtz3dDoubleLayerBoundaryOperator<BFT, RT, RT>( SHARED(context), SHARED(HplusHalfSpace1), SHARED(HplusHalfSpace1), SHARED(HplusHalfSpace1), waveNumber1); BoundaryOperator<BFT, RT> id11 = identityOperator<BFT, RT>( SHARED(context), SHARED(HplusHalfSpace1), SHARED(HplusHalfSpace1), SHARED(HplusHalfSpace1)); // mesh2 x mesh2, wavenumber 1 BoundaryOperator<BFT, RT> slp22_w1 = modifiedHelmholtz3dSingleLayerBoundaryOperator<BFT, RT, RT>( SHARED(context), SHARED(HplusHalfSpace2), SHARED(HplusHalfSpace2), SHARED(HplusHalfSpace2), waveNumber1); BoundaryOperator<BFT, RT> dlp22_w1 = modifiedHelmholtz3dDoubleLayerBoundaryOperator<BFT, RT, RT>( SHARED(context), SHARED(HplusHalfSpace2), SHARED(HplusHalfSpace2), SHARED(HplusHalfSpace2), waveNumber1); BoundaryOperator<BFT, RT> id22 = identityOperator<BFT, RT>( SHARED(context), SHARED(HplusHalfSpace2), SHARED(HplusHalfSpace2), SHARED(HplusHalfSpace2)); // mesh2 x mesh2, wavenumber 2 BoundaryOperator<BFT, RT> slp22_w2 = modifiedHelmholtz3dSingleLayerBoundaryOperator<BFT, RT, RT>( SHARED(context), SHARED(HplusHalfSpace2), SHARED(HplusHalfSpace2), SHARED(HplusHalfSpace2), waveNumber2); BoundaryOperator<BFT, RT> dlp22_w2 = modifiedHelmholtz3dDoubleLayerBoundaryOperator<BFT, RT, RT>( SHARED(context), SHARED(HplusHalfSpace2), SHARED(HplusHalfSpace2), SHARED(HplusHalfSpace2), waveNumber2); // mesh1 x mesh2 BoundaryOperator<BFT, RT> slp12 = modifiedHelmholtz3dSingleLayerBoundaryOperator<BFT, RT, RT>( SHARED(context), SHARED(HplusHalfSpace2), SHARED(HplusHalfSpace1), SHARED(HplusHalfSpace1), waveNumber1); BoundaryOperator<BFT, RT> dlp12 = modifiedHelmholtz3dDoubleLayerBoundaryOperator<BFT, RT, RT>( SHARED(context), SHARED(HplusHalfSpace2), SHARED(HplusHalfSpace1), SHARED(HplusHalfSpace1), waveNumber1); // mesh2 x mesh1 BoundaryOperator<BFT, RT> slp21 = modifiedHelmholtz3dSingleLayerBoundaryOperator<BFT, RT, RT>( SHARED(context), SHARED(HplusHalfSpace1), SHARED(HplusHalfSpace2), SHARED(HplusHalfSpace2), waveNumber1); BoundaryOperator<BFT, RT> dlp21 = modifiedHelmholtz3dDoubleLayerBoundaryOperator<BFT, RT, RT>( SHARED(context), SHARED(HplusHalfSpace1), SHARED(HplusHalfSpace2), SHARED(HplusHalfSpace2), waveNumber1); BFT scale = 1.0/(2.0*alpha*kappa1); BoundaryOperator<BFT, RT> lhs_k11 = 0.5*id11 + dlp11 + scale*slp11; BoundaryOperator<BFT, RT> lhs_k12 = -1.0*dlp12; // sign flipped to accommodate normal direction BoundaryOperator<BFT, RT> lhs_k13 = -(1.0/kappa1)*slp12; BoundaryOperator<BFT, RT> lhs_k21 = dlp21 + scale*slp21; BoundaryOperator<BFT, RT> lhs_k22 = 0.5*id22 - dlp22_w1; // sign flipped to accommodate normal direction BoundaryOperator<BFT, RT> lhs_k23 = -(1.0/kappa1)*slp22_w1; // BoundaryOperator<BFT, RT> lhs_k31 -- empty BoundaryOperator<BFT, RT> lhs_k32 = 0.5*id22 + dlp22_w2; BoundaryOperator<BFT, RT> lhs_k33 = (1.0/kappa2) * slp22_w2; BlockedOperatorStructure<BFT, RT> structure; structure.setBlock(0, 0, lhs_k11); structure.setBlock(0, 1, lhs_k12); structure.setBlock(0, 2, lhs_k13); structure.setBlock(1, 0, lhs_k21); structure.setBlock(1, 1, lhs_k22); structure.setBlock(1, 2, lhs_k23); // structure.setBlock(2, 0, ...); -- empty structure.setBlock(2, 1, lhs_k32); structure.setBlock(2, 2, lhs_k33); BlockedBoundaryOperator<BFT, RT> blockedOp(structure); // Grid functions for the RHS // TODO: remove the necessity of creating "dummy" functions // corresponding to zero blocks. BoundaryOperator<BFT, RT> rhs1 = scale*slp11; BoundaryOperator<BFT, RT> rhs2 = scale*slp21; std::vector<GridFunction<BFT, RT> > blockedRhs(3); blockedRhs[0] = rhs1 * GridFunction<BFT, RT>( SHARED(context), SHARED(HplusHalfSpace1), SHARED(HplusHalfSpace1), //surfaceNormalIndependentFunction(NullFunctor())); surfaceNormalIndependentFunction(MyFunctor(waveNumber1))); blockedRhs[1] = rhs2 * GridFunction<BFT, RT>( SHARED(context), SHARED(HplusHalfSpace1), SHARED(HplusHalfSpace1), //surfaceNormalIndependentFunction(NullFunctor())); surfaceNormalIndependentFunction(MyFunctor(waveNumber1))); blockedRhs[2] = GridFunction<BFT, RT>( SHARED(context), SHARED(HplusHalfSpace2), SHARED(HplusHalfSpace2), //surfaceNormalIndependentFunction(MyFunctor(waveNumber2))); surfaceNormalIndependentFunction(NullFunctor())); // Initialize the solver const double solverTol = 1e-10; DefaultIterativeSolver<BFT, RT> solver(blockedOp); solver.initializeSolver(defaultGmresParameterList(solverTol)); // Solve BlockedSolution<BFT, RT> solution = solver.solve(blockedRhs); std::cout << solution.solverMessage() << std::endl; arma::Col<RT> solutionVectorBlock1 = solution.gridFunction(0).coefficients(); arma::Col<RT> solutionVectorBlock2 = solution.gridFunction(1).coefficients(); arma::Col<RT> solutionVectorBlock3 = solution.gridFunction(2).coefficients(); arma::diskio::save_raw_ascii(solutionVectorBlock1, "sol1.txt"); arma::diskio::save_raw_ascii(solutionVectorBlock2, "sol2.txt"); arma::diskio::save_raw_ascii(solutionVectorBlock3, "sol3.txt"); solution.gridFunction(0).exportToVtk(VtkWriter::VERTEX_DATA, "gf1", "gf1"); solution.gridFunction(1).exportToVtk(VtkWriter::VERTEX_DATA, "gf2", "gf2"); solution.gridFunction(2).exportToVtk(VtkWriter::VERTEX_DATA, "gf3", "gf3"); }
int main(int argc, char* argv[]) { // Load mesh if (argc != 2) { std::cout << "Solve a Dirichlet problem for the Laplace equation.\n" "Usage: " << argv[0] << " <mesh_file>" << std::endl; return 1; } shared_ptr<Grid> grid = loadTriangularMeshFromFile(argv[1]); //std::cout << grid->gridTopology() << std::endl; // Initialize the spaces PiecewiseLinearContinuousScalarSpace<BFT> HplusHalfSpace(grid); PiecewiseConstantScalarSpace<BFT> HminusHalfSpace(grid); // Define some default options. AssemblyOptions assemblyOptions; // We want to use ACA AcaOptions acaOptions; // Default parameters for ACA acaOptions.eps = 1e-5; assemblyOptions.switchToAcaMode(acaOptions); // Define the standard integration factory AccuracyOptions accuracyOptions; accuracyOptions.doubleRegular.setRelativeQuadratureOrder(1); NumericalQuadratureStrategy<BFT, RT> quadStrategy(accuracyOptions); Context<BFT, RT> context(make_shared_from_ref(quadStrategy), assemblyOptions); // We need the single layer, double layer, and the identity operator BoundaryOperator<BFT, RT> slpOp = laplace3dSingleLayerBoundaryOperator<BFT, RT >( make_shared_from_ref(context), make_shared_from_ref(HminusHalfSpace), make_shared_from_ref(HplusHalfSpace), make_shared_from_ref(HminusHalfSpace), "SLP"); BoundaryOperator<BFT, RT> dlpOp = laplace3dDoubleLayerBoundaryOperator<BFT, RT >( make_shared_from_ref(context), make_shared_from_ref(HplusHalfSpace), make_shared_from_ref(HplusHalfSpace), make_shared_from_ref(HminusHalfSpace), "DLP"); BoundaryOperator<BFT, RT> id = identityOperator<BFT, RT>( make_shared_from_ref(context), make_shared_from_ref(HplusHalfSpace), make_shared_from_ref(HplusHalfSpace), make_shared_from_ref(HminusHalfSpace), "I"); // Form the right-hand side sum BoundaryOperator<BFT, RT> rhsOp = -0.5 * id + dlpOp; // We also want a grid function GridFunction<BFT, RT> u( make_shared_from_ref(context), make_shared_from_ref(HplusHalfSpace), make_shared_from_ref(HplusHalfSpace), // is this the right choice? surfaceNormalIndependentFunction(MyFunctor())); // Assemble the rhs std::cout << "Assemble rhs" << std::endl; GridFunction<BFT, RT> rhs = rhsOp * u; // Initialize the solver std::cout << "Initialize solver" << std::endl; #ifdef WITH_TRILINOS DefaultIterativeSolver<BFT, RT> solver(slpOp,ConvergenceTestMode::TEST_CONVERGENCE_IN_DUAL_TO_RANGE); solver.initializeSolver(defaultGmresParameterList(1e-5)); Solution<BFT, RT> solution = solver.solve(rhs); std::cout << solution.solverMessage() << std::endl; #else DefaultDirectSolver<BFT, RT> solver(slp, rhs); solver.solve(); #endif // Extract the solution const GridFunction<BFT, RT>& solFun = solution.gridFunction(); // Write out as VTK solFun.exportToVtk(VtkWriter::CELL_DATA, "Neumann_data", "calculated_neumann_data_cell"); solFun.exportToVtk(VtkWriter::VERTEX_DATA, "Neumann_data", "calculated_neumann_data_vertex"); // Uncomment the block below if you are solving the problem on a sphere and // you want to compare the numerical and analytical solution. // arma::Col<RT> solutionCoefficients = solFun.coefficients(); // std::cout << solutionCoefficients << std::endl; // arma::Col<RT> deviation = solutionCoefficients - static_cast<RT>(-1.); // // % in Armadillo -> elementwise multiplication // RT stdDev = sqrt(arma::accu(deviation % deviation) / // static_cast<RT>(solutionCoefficients.n_rows)); // std::cout << "Standard deviation: " << stdDev << std::endl; }
int main(int argc, char* argv[]) { // Process command-line args if (argc < 7 || argc % 2 != 1) { std::cout << "Solve a Maxwell Dirichlet problem in an exterior domain.\n" << "Usage: " << argv[0] << " <mesh_file> <n_threads> <aca_eps> <solver_tol>" << " <singular_order_increment>" << " [<regular_order_increment_1> <min_relative_distance_1>]" << " [<regular_order_increment_2> <min_relative_distance_2>]" << " [...] <regular_order_increment_n>" << std::endl; return 1; } int maxThreadCount = atoi(argv[2]); double acaEps = atof(argv[3]); double solverTol = atof(argv[4]); int singOrderIncrement = atoi(argv[5]); if (acaEps > 1. || acaEps < 0.) { std::cout << "Invalid aca_eps: " << acaEps << std::endl; return 1; } if (solverTol > 1. || solverTol < 0.) { std::cout << "Invalid solver_tol: " << solverTol << std::endl; return 1; } AccuracyOptionsEx accuracyOptions; std::vector<double> maxNormDists; std::vector<int> orderIncrements; for (int i = 6; i < argc - 1; i += 2) { orderIncrements.push_back(atoi(argv[i])); maxNormDists.push_back(atof(argv[i + 1])); } orderIncrements.push_back(atoi(argv[argc - 1])); accuracyOptions.setDoubleRegular(maxNormDists, orderIncrements); accuracyOptions.setDoubleSingular(singOrderIncrement); accuracyOptions.setSingleRegular(2); // Load mesh GridParameters params; params.topology = GridParameters::TRIANGULAR; shared_ptr<Grid> grid = GridFactory::importGmshGrid(params, argv[1]); // Initialize the space RaviartThomas0VectorSpace<BFT> HdivSpace(grid); // Set assembly mode and options AssemblyOptions assemblyOptions; assemblyOptions.setMaxThreadCount(maxThreadCount); if (acaEps > 0.) { AcaOptions acaOptions; acaOptions.eps = acaEps; assemblyOptions.switchToAcaMode(acaOptions); } NumericalQuadratureStrategy<BFT, RT> quadStrategy(accuracyOptions); Context<BFT, RT> context(make_shared_from_ref(quadStrategy), assemblyOptions); // Construct operators BoundaryOperator<BFT, RT> slpOp = maxwell3dSingleLayerBoundaryOperator<BFT>( make_shared_from_ref(context), make_shared_from_ref(HdivSpace), make_shared_from_ref(HdivSpace), make_shared_from_ref(HdivSpace), k, "SLP"); BoundaryOperator<BFT, RT> dlpOp = maxwell3dDoubleLayerBoundaryOperator<BFT>( make_shared_from_ref(context), make_shared_from_ref(HdivSpace), make_shared_from_ref(HdivSpace), make_shared_from_ref(HdivSpace), k, "DLP"); BoundaryOperator<BFT, RT> idOp = maxwell3dIdentityOperator<BFT, RT>( make_shared_from_ref(context), make_shared_from_ref(HdivSpace), make_shared_from_ref(HdivSpace), make_shared_from_ref(HdivSpace), "Id"); // Construct a grid function representing the Dirichlet data GridFunction<BFT, RT> dirichletData( make_shared_from_ref(context), make_shared_from_ref(HdivSpace), make_shared_from_ref(HdivSpace), surfaceNormalDependentFunction(DirichletData())); dirichletData.exportToVtk(VtkWriter::CELL_DATA, "Dirichlet_data", "input_dirichlet_data_cell"); dirichletData.exportToVtk(VtkWriter::VERTEX_DATA, "Dirichlet_data", "input_dirichlet_data_vertex"); // Construct a grid function representing the right-hand side GridFunction<BFT, RT> rhs = -((0.5 * idOp + dlpOp) * dirichletData); // Solve the equation Solution<BFT, RT> solution; #ifdef WITH_AHMED if (solverTol > 0.) { DefaultIterativeSolver<BFT, RT> solver(slpOp); AcaApproximateLuInverse<RT> slpOpLu( DiscreteAcaBoundaryOperator<RT>::castToAca( *slpOp.weakForm()), /* LU factorisation accuracy */ 0.01); Preconditioner<RT> prec = discreteOperatorToPreconditioner<RT>( make_shared_from_ref(slpOpLu)); solver.initializeSolver(defaultGmresParameterList(solverTol, 10000), prec); solution = solver.solve(rhs); } else { DefaultDirectSolver<BFT, RT> solver(slpOp); solution = solver.solve(rhs); } #else // WITH_AHMED DefaultDirectSolver<BFT, RT> solver(slpOp); solution = solver.solve(rhs); #endif std::cout << solution.solverMessage() << std::endl; // Extract the solution const GridFunction<BFT, RT>& neumannData = solution.gridFunction(); neumannData.exportToVtk(VtkWriter::CELL_DATA, "Neumann_data", "calculated_neumann_data_cell"); neumannData.exportToVtk(VtkWriter::VERTEX_DATA, "Neumann_data", "calculated_neumann_data_vertex"); // Compare the solution against the analytical result GridFunction<BFT, RT> exactNeumannData( make_shared_from_ref(context), make_shared_from_ref(HdivSpace), make_shared_from_ref(HdivSpace), surfaceNormalDependentFunction(ExactNeumannData())); exactNeumannData.exportToVtk(VtkWriter::CELL_DATA, "Neumann_data", "exact_neumann_data_cell"); exactNeumannData.exportToVtk(VtkWriter::VERTEX_DATA, "Neumann_data", "exact_neumann_data_vertex"); EvaluationOptions evaluationOptions; CT absoluteError = L2NormOfDifference( neumannData, surfaceNormalDependentFunction(ExactNeumannData()), quadStrategy, evaluationOptions); CT exactSolNorm = L2NormOfDifference( 0. * neumannData, surfaceNormalDependentFunction(ExactNeumannData()), quadStrategy, evaluationOptions); std::cout << "Relative L^2 error: " << absoluteError / exactSolNorm << "\nAbsolute L^2 error: " << absoluteError << std::endl; // Evaluate the solution at a few points Maxwell3dSingleLayerPotentialOperator<BFT> slpPotOp(k); Maxwell3dDoubleLayerPotentialOperator<BFT> dlpPotOp(k); const int dimWorld = 3; const int pointCount = 3; arma::Mat<CT> points(dimWorld, pointCount * pointCount); for (int i = 0; i < pointCount; ++i) for (int j = 0; j < pointCount; ++j) { points(0, i * pointCount + j) = 3. + i / CT(pointCount - 1); points(1, i * pointCount + j) = 2. + j / CT(pointCount - 1); points(2, i * pointCount + j) = 0.5; } arma::Mat<RT> slpContrib = slpPotOp.evaluateAtPoints( neumannData, points, quadStrategy, evaluationOptions); arma::Mat<RT> dlpContrib = dlpPotOp.evaluateAtPoints( dirichletData, points, quadStrategy, evaluationOptions); arma::Mat<RT> values = -slpContrib - dlpContrib; // Evaluate the analytical solution at the same points ExactSolution exactSolution; arma::Mat<RT> exactValues(dimWorld, pointCount * pointCount); for (int i = 0; i < pointCount * pointCount; ++i) { arma::Col<RT> activeResultColumn = exactValues.unsafe_col(i); exactSolution.evaluate(points.unsafe_col(i), activeResultColumn); } // Compare the numerical and analytical solutions std::cout << "Numerical | analytical\n"; for (int i = 0; i < pointCount * pointCount; ++i) std::cout << values(0, i) << " " << values(1, i) << " " << values(2, i) << " | " << exactValues(0, i) << " " << exactValues(1, i) << " " << exactValues(2, i) << "\n"; }