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));
}
Пример #4
0
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';
}
Пример #5
0
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");
}
Пример #6
0
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;


}
Пример #7
0
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";
}