C++ AssemblyOptions类代码示例

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));
}

    DefaultLocalAssemblerForIntegralOperatorsOnSurfacesManager(
            bool cacheSingularIntegrals)
    {
        // Create a Bempp grid
        shared_ptr<Grid> grid = createGrid();

        // These important thing is that the domain and dualToRange spaces are
        // different
        piecewiseConstantSpace = std::auto_ptr<PiecewiseConstantSpace>(
                    new PiecewiseConstantSpace(grid));
        piecewiseLinearSpace = std::auto_ptr<PiecewiseLinearSpace>(
                    new PiecewiseLinearSpace(grid));

        op = std::auto_ptr<Operator>(new Operator(
                                         make_shared_from_ref(*piecewiseConstantSpace),
                                         make_shared_from_ref(*piecewiseLinearSpace),
                                         make_shared_from_ref(*piecewiseLinearSpace),
                                         "SLP"));

        // Construct local assembler

        Fiber::AccuracyOptions options;
        options.doubleRegular.setRelativeQuadratureOrder(1);
        quadStrategy = std::auto_ptr<QuadratureStrategy>(new QuadratureStrategy);

        AssemblyOptions assemblyOptions;
        assemblyOptions.setVerbosityLevel(VerbosityLevel::LOW);
        assemblyOptions.enableSingularIntegralCaching(cacheSingularIntegrals);
        assembler = op->makeAssembler(*quadStrategy, assemblyOptions);
    }

BOOST_AUTO_TEST_CASE_TEMPLATE(L2Norm_works_for_constant_function_and_piecewise_constants, ResultType, result_types)
{
    typedef ResultType RT;
    typedef typename ScalarTraits<RT>::RealType BFT;
    typedef typename ScalarTraits<RT>::RealType CT;

    GridParameters params;
    params.topology = GridParameters::TRIANGULAR;
    shared_ptr<Grid> grid = GridFactory::importGmshGrid(
        params, "../../meshes/sphere-h-0.1.msh", false /* verbose */);

    shared_ptr<Space<BFT> > space(
        new PiecewiseConstantScalarSpace<BFT>(grid));

    AccuracyOptions accuracyOptions;
    shared_ptr<NumericalQuadratureStrategy<BFT, RT> > quadStrategy(
                new NumericalQuadratureStrategy<BFT, RT>(accuracyOptions));
    AssemblyOptions assemblyOptions;
    assemblyOptions.setVerbosityLevel(VerbosityLevel::LOW);
    shared_ptr<Context<BFT, RT> > context(
        new Context<BFT, RT>(quadStrategy, assemblyOptions));

    Bempp::GridFunction<BFT, RT> fun(context, space, space,
                surfaceNormalIndependentFunction(
                    ConstantFunction<RT>()));

    CT norm = fun.L2Norm();
    CT expectedNorm = sqrt(2. * 2. * 4. * M_PI);
    BOOST_CHECK_CLOSE(norm, expectedNorm, 1 /* percent */);
}

BOOST_AUTO_TEST_CASE_TEMPLATE(cubic_function_can_be_expanded_in_cubic_space, ResultType, result_types)
{
    typedef ResultType RT;
    typedef typename ScalarTraits<RT>::RealType BFT;
    typedef typename ScalarTraits<RT>::RealType CT;

    GridParameters params;
    params.topology = GridParameters::TRIANGULAR;
    shared_ptr<Grid> grid = GridFactory::importGmshGrid(
        params, "../../examples/meshes/sphere-h-0.2.msh", false /* verbose */);

    shared_ptr<Space<BFT> > space(
        new PiecewisePolynomialDiscontinuousScalarSpace<BFT>(grid, 3));

    AccuracyOptions accuracyOptions;
    accuracyOptions.singleRegular.setRelativeQuadratureOrder(2);
    shared_ptr<NumericalQuadratureStrategy<BFT, RT> > quadStrategy(
        new NumericalQuadratureStrategy<BFT, RT>(accuracyOptions));
    AssemblyOptions assemblyOptions;
    assemblyOptions.setVerbosityLevel(VerbosityLevel::LOW);
    shared_ptr<Context<BFT, RT> > context(
        new Context<BFT, RT>(quadStrategy, assemblyOptions));

    GridFunction<BFT, RT> function(
        context, space, space,
        surfaceNormalIndependentFunction(CubicFunction<RT>()));
    CT absoluteError, relativeError;
    estimateL2Error(
        function, surfaceNormalIndependentFunction(CubicFunction<RT>()),
        *quadStrategy, absoluteError, relativeError);
    BOOST_CHECK_SMALL(relativeError, 1000 * std::numeric_limits<CT>::epsilon() /* percent */);
}

inline bool shouldUseBlasInQuadrature(const AssemblyOptions& assemblyOptions,
                                      const Space<BasisFunctionType>& domain,
                                      const Space<BasisFunctionType>& dualToRange)
{
    return assemblyOptions.isBlasEnabledInQuadrature() == AssemblyOptions::YES ||
        (assemblyOptions.isBlasEnabledInQuadrature() == AssemblyOptions::AUTO &&
         (maximumShapesetOrder(domain) >= 2 || 
	  maximumShapesetOrder(dualToRange) >= 2));
}

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(interpolated_matches_noniterpolated,
                              BasisFunctionType, basis_function_types)
{
    typedef BasisFunctionType BFT;
    typedef typename Fiber::ScalarTraits<BFT>::ComplexType RT;
    typedef typename Fiber::ScalarTraits<BFT>::ComplexType KT;
    typedef typename Fiber::ScalarTraits<BFT>::RealType CT;

    GridParameters params;
    params.topology = GridParameters::TRIANGULAR;
    shared_ptr<Grid> grid = GridFactory::importGmshGrid(
                params, "meshes/two_disjoint_triangles.msh",
                false /* verbose */);

    PiecewiseLinearContinuousScalarSpace<BFT> pwiseLinears(grid);
    PiecewiseConstantScalarSpace<BFT> pwiseConstants(grid);

    AssemblyOptions assemblyOptions;
    assemblyOptions.setVerbosityLevel(VerbosityLevel::LOW);
    AccuracyOptions accuracyOptions;
    accuracyOptions.doubleRegular.setAbsoluteQuadratureOrder(5);
    accuracyOptions.doubleSingular.setAbsoluteQuadratureOrder(5);
    NumericalQuadratureStrategy<BFT, RT> quadStrategy(accuracyOptions);

    Context<BFT, RT> context(make_shared_from_ref(quadStrategy), assemblyOptions);

    const KT waveNumber(3.23, 0.31);

    BoundaryOperator<BFT, RT> opNoninterpolated =
            modifiedHelmholtz3dSingleLayerBoundaryOperator<BFT, KT, RT>(
                make_shared_from_ref(context),
                make_shared_from_ref(pwiseLinears),
                make_shared_from_ref(pwiseLinears),
                make_shared_from_ref(pwiseLinears),
                waveNumber,
                "", NO_SYMMETRY,
                false);
    BoundaryOperator<BFT, RT> opInterpolated =
            modifiedHelmholtz3dSingleLayerBoundaryOperator<BFT, KT, RT>(
                make_shared_from_ref(context),
                make_shared_from_ref(pwiseLinears),
                make_shared_from_ref(pwiseLinears),
                make_shared_from_ref(pwiseLinears),
                waveNumber,
                "", NO_SYMMETRY,
                true);

    arma::Mat<RT> matNoninterpolated = opNoninterpolated.weakForm()->asMatrix();
    arma::Mat<RT> matInterpolated = opInterpolated.weakForm()->asMatrix();

    const CT eps = std::numeric_limits<CT>::epsilon();
    BOOST_CHECK(check_arrays_are_close<RT>(
                    matNoninterpolated, matInterpolated, 100 * eps));
}

inline bool
shouldUseBlasInQuadrature(const AssemblyOptions &assemblyOptions,
                          const Space<BasisFunctionType> &domain,
                          const Space<BasisFunctionType> &dualToRange) {
// Disabled as BLAS quadrature causes crashes in the hypersingular operator for
// unknown reasons.
  return assemblyOptions.isBlasEnabledInQuadrature() == AssemblyOptions::YES ||
         (assemblyOptions.isBlasEnabledInQuadrature() ==
              AssemblyOptions::AUTO &&
          (maximumShapesetOrder(domain) >= 2 ||
           maximumShapesetOrder(dualToRange) >= 2));
}

void
AbstractBoundaryOperator<BasisFunctionType, ResultType>::
collectOptionsDependentDataForAssemblerConstruction(
        const AssemblyOptions& options,
        const shared_ptr<Fiber::RawGridGeometry<CoordinateType> >& testRawGeometry,
        const shared_ptr<Fiber::RawGridGeometry<CoordinateType> >& trialRawGeometry,
        shared_ptr<Fiber::OpenClHandler>& openClHandler,
        bool& cacheSingularIntegrals) const
{
    typedef LocalAssemblerConstructionHelper Helper;

    Helper::makeOpenClHandler(options.parallelizationOptions().openClOptions(),
                              testRawGeometry, trialRawGeometry, openClHandler);
    cacheSingularIntegrals = options.isSingularIntegralCachingEnabled();
}

std::unique_ptr<typename ElementaryLocalOperator<BasisFunctionType,
                                                 ResultType>::LocalAssembler>
ElementaryLocalOperator<BasisFunctionType, ResultType>::makeAssembler(
    const QuadratureStrategy &quadStrategy,
    const AssemblyOptions &options) const {
  typedef Fiber::RawGridGeometry<CoordinateType> RawGridGeometry;
  typedef std::vector<const Fiber::Shapeset<BasisFunctionType> *>
  ShapesetPtrVector;

  const bool verbose = (options.verbosityLevel() >= VerbosityLevel::DEFAULT);

  shared_ptr<RawGridGeometry> testRawGeometry, trialRawGeometry;
  shared_ptr<GeometryFactory> testGeometryFactory, trialGeometryFactory;
  shared_ptr<Fiber::OpenClHandler> openClHandler;
  shared_ptr<ShapesetPtrVector> testShapesets, trialShapesets;
  bool cacheSingularIntegrals;

  if (verbose)
    std::cout << "Collecting data for assembler construction..." << std::endl;
  this->collectDataForAssemblerConstruction(
      options, testRawGeometry, trialRawGeometry, testGeometryFactory,
      trialGeometryFactory, testShapesets, trialShapesets, openClHandler,
      cacheSingularIntegrals);
  if (verbose)
    std::cout << "Data collection finished." << std::endl;
  assert(testRawGeometry == trialRawGeometry);
  assert(testGeometryFactory == trialGeometryFactory);

  return quadStrategy.makeAssemblerForLocalOperators(
      testGeometryFactory, testRawGeometry, testShapesets, trialShapesets,
      make_shared_from_ref(testTransformations()),
      make_shared_from_ref(trialTransformations()),
      make_shared_from_ref(integral()), openClHandler);
}

std::pair<
shared_ptr<typename HypersingularIntegralOperator<
BasisFunctionType, KernelType, ResultType>::LocalAssembler>,
shared_ptr<typename HypersingularIntegralOperator<
BasisFunctionType, KernelType, ResultType>::LocalAssembler>
>
HypersingularIntegralOperator<BasisFunctionType, KernelType, ResultType>::makeAssemblers(
        const QuadratureStrategy& quadStrategy,
        const AssemblyOptions& options) const
{
    typedef Fiber::RawGridGeometry<CoordinateType> RawGridGeometry;
    typedef std::vector<const Fiber::Shapeset<BasisFunctionType>*> ShapesetPtrVector;

    const bool verbose = (options.verbosityLevel() >= VerbosityLevel::DEFAULT);

    shared_ptr<RawGridGeometry> testRawGeometry, trialRawGeometry;
    shared_ptr<GeometryFactory> testGeometryFactory, trialGeometryFactory;
    shared_ptr<Fiber::OpenClHandler> openClHandler;
    shared_ptr<ShapesetPtrVector> testShapesets, trialShapesets;
    bool cacheSingularIntegrals;

    if (verbose)
        std::cout << "Collecting data for assembler construction..." << std::endl;
       this->collectDataForAssemblerConstruction(options,
                                        testRawGeometry, trialRawGeometry,
                                        testGeometryFactory, trialGeometryFactory,
                                        testShapesets, trialShapesets,
                                        openClHandler, cacheSingularIntegrals);
    if (verbose)
        std::cout << "Data collection finished." << std::endl;

    bool makeSeparateOffDiagonalAssembler =
        options.assemblyMode() == AssemblyOptions::ACA &&
        options.acaOptions().mode == AcaOptions::HYBRID_ASSEMBLY;

    return reallyMakeAssemblers(quadStrategy,
                                testGeometryFactory, trialGeometryFactory,
                                testRawGeometry, trialRawGeometry,
                                testShapesets, trialShapesets, openClHandler,
                                options.parallelizationOptions(),
                                options.verbosityLevel(),
                                cacheSingularIntegrals,
                                makeSeparateOffDiagonalAssembler);
}

    DefaultLocalAssemblerForIntegralOperatorsOnSurfacesManager(
            bool cacheSingularIntegrals)
    {
        // Create a Bempp grid
        shared_ptr<Grid> grid = createGrid();

        // Create context
        Fiber::AccuracyOptions options;
        options.doubleRegular.setRelativeQuadratureOrder(1);
        quadStrategy.reset(new QuadratureStrategy);

        AssemblyOptions assemblyOptions;
        assemblyOptions.setVerbosityLevel(VerbosityLevel::LOW);
        assemblyOptions.enableSingularIntegralCaching(cacheSingularIntegrals);
        Context<BFT, RT> context(quadStrategy, assemblyOptions);

        // These important thing is that the domain and dualToRange spaces are
        // different
        piecewiseConstantSpace.reset(new PiecewiseConstantSpace(grid));
        piecewiseLinearSpace.reset(new PiecewiseLinearSpace(grid));

        bop = laplace3dSingleLayerBoundaryOperator<BFT, RT>(
                    make_shared_from_ref(context),
                    piecewiseConstantSpace,
                    piecewiseLinearSpace,
                    piecewiseLinearSpace,
                    "SLP");
        const Operator& op = static_cast<const Operator&>(*bop.abstractOperator());

        // This would be more elegant than the above, but it doesn't
        // work on Mac because of a problem with RTTI across
        // shared-library boundaries.

        // op = boost::dynamic_pointer_cast<const Operator>(bop.abstractOperator());

        // Construct local assembler

        assembler = op.makeAssembler(*quadStrategy, assemblyOptions);
    }

std::unique_ptr<DiscreteBoundaryOperator<ResultType>>
ElementaryLocalOperator<BasisFunctionType, ResultType>::
    assembleWeakFormInSparseMode(LocalAssembler &assembler,
                                 const AssemblyOptions &options) const {
#ifdef WITH_TRILINOS
  if (boost::is_complex<BasisFunctionType>::value)
    throw std::runtime_error(
        "ElementaryLocalOperator::assembleWeakFormInSparseMode(): "
        "sparse-mode assembly of identity operators for "
        "complex-valued basis functions is not supported yet");

  const Space<BasisFunctionType> &testSpace = *this->dualToRange();
  const Space<BasisFunctionType> &trialSpace = *this->domain();

  // Fill local submatrices
  const GridView &view = testSpace.gridView();
  const size_t elementCount = view.entityCount(0);
  std::vector<int> elementIndices(elementCount);
  for (size_t i = 0; i < elementCount; ++i)
    elementIndices[i] = i;
  std::vector<arma::Mat<ResultType>> localResult;
  assembler.evaluateLocalWeakForms(elementIndices, localResult);

  // Global DOF indices corresponding to local DOFs on elements
  std::vector<std::vector<GlobalDofIndex>> testGdofs(elementCount);
  std::vector<std::vector<GlobalDofIndex>> trialGdofs(elementCount);
  std::vector<std::vector<BasisFunctionType>> testLdofWeights(elementCount);
  std::vector<std::vector<BasisFunctionType>> trialLdofWeights(elementCount);
  gatherGlobalDofs(testSpace, trialSpace, testGdofs, trialGdofs,
                   testLdofWeights, trialLdofWeights);

  // Multiply matrix entries by DOF weights
  for (size_t e = 0; e < elementCount; ++e)
    for (size_t trialDof = 0; trialDof < trialGdofs[e].size(); ++trialDof)
      for (size_t testDof = 0; testDof < testGdofs[e].size(); ++testDof)
        localResult[e](testDof, trialDof) *=
            conj(testLdofWeights[e][testDof]) * trialLdofWeights[e][trialDof];

  // Estimate number of entries in each row

  //    This will be useful when we begin to use MPI
  //    // Get global DOF indices for which this process is responsible
  //    const int testGlobalDofCount = testSpace.globalDofCount();
  //    Epetra_Map rowMap(testGlobalDofCount, 0 /* index-base */, comm);
  //    std::vector<int> myTestGlobalDofs(rowMap.MyGlobalElements(),
  //                                      rowMap.MyGlobalElements() +
  //                                      rowMap.NumMyElements());
  //    const int myTestGlobalDofCount = myTestGlobalDofs.size();

  const int testGlobalDofCount = testSpace.globalDofCount();
  const int trialGlobalDofCount = trialSpace.globalDofCount();
  arma::Col<int> nonzeroEntryCountEstimates(testGlobalDofCount);
  nonzeroEntryCountEstimates.fill(0);

  // Upper estimate for the number of global trial DOFs coupled to a given
  // global test DOF: sum of the local trial DOF counts for each element that
  // contributes to the global test DOF in question
  for (size_t e = 0; e < elementCount; ++e)
    for (size_t testLdof = 0; testLdof < testGdofs[e].size(); ++testLdof) {
      int testGdof = testGdofs[e][testLdof];
      if (testGdof >= 0)
        nonzeroEntryCountEstimates(testGdof) += trialGdofs[e].size();
    }

  Epetra_SerialComm comm; // To be replaced once we begin to use MPI
  Epetra_LocalMap rowMap(testGlobalDofCount, 0 /* index_base */, comm);
  Epetra_LocalMap colMap(trialGlobalDofCount, 0 /* index_base */, comm);
  shared_ptr<Epetra_FECrsMatrix> result =
      boost::make_shared<Epetra_FECrsMatrix>(
          Copy, rowMap, colMap, nonzeroEntryCountEstimates.memptr());

  // TODO: make each process responsible for a subset of elements
  // Find maximum number of local dofs per element
  size_t maxLdofCount = 0;
  for (size_t e = 0; e < elementCount; ++e)
    maxLdofCount =
        std::max(maxLdofCount, testGdofs[e].size() * trialGdofs[e].size());

  // Initialise sparse matrix with zeros at required positions
  arma::Col<double> zeros(maxLdofCount);
  zeros.fill(0.);
  for (size_t e = 0; e < elementCount; ++e)
    result->InsertGlobalValues(testGdofs[e].size(), &testGdofs[e][0],
                               trialGdofs[e].size(), &trialGdofs[e][0],
                               zeros.memptr());
  // Add contributions from individual elements
  for (size_t e = 0; e < elementCount; ++e)
    epetraSumIntoGlobalValues(*result, testGdofs[e], trialGdofs[e],
                              localResult[e]);
  result->GlobalAssemble();

  // If assembly mode is equal to ACA and we have AHMED,
  // construct the block cluster tree. Otherwise leave it uninitialized.
  typedef ClusterConstructionHelper<BasisFunctionType> CCH;
  typedef AhmedDofWrapper<CoordinateType> AhmedDofType;
  typedef ExtendedBemCluster<AhmedDofType> AhmedBemCluster;
  typedef bbxbemblcluster<AhmedDofType, AhmedDofType> AhmedBemBlcluster;

  shared_ptr<AhmedBemBlcluster> blockCluster;
  shared_ptr<IndexPermutation> test_o2pPermutation, test_p2oPermutation;
//.........这里部分代码省略.........

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
//.........这里部分代码省略.........

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
//.........这里部分代码省略.........