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));
}
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(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 */);
}
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(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));
}
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);
}
BOOST_AUTO_TEST_CASE_TEMPLATE(works, BasisFunctionType, basis_function_types)
{
typedef BasisFunctionType BFT;
typedef typename Fiber::ScalarTraits<BFT>::ComplexType RT;
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 RT waveNumber(1.23, 0.31);
BoundaryOperator<BFT, RT> slpOpConstants = Bempp::helmholtz3dSingleLayerBoundaryOperator<BFT>(
make_shared_from_ref(context),
make_shared_from_ref(pwiseConstants),
make_shared_from_ref(pwiseConstants),
make_shared_from_ref(pwiseConstants),
waveNumber);
BoundaryOperator<BFT, RT> slpOpLinears = helmholtz3dSingleLayerBoundaryOperator<BFT>(
make_shared_from_ref(context),
make_shared_from_ref(pwiseLinears),
make_shared_from_ref(pwiseLinears),
make_shared_from_ref(pwiseLinears),
waveNumber);
BoundaryOperator<BFT, RT> hypOp = helmholtz3dHypersingularBoundaryOperator<BFT>(
make_shared_from_ref(context),
make_shared_from_ref(pwiseLinears),
make_shared_from_ref(pwiseLinears),
make_shared_from_ref(pwiseLinears),
waveNumber);
// Get the matrix repr. of the hypersingular operator
arma::Mat<RT> hypMat = hypOp.weakForm()->asMatrix();
// Construct the expected hypersingular operator matrix. For this, we need:
// * the surface curls of all basis functions (which are constant)
typedef Fiber::SurfaceCurl3dElementaryFunctor<CT> ElementaryFunctor;
typedef Fiber::ElementaryBasisTransformationFunctorWrapper<ElementaryFunctor> Functor;
Functor functor;
size_t basisDeps = 0, geomDeps = 0;
functor.addDependencies(basisDeps, geomDeps);
arma::Mat<CT> points(2, 1);
points.fill(0.);
typedef Fiber::PiecewiseLinearContinuousScalarBasis<3, BFT> Basis;
Basis basis;
Fiber::BasisData<BFT> basisData;
basis.evaluate(basisDeps, points, Fiber::ALL_DOFS, basisData);
Fiber::GeometricalData<CT> geomData[2];
std::unique_ptr<GridView> view = grid->leafView();
std::unique_ptr<EntityIterator<0> > it = view->entityIterator<0>();
it->entity().geometry().getData(geomDeps, points, geomData[0]);
it->next();
it->entity().geometry().getData(geomDeps, points, geomData[1]);
Fiber::DefaultCollectionOfBasisTransformations<Functor> transformations(functor);
Fiber::CollectionOf3dArrays<BFT> surfaceCurl[2];
transformations.evaluate(basisData, geomData[0], surfaceCurl[0]);
transformations.evaluate(basisData, geomData[1], surfaceCurl[1]);
// * the single-layer potential matrix for constant basis functions
arma::Mat<RT> slpMatConstants = slpOpConstants.weakForm()->asMatrix();
// * the single-layer potential matrix for linear basis functions
arma::Mat<RT> slpMatLinears = slpOpLinears.weakForm()->asMatrix();
arma::Mat<RT> expectedHypMat(6, 6);
for (size_t testElement = 0; testElement < 2; ++testElement)
for (size_t trialElement = 0; trialElement < 2; ++trialElement)
for (size_t r = 0; r < 3; ++r)
for (size_t c = 0; c < 3; ++c) {
RT curlMultiplier = 0.;
for (size_t dim = 0; dim < 3; ++dim)
curlMultiplier += surfaceCurl[testElement][0](dim, r, 0) *
surfaceCurl[trialElement][0](dim, c, 0);
RT valueMultiplier = 0.;
for (size_t dim = 0; dim < 3; ++dim)
valueMultiplier += geomData[testElement].normals(dim, 0) *
geomData[trialElement].normals(dim, 0);
expectedHypMat(3 * testElement + r, 3 * trialElement + c) =
curlMultiplier * slpMatConstants(testElement, trialElement) -
waveNumber * waveNumber * valueMultiplier *
slpMatLinears(3 * testElement + r, 3 * trialElement + c);
}
BOOST_CHECK(check_arrays_are_close<RT>(expectedHypMat, hypMat, 1e-6));
}