Local computation of general element (load) vector for scalar finite elements; volume contributions only. More...

#include <lf/fe/fe.h>

Public Types
using	scalar_t

using	ElemVec = Eigen::Matrix<scalar_t, Eigen::Dynamic, 1>

Public Member Functions
	ScalarLoadElementVectorProvider (std::shared_ptr< const ScalarFESpace< SCALAR > > fe_space, MESH_FUNCTION f)
	Constructor, performs precomputations.

bool	isActive (const lf::mesh::Entity &) const
	all cells are active

ElemVec	Eval (const lf::mesh::Entity &cell) const

	~ScalarLoadElementVectorProvider ()=default

standard constructors
	ScalarLoadElementVectorProvider (const ScalarLoadElementVectorProvider &)=delete

	ScalarLoadElementVectorProvider (ScalarLoadElementVectorProvider &&) noexcept=default

ScalarLoadElementVectorProvider &	operator= (const ScalarLoadElementVectorProvider &)=delete

ScalarLoadElementVectorProvider &	operator= (ScalarLoadElementVectorProvider &&)=delete

Private Attributes
MESH_FUNCTION	f_
	An object providing the source function.

std::shared_ptr< const ScalarFESpace< SCALAR > >	fe_space_

quad::QuadRuleCache	qr_cache_

Detailed Description

template<base::Scalar SCALAR, mesh::utils::MeshFunction MESH_FUNCTION>
class lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >

Local computation of general element (load) vector for scalar finite elements; volume contributions only.

Template Parameters

SCALAR	underlying scalar type of the ScalarFESpace, usually double or complex<double>
MESH_FUNCTION	MeshFunction which defines the source function \( f \)

The underlying local linear form is

\[ v \mapsto \int_K f(\mathbf{x})\,\overline{v(\mathbf{x})}\,\mathrm{d}\mathbf{x}\;, \]

where \(f\) is supposed to be a locally continuous source function.

Computation is based on a quadrature rules supplied by the LehrFEM++ lf::quad::QuadRule module.

This class complies with the requirements for the template parameter ELEM_VEC_COMP of the function assemble::AssembleVectorLocally().

Example usage

The following code snippet computes the solution of the BVP

\begin{align} - \Delta u &= 1 && \text{on }\Omega := [0,1]^2 \\ u &= 0 && \text{on }\partial \Omega \end{align}

  // Get a mesh
  auto mesh_p = lf::mesh::test_utils::GenerateHybrid2DTestMesh();
  // Create HierarchicalFESpace with uniform degree 5.
  const unsigned degree = 5;
  const auto fe_space =
      std::make_shared<lf::fe::HierarchicScalarFESpace<double>>(mesh_p, degree);
 
  // define diffusion coefficient
  const lf::mesh::utils::MeshFunctionConstant mf_alpha(1);
  // define rhs load
  auto mf_load = lf::mesh::utils::MeshFunctionConstant(1.);
 
  // Assemble the system matrix and right hand side
  Eigen::VectorXd rhs = Eigen::VectorXd::Zero(fe_space->LocGlobMap().NumDofs());
  const assemble::DofHandler &dofh = fe_space->LocGlobMap();
  assemble::COOMatrix<double> A_COO(dofh.NumDofs(), dofh.NumDofs());
 
  DiffusionElementMatrixProvider element_matrix_provider(fe_space, mf_alpha);
  AssembleMatrixLocally(0, dofh, dofh, element_matrix_provider, A_COO);
  ScalarLoadElementVectorProvider element_vector_provider(fe_space, mf_load);
  AssembleVectorLocally(0, dofh, element_vector_provider, rhs);
 
  // Enforce zero dirichlet boundary conditions
 
  const auto boundary = lf::mesh::utils::flagEntitiesOnBoundary(mesh_p);
  const auto selector = [&](unsigned int idx) -> std::pair<bool, double> {
    const auto &entity = dofh.Entity(idx);
    return {entity.Codim() > 0 && boundary(entity), 0};
  };
  FixFlaggedSolutionComponents(selector, A_COO, rhs);
 
  // Solve the LSE using the cholesky decomposition
  Eigen::SparseMatrix<double> A = A_COO.makeSparse();
  Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>> solver(A);
  const Eigen::VectorXd solution = solver.solve(rhs);
 
  // visualize the solution:
  io::VtkWriter vtk(mesh_p, "solution.vtk", 0, 5);
  vtk.WritePointData("solution", MeshFunctionFE(fe_space, solution));

Definition at line 569 of file loc_comp_ellbvp.h.

Member Typedef Documentation

◆ ElemVec

template<base::Scalar SCALAR, mesh::utils::MeshFunction MESH_FUNCTION>

using lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::ElemVec = Eigen::Matrix<scalar_t, Eigen::Dynamic, 1>

Definition at line 575 of file loc_comp_ellbvp.h.

◆ scalar_t

template<base::Scalar SCALAR, mesh::utils::MeshFunction MESH_FUNCTION>

using lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::scalar_t

Initial value:

 
      decltype(static_cast<SCALAR>(0) *
               static_cast<mesh::utils::MeshFunctionReturnType<MESH_FUNCTION>>(
                   0))

Definition at line 571 of file loc_comp_ellbvp.h.

Constructor & Destructor Documentation

◆ ScalarLoadElementVectorProvider() [1/3]

template<base::Scalar SCALAR, mesh::utils::MeshFunction MESH_FUNCTION>

lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::ScalarLoadElementVectorProvider ( const ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION > & )

delete

◆ ScalarLoadElementVectorProvider() [2/3]

template<base::Scalar SCALAR, mesh::utils::MeshFunction MESH_FUNCTION>

lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::ScalarLoadElementVectorProvider ( ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION > && )

defaultnoexcept

◆ ScalarLoadElementVectorProvider() [3/3]

template<base::Scalar SCALAR, mesh::utils::MeshFunction MESH_FUNCTION>

lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::ScalarLoadElementVectorProvider	(	std::shared_ptr< const ScalarFESpace< SCALAR > >	fe_space,
		MESH_FUNCTION	f )

Constructor, performs precomputations.

Parameters

fe_space	specification of local shape functions
f	functor object for source function

Uses quadrature rule of double the degree of exactness compared to the degree of the finite element space.

Definition at line 634 of file loc_comp_ellbvp.h.

◆ ~ScalarLoadElementVectorProvider()

template<base::Scalar SCALAR, mesh::utils::MeshFunction MESH_FUNCTION>

lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::~ScalarLoadElementVectorProvider ( )

default

Member Function Documentation

◆ Eval()

template<base::Scalar SCALAR, mesh::utils::MeshFunction MESH_FUNCTION>

ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::ElemVec lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::Eval ( const lf::mesh::Entity & cell ) const

Definition at line 644 of file loc_comp_ellbvp.h.

References lf::geometry::Geometry::DimLocal(), lf::mesh::Entity::Geometry(), lf::geometry::Geometry::Global(), lf::geometry::Geometry::IntegrationElement(), lf::base::RefEl::NodeCoords(), lf::quad::QuadRule::NumPoints(), lf::quad::QuadRule::Points(), lf::mesh::Entity::RefEl(), lf::fe::ScalarLoadElementVectorProviderLogger(), and lf::quad::QuadRule::Weights().

◆ isActive()

template<base::Scalar SCALAR, mesh::utils::MeshFunction MESH_FUNCTION>

bool lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::isActive ( const lf::mesh::Entity & ) const

inline

all cells are active

Definition at line 600 of file loc_comp_ellbvp.h.

◆ operator=() [1/2]

template<base::Scalar SCALAR, mesh::utils::MeshFunction MESH_FUNCTION>

ScalarLoadElementVectorProvider & lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::operator= ( const ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION > & )

delete

◆ operator=() [2/2]

template<base::Scalar SCALAR, mesh::utils::MeshFunction MESH_FUNCTION>

ScalarLoadElementVectorProvider & lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::operator= ( ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION > && )

delete

Member Data Documentation

◆ f_

template<base::Scalar SCALAR, mesh::utils::MeshFunction MESH_FUNCTION>

MESH_FUNCTION lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::f_

private

An object providing the source function.

Definition at line 614 of file loc_comp_ellbvp.h.

◆ fe_space_

template<base::Scalar SCALAR, mesh::utils::MeshFunction MESH_FUNCTION>

std::shared_ptr<const ScalarFESpace<SCALAR> > lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::fe_space_

private

Definition at line 616 of file loc_comp_ellbvp.h.

◆ qr_cache_

template<base::Scalar SCALAR, mesh::utils::MeshFunction MESH_FUNCTION>

quad::QuadRuleCache lf::fe::ScalarLoadElementVectorProvider< SCALAR, MESH_FUNCTION >::qr_cache_

private

Definition at line 618 of file loc_comp_ellbvp.h.

The documentation for this class was generated from the following file:

/__w/lehrfempp/lehrfempp/lib/lf/fe/loc_comp_ellbvp.h

Public Types

Public Member Functions

Private Attributes

Detailed Description

Example usage

Member Typedef Documentation

◆ ElemVec

◆ scalar_t

Constructor & Destructor Documentation

◆ ScalarLoadElementVectorProvider() [1/3]

◆ ScalarLoadElementVectorProvider() [2/3]

◆ ScalarLoadElementVectorProvider() [3/3]

◆ ~ScalarLoadElementVectorProvider()

Member Function Documentation

◆ Eval()

◆ isActive()

◆ operator=() [1/2]

◆ operator=() [2/2]

Member Data Documentation

◆ f_

◆ fe_space_

◆ qr_cache_