lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF > Class Template Reference

A MeshFunction representing an element from a ScalarFESpace (e.g. solution of BVP) More...

#include <lf/fe/fe.h>

Public Types
using	Scalar = decltype(SCALAR_FE(0) * SCALAR_COEFF(0))

Public Member Functions
	MeshFunctionFE (std::shared_ptr< const ScalarFESpace< SCALAR_FE > > fe_space, Eigen::Matrix< SCALAR_COEFF, Eigen::Dynamic, 1 > coeff_vector)
	Create a new MeshFunctionFE from a ScalarFESpace and a coefficient vector.
std::vector< Scalar >	operator() (const lf::mesh::Entity &e, const Eigen::MatrixXd &local) const
	Evaluate the mesh function on a MeshEntity.
std::shared_ptr< const mesh::Mesh >	getMesh () const
	Convenience method to retrieve the underlying mesh.
std::shared_ptr< const ScalarFESpace< SCALAR_FE > >	getFESpace () const
	Convenience method to retrieve the finite element space in which the mesh function lives.

Private Attributes
std::shared_ptr< const ScalarFESpace< SCALAR_FE > >	fe_space_
Eigen::Matrix< SCALAR_COEFF, Eigen::Dynamic, 1 >	dof_vector_

Detailed Description

template<class SCALAR_FE, class SCALAR_COEFF>
class lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >

A MeshFunction representing an element from a ScalarFESpace (e.g. solution of BVP)

Template Parameters

SCALAR_FE	The scalar type of the finite element basis functions.
SCALAR_COEFF	The scalar type of the coefficient vector

The MeshFunctionFE takes essentially two parameters:

• A ScalarFESpace which defines the space of all approximation functions.
• A Coefficient Vector which defines what element should be picked from the FeSpace. This is a simple Eigen::Vector which defines the coefficient in front of every basis function of the FeSpace (same ordering).

Note

A MeshFunctionFE can be evaluated on entities of all codimensions. The mesh function will simply use the ScalarReferenceFiniteElement from the feSpace.

Use case

double computeL2ErrorNorm(
    std::shared_ptr<const lf::uscalfe::UniformScalarFESpace<double>> fe_space_p,
    const Eigen::VectorXd& mu) {
  // Reference to underlying mesh
  const lf::mesh::Mesh& mesh{*(fe_space_p->Mesh())};
  // Lambda function providing the "exact solution"
  auto u = [](Eigen::Vector2d x) -> double {
    return std::log(x[0] * x[0] + x[1] + 1.0);
  };
  // Has to be wrapped into a mesh function for error computation
  lf::mesh::utils::MeshFunctionGlobal mf_u{u};
  // create mesh functions representing solution
  auto mf_sol = lf::fe::MeshFunctionFE<double, double>(fe_space_p, mu);
  // compute errors with 10-th order quadrature rules
  double L2err_2 =  // NOLINT
      std::sqrt(IntegrateMeshFunction(mesh, squaredNorm(mf_sol - mf_u), 2));
  return std::sqrt(L2err_2);
}

Definition at line 44 of file mesh_function_fe.h.

Member Typedef Documentation

Scalar

template<class SCALAR_FE , class SCALAR_COEFF >

using lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >::Scalar = decltype(SCALAR_FE(0) * SCALAR_COEFF(0))

Definition at line 48 of file mesh_function_fe.h.

Constructor & Destructor Documentation

MeshFunctionFE()

template<class SCALAR_FE , class SCALAR_COEFF >

lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >::MeshFunctionFE ( std::shared_ptr< const ScalarFESpace< SCALAR_FE > > fe_space, Eigen::Matrix< SCALAR_COEFF, Eigen::Dynamic, 1 > coeff_vector )

inline

Create a new MeshFunctionFE from a ScalarFESpace and a coefficient vector.

Parameters

fe_space	the approximation space in which the function lies.
coeff_vector	Defines the coefficients in front of the basis functions of fe_space

Warning

This constructor just takes a reference to the vector of basis expansion coefficients. Thus, this vector has to be "kept alive" as long as the mesh function exists.

Definition at line 61 of file mesh_function_fe.h.

Member Function Documentation

getFESpace()

template<class SCALAR_FE , class SCALAR_COEFF >

std::shared_ptr< const ScalarFESpace< SCALAR_FE > > lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >::getFESpace ( ) const

inline

Convenience method to retrieve the finite element space in which the mesh function lives.

Returns

shared_ptr to ScalarFESpace in which the mesh function lives.

Definition at line 107 of file mesh_function_fe.h.

References lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >::fe_space_.

getMesh()

template<class SCALAR_FE , class SCALAR_COEFF >

std::shared_ptr< const mesh::Mesh > lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >::getMesh ( ) const

inline

Convenience method to retrieve the underlying mesh.

Returns

The mesh on which this mesh function is defined.

Definition at line 97 of file mesh_function_fe.h.

References lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >::fe_space_.

operator()()

template<class SCALAR_FE , class SCALAR_COEFF >

std::vector< Scalar > lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >::operator() ( const lf::mesh::Entity & e, const Eigen::MatrixXd & local ) const

inline

Evaluate the mesh function on a MeshEntity.

Parameters

e	the relevant mesh entity
local	reference coordinates of evalation points passed in the columns of a matrix

Returns

values of the function at evaluation points

Definition at line 72 of file mesh_function_fe.h.

References lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >::dof_vector_, and lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >::fe_space_.

Member Data Documentation

dof_vector_

template<class SCALAR_FE , class SCALAR_COEFF >

Eigen::Matrix<SCALAR_COEFF, Eigen::Dynamic, 1> lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >::dof_vector_

private

Definition at line 114 of file mesh_function_fe.h.

Referenced by lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >::operator()().

fe_space_

template<class SCALAR_FE , class SCALAR_COEFF >

std::shared_ptr<const ScalarFESpace<SCALAR_FE> > lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >::fe_space_

private

Definition at line 113 of file mesh_function_fe.h.

Referenced by lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >::getFESpace(), lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >::getMesh(), and lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >::operator()().

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

• /__w/lehrfempp/lehrfempp/lib/lf/fe/mesh_function_fe.h