A MeshFunction representing the gradient of a function from a scalar finite element space (e.g. gradient of a solution of BVP). More...

#include <lf/fe/fe.h>

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

Public Member Functions
	MeshFunctionGradFE (std::shared_ptr< const ScalarFESpace< SCALAR_FE > > fe_space, Eigen::Matrix< SCALAR_COEFF, Eigen::Dynamic, 1 > dof_vector)
	Create a new MeshFunctionGradFE from a ScalarFESpace and a coefficient vector.

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 to which the original function belongs (i.e. before taking the gradient)

std::vector< Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > >	operator() (const lf::mesh::Entity &e, const Eigen::MatrixXd &local) const
	Evaluate the mesh function on a MeshEntity.

Private Attributes
std::shared_ptr< const ScalarFESpace< SCALAR_FE > >	fe_space_
	Pointer to underlying finite element space.

Eigen::Matrix< SCALAR_COEFF, Eigen::Dynamic, 1 >	dof_vector_
	Reference to basis expansion coefficient vector for finite-element function

Detailed Description

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

A MeshFunction representing the gradient of a function from a scalar finite element space (e.g. gradient of a 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 MeshFunctionGradFE takes essentially two parameters:

A ScalarFESpace which defines the space of all approximation functions. This should be a finite element space of globally continuous functions. Otherwise the evaluation for non-cell entities is not possible.
A Coefficient Vector which defines what element should be picked from the FeSpace. This is a simple Eigen::Vector which defines the coefficient for every basis function of the FeSpace (same ordering).

Note: A MeshFunctionGradFE can be evaluated on entities of all codimensions except for points.; The gradient that is returned by this mesh function is w.r.t. to the global coordinate system of the mesh, i.e. the gradients of the shape function are multiplied by Geometry::JacobianInverseGramian(). Hence, what is returned is a "tangential gradient". For instance, if the evaluation operator is invoked for an edge of a 2D mesh, the gradient of the finite element function in the direction of that edge is returned. If the evaluation is requested for a (curved) triangle in 3D, then a gradient with 3 components is retrurned, which represents the tangential gradient of the finite element function in global 3D Euclidean coordinates.

Definition at line 47 of file mesh_function_grad_fe.h.

Member Typedef Documentation

◆ Scalar

template<class SCALAR_FE , class SCALAR_COEFF >

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

Definition at line 49 of file mesh_function_grad_fe.h.

Constructor & Destructor Documentation

◆ MeshFunctionGradFE()

template<class SCALAR_FE , class SCALAR_COEFF >

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

inline

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

Parameters

fe_space	the approximation space in which the function lies.
dof_vector	passes the basis expansion coefficients

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_grad_fe.h.

Member Function Documentation

◆ getFESpace()

template<class SCALAR_FE , class SCALAR_COEFF >

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

inline

Convenience method to retrieve the finite element space to which the original function belongs (i.e. before taking the gradient)

Returns: shared_ptr to UniformScalarFESpace to which the original function belongs (i.e. before taking the gradient)

Definition at line 79 of file mesh_function_grad_fe.h.

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

◆ getMesh()

template<class SCALAR_FE , class SCALAR_COEFF >

std::shared_ptr< const mesh::Mesh > lf::fe::MeshFunctionGradFE< 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 69 of file mesh_function_grad_fe.h.

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

◆ operator()()

template<class SCALAR_FE , class SCALAR_COEFF >

std::vector< Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > > lf::fe::MeshFunctionGradFE< 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	reference to a mesh entity
local	matrix whose columns contain reference coordinates of the evaluation points on the entity e

Returns: array of column vectors containing the gradients.

Definition at line 92 of file mesh_function_grad_fe.h.

References lf::base::RefEl::Dimension(), lf::fe::MeshFunctionGradFE< SCALAR_FE, SCALAR_COEFF >::dof_vector_, lf::fe::MeshFunctionGradFE< SCALAR_FE, SCALAR_COEFF >::fe_space_, lf::mesh::Entity::Geometry(), lf::geometry::Geometry::JacobianInverseGramian(), and lf::mesh::Entity::RefEl().

Member Data Documentation

◆ dof_vector_

template<class SCALAR_FE , class SCALAR_COEFF >

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

private

Reference to basis expansion coefficient vector for finite-element function

Definition at line 125 of file mesh_function_grad_fe.h.

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

◆ fe_space_

template<class SCALAR_FE , class SCALAR_COEFF >

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

private

Pointer to underlying finite element space.

Definition at line 122 of file mesh_function_grad_fe.h.

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

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

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

Public Types

Public Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ Scalar

Constructor & Destructor Documentation

◆ MeshFunctionGradFE()

Member Function Documentation

◆ getFESpace()

◆ getMesh()

◆ operator()()

Member Data Documentation

◆ dof_vector_

◆ fe_space_