lf::mesh::utils::MeshFunction Concept Reference

A MeshFunction is a function object that can be evaluated at any point on the mesh. More...

#include <lf/mesh/utils/mesh_function_traits.h>

Concept definition

template<class MF, class R void>
concept lf::mesh::utils::MeshFunction = 
    
    
    
    std::is_object_v<MF> && std::copy_constructible<MF> &&
    internal::IsMeshFunctionCallable<MF, R>(0)

Detailed Description

A MeshFunction is a function object that can be evaluated at any point on the mesh.

Template Parameters

MF	The type which should fulfill the MeshFunction concept.
R	If specified, check additionally, that the MeshFunction returns objects of type R. If R is void, the MeshFunction can return any type.

Description

Conceptually, a mesh function assigns to every point on the mesh an object of type R (e.g. double or an Eigen::Matrix2d).

For efficiency reasons, a mesh function is normally evaluated at a number of points at once. Hence a mesh function must overload the bracket operator as follows:

std::vector<R> operator()(
  const lf::mesh::Entity& e, const Eigen::MatrixXd& local) const

Here

• e is a mesh entity
• local is a matrix of size (e.RefEl().Dimension()) x NumPoints and lists the local coordinates of the evaluation points (with respect to the reference element e.RefEl()).
• R is more or less arbitrary type such as a double or a Eigen::Matrix2d

The return type of operator() is a std::vector<R> with NumPoints length.

Requirements

The type MF satisfies the concept MeshFunction if

Given

• R, the type of objects returned by the mesh function
• e, a mesh entity of type lf::mesh::Entity,
• local, a set of local coordinates of type Eigen::MatrixXd
• mf object of type const MF

the following expressions are valid:

expression	return type	semantics
MF(a)	MF	Creates a copy of a
MF(std::move(a))	MF	"steals" a to create a new MeshFunction
a(e, local)	std::vector<R>	Evaluates mesh function at points local on the entity e

Usage scenarios

The concept of a MeshFunction is used widely in the lf::uscalfe module:

• Assembler classes such as lf::uscalfe::ScalarLoadEdgeVectorProvider or lf::uscalfe::ReactionDiffusionElementMatrixProvider accept MeshFunctions that describe coefficients or source functions.

Archetype

• lf::mesh::utils::MeshFunctionAT

See also

• lf::mesh::utils::MeshFunctionReturnType to retrieve the type R of a mesh function.

Classes modelling the MeshFunction concept

• lf::fe::MeshFunctionFE
• lf::fe::MeshFunctionGradFE
• lf::mesh::utils::MeshFunctionBinary with it's operator overloads
• lf::mesh::utils::MeshFunctionConstant
• lf::mesh::utils::MeshFunctionGlobal
• lf::mesh::utils::MeshFunctionUnary with it's operator overloads
• lf::refinement::MeshFunctionTransfer

Definition at line 149 of file mesh_function_traits.h.