MeshFunction

Detailed Description

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

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
• a, b objects of type 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<T>	Evaluates mesh function at points local

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.

See also

• lf::uscalfe::isMeshFunction<> to determine if a type fulfills the mesh function concept at compile time.
• lf::uscalfe::MeshFunctionReturnType<> to retrieve the type R of a mesh function.

Classes
class	lf::fe::MeshFunctionFE< SCALAR_FE, SCALAR_COEFF >
	A MeshFunction representing an element from a ScalarFESpace (e.g. solution of BVP) More...
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). More...
class	lf::mesh::utils::MeshFunctionBinary< OP, A, B >
	A MeshFunction which combines two other mesh functions using a binary operator (advanced use). More...
class	lf::mesh::utils::MeshFunctionConstant< R >
	A MeshFunction which takes the same constant value on the whole mesh. More...
class	lf::mesh::utils::MeshFunctionGlobal< F >
	MeshFunction wrapper for a simple function of physical coordinates. More...
class	lf::mesh::utils::MeshFunctionUnary< OP, MF >
	A mesh function representing another mesh function under a pointwise, unary operation. More...