EntityMatrixProvider

Detailed Description

Provides the local element matrix for a mesh entity.

Description

An EntityMatrixProvider is an object that provides a local element matrix for a given mesh entity. EntityMatrixProvider's are mostly used together with lf::assemble::AssembleMatrixLocally to assemble a sparse system matrix.

Requirements

The type EMP satisfies the Concept EntityMatrixProvider if given

• emp an object of type EMP
• e is a lf::mesh::Entity object
• SCALAR is an Eigen supported scalar datatype (e.g. double)
• ROWS is the number of rows of the local element matrix or Eigen::Dynamic
• COLS is the number of columns of the local element matrix or Eigen::Dynamic

the following expressions are valid:

expression	return type	semantics
emp.isActive(e)	bool	Defines whether the entity e is taken into account by the assembly routine.
emp.Eval(e)	Eigen::Matrix<SCALAR, ROWS, COLS>	Returns the local element matrix for mesh entity e. Is only called if emp.isActive(e)==true.

Typical class definition

class ElemMatProvider {
 public:
  // Constructor can be used to pass data required for local computations
  ElemMatProvider() = default;
  // Select cells taken into account during cell-oriented assembly
  virtual bool isActive(const lf::mesh::Entity& cell);
  // Compute element matrix for a cell, here a fixed-size matrix
  Eigen::Matrix<double, 3, 3> Eval(const lf::mesh::Entity& cell);
};

Note

returning a matix object through Eval() may sacrifice efficiency because it may entail additional allocation of dynamic memory. However, this design was chosen for the sake of readability of the code and in order to avoid nasty memory access errors that often occur when passing a matrix by reference.

Usage scenarios

The concept of a EntityMatrixProvider is widely used in the lf::assemble and lf::uscalfe modules:

• The function lf::assemble::AssembleMatrixLocally() accepts an EntityMatrixProvider which in turn defines how the (sparse) system matrix is assembled.

Implementations

Examples for classes implementing the concept EntityMatrixProvider are lf::uscalfe::LinearFELaplaceElementMatrix and lf::uscalfe::ReactionDiffusionElementMatrixProvider

See also

• The concept EntityVectorProvider
• The cell-oriented assembly functions Cell-Oriented Assembly of Galerkin Matrices
• Lecture Document Example 2.7.4.29
• Lecture Document Example 2.7.4.37

Implementing Classes
class	lf::fe::DiffusionElementMatrixProvider< SCALAR, DIFF_COEFF >
	Class for computing element matrices for general scalar-valued finite elements and homogeneous 2nd-order elliptic bilinear forms. More...
class	lf::fe::MassElementMatrixProvider< SCALAR, REACTION_COEFF >
	Class for local quadrature based computation of element matrix for Lagrangian finite elements and a weighted \(L^2\) inner product. More...
class	lf::fe::MassEdgeMatrixProvider< SCALAR, COEFF, EDGESELECTOR >
	Quadrature-based computation of local mass matrix for an edge. More...
class	lf::uscalfe::LinearFELaplaceElementMatrix
	Computing the element matrix for the (negative) Laplacian and linear finite elements. More...
class	lf::uscalfe::ReactionDiffusionElementMatrixProvider< SCALAR, DIFF_COEFF, REACTION_COEFF >
	Class for local quadrature based computations for Lagrangian finite elements and second-order scalar elliptic BVPs. More...
class	lf::uscalfe::MassEdgeMatrixProvider< SCALAR, COEFF, EDGESELECTOR >
	Quadrature-based computation of local mass matrix for an edge. More...