Concept definition

template<class EMP>
concept lf::assemble::EntityMatrixProvider =  requires(EMP& emp, const mesh::Entity& e) {
  { emp.isActive(e) } -> std::same_as<bool>;
  { emp.Eval(e) } -> base::EigenMatrix<void, -1, -1>;
}

Detailed Description

Provides the local element matrix for a mesh entity.

Template Parameters

EMP	Entity-Matrix-Provider (EMP) Type to be tested for satisfaction of the concept

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 a const 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
  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 matrix 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.

Archetype

EntityMatrixProviderAT.

Classes modelling this concept

Definition at line 96 of file assemble_concepts.h.