Element Matrix Provider for the Laplace operator using picewise linear barycentric basis functions. More...

#include </home/nico/bildung/SemVI/thesis/lehrfempp/projects/hldo_sphere/assemble/laplace_matrix_provider.h>

Public Member Functions
	LaplaceMatrixProvider ()
	Constructor. More...

Eigen::MatrixXd	Eval (const lf::mesh::Entity &entity) const
	Compute the element matrix for a given cell of a mesh. More...

bool	isActive (const lf::mesh::Entity &entity) const
	All entities are regarded as active. More...

Detailed Description

Element Matrix Provider for the Laplace operator using picewise linear barycentric basis functions.

The element matrix provider works in a 3 dimensional world with 2 dimensional triangular cells.

The locally evaluated bilinear form is

\[ (u,v) \mapsto \int\limits_{K} \mathbf{grad}_{\Gamma}(u) \cdot \mathbf{grad}_{\Gamma}(v) dx \]

Where \( \mathbf{grad}_{\Gamma} \) denotes the tangential gradient on the triangle.

Details regarding the mathematical derivations can be found in the thesis Hodge-Laplacians and Dirac Operators on the Surface of the 3-Sphere section 4.2.1.

Note: This class complies with the type requirements for the template argument ENTITY_MATRIX_PROVIDER of the function lf::assemble::AssembleMatrixLocally().; Only triangular meshes are supported

Definition at line 43 of file laplace_matrix_provider.h.

Constructor & Destructor Documentation

◆ LaplaceMatrixProvider()

projects::hldo_sphere::assemble::LaplaceMatrixProvider::LaplaceMatrixProvider ( )

inline

Constructor.

Definition at line 48 of file laplace_matrix_provider.h.

Member Function Documentation

◆ Eval()

Eigen::MatrixXd projects::hldo_sphere::assemble::LaplaceMatrixProvider::Eval ( const lf::mesh::Entity & entity ) const

Compute the element matrix for a given cell of a mesh.

Parameters

entity The mesh cell on which the element matrix will be computed

Returns: The 3 by 3 element matrix of the cell

Note: Only triangular cells are supported

Definition at line 11 of file laplace_matrix_provider.cc.

References lf::mesh::Entity::Geometry(), lf::geometry::Geometry::Global(), lf::uscalfe::FeLagrangeO1Tria< SCALAR >::GradientsReferenceShapeFunctions(), lf::base::RefEl::kTria(), lf::base::RefEl::NodeCoords(), lf::mesh::Entity::RefEl(), and lf::geometry::Volume().

◆ isActive()

bool projects::hldo_sphere::assemble::LaplaceMatrixProvider::isActive ( const lf::mesh::Entity & entity ) const

inline

All entities are regarded as active.

Definition at line 63 of file laplace_matrix_provider.h.

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