Element matrix provider for the Whitney one mass matrix that is the dot product of two Whitney one basis functions. More...

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

Public Member Functions
	WhitneyOneMassMatrixProvider ()
	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 Whitney one mass matrix that is the dot product of two Whitney one basis functions.

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

\[ (\textbf{u}, \textbf{v}) \mapsto \int\limits_{K} \textbf{u} \cdot \textbf{v} dx \]

The whitney 1-forms, surface edge elements are associated with edges and defined as

\[ \mathbf{b}_i = s_i (\lambda_i \mathbf{grad}_{\Gamma}(\lambda_{i+1}) - \lambda_{i+1} \mathbf{grad}_{\Gamma}(\lambda_{i})) \]

with \( \lambda_i \) barycentric basis functions and \( s_i \) is a sign of the function based on the relative orientation of the edge in the mesh.

Details regarding the mathematical derivations can be found in the thesis Hodge-Laplacians and Dirac Operators on the Surface of the 3-Sphere section 4.2.5.

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 50 of file whitney_one_mass_matrix_provider.h.

Constructor & Destructor Documentation

◆ WhitneyOneMassMatrixProvider()

projects::hldo_sphere::assemble::WhitneyOneMassMatrixProvider::WhitneyOneMassMatrixProvider ( )

inline

Constructor.

Definition at line 55 of file whitney_one_mass_matrix_provider.h.

Member Function Documentation

◆ Eval()

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

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

Parameters

entity The mesh cell to compute the element matrix for

Returns: The 3 by 3 element matrix of the cell

Note: Only triangular cells are supported

Definition at line 11 of file whitney_one_mass_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(), lf::mesh::Entity::RelativeOrientations(), lf::mesh::to_sign(), and lf::geometry::Volume().

◆ isActive()

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

inline

All entities are regarded as active.

Definition at line 69 of file whitney_one_mass_matrix_provider.h.

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