Computes the Galerkin LSE for the Hodge Laplacian of the whitney one form. More...

#include </home/nico/bildung/SemVI/thesis/lehrfempp/projects/hldo_sphere/operators/whitney_one_hodge_laplacian.h>

Public Member Functions
	WhitneyOneHodgeLaplace ()
	Constructor initializes basic mesh (Octaeder with radius 1.0) initializes zerovalued function f. More...

void	Compute ()
	Computes the Galerkin LSE. More...

void	SetMesh (std::shared_ptr< const lf::mesh::Mesh > mesh_p)
	Sets the mesh and creates dof_handler. More...

void	SetLoadFunction (std::function< Eigen::Matrix< SCALAR, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)> &f)
	Sets the load function. More...

Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 >	GetLoadVector ()
	returns the Loadvector More...

lf::assemble::COOMatrix< SCALAR >	GetGalerkinMatrix ()
	returns the Galerkin Matrix More...

Private Attributes
std::shared_ptr< const lf::mesh::Mesh >	mesh_p_

std::function< Eigen::Matrix< SCALAR, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)>	f_

lf::assemble::COOMatrix< SCALAR >	coo_matrix_

Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 >	phi_

Detailed Description

template<typename SCALAR>
class projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >

Computes the Galerkin LSE for the Hodge Laplacian of the whitney one form.

\[ \Delta_1 \mathbf{u} = -\mathbf{curl}_{\Gamma} \circ \text{curl}_{\Gamma} \, \mathbf{u} + \mathbf{grad}_{\Gamma} \circ \text{div}_{\Gamma} \, \mathbf{u} \\ -\Delta_1 \mathbf{u} = \mathbf{f} \]

Basis functions are the Whitney 1-forms and the barycentric coordinate functions

Details regarding the mathematical derivations can be found in the thesis Hodge-Laplacians and Dirac Operators on the Surface of the 3-Sphere section 4.3.2.

Note: Only triangular meshes are supported

Definition at line 54 of file whitney_one_hodge_laplacian.h.

Constructor & Destructor Documentation

◆ WhitneyOneHodgeLaplace()

template<typename SCALAR >

projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::WhitneyOneHodgeLaplace ( )

inline

Constructor initializes basic mesh (Octaeder with radius 1.0) initializes zerovalued function f.

Definition at line 62 of file whitney_one_hodge_laplacian.h.

References projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::f_, projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::mesh_p_, and projects::hldo_sphere::mesh::SphereTriagMeshBuilder::setRefinementLevel().

Member Function Documentation

◆ Compute()

template<typename SCALAR >

void projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::Compute ( )

inline

Computes the Galerkin LSE.

The Galerkin matrix will be accessable with GetGalerkinMatrix() The load vector will be accessable with GetLoadVector()

Definition at line 91 of file whitney_one_hodge_laplacian.h.

References lf::assemble::AssembleVectorLocally(), projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::coo_matrix_, projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::f_, lf::base::RefEl::kPoint(), lf::base::RefEl::kSegment(), projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::mesh_p_, lf::assemble::DofHandler::NumDofs(), projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::phi_, lf::assemble::COOMatrix< SCALAR >::setZero(), and lf::assemble::COOMatrix< SCALAR >::triplets().

Referenced by projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::Compute().

◆ GetGalerkinMatrix()

template<typename SCALAR >

lf::assemble::COOMatrix< SCALAR > projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::GetGalerkinMatrix ( )

inline

returns the Galerkin Matrix

This is the Matrix of the LSE

Note: The Galerkin matrix must be computed with Compute() before calling this funciton

Definition at line 252 of file whitney_one_hodge_laplacian.h.

References projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::coo_matrix_.

Referenced by projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::Compute().

◆ GetLoadVector()

template<typename SCALAR >

Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 > projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::GetLoadVector ( )

inline

returns the Loadvector

This is the righthandside of the LSE

Note: The loadvector must be computed with Compute() before calling this function

Definition at line 241 of file whitney_one_hodge_laplacian.h.

References projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::phi_.

Referenced by projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::Compute().

◆ SetLoadFunction()

template<typename SCALAR >

void projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::SetLoadFunction ( std::function< Eigen::Matrix< SCALAR, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)> & f )

inline

Sets the load function.

Parameters

f	load function

\[ \Delta_1 \mathbf{u} = -\mathbf{curl}_{\Gamma} \circ \text{curl}_{\Gamma} \, \mathbf{u} + \mathbf{grad}_{\Gamma} \circ \text{div}_{\Gamma} \, \mathbf{u} \\ -\Delta_1 \mathbf{u} = \mathbf{f} \]

Definition at line 227 of file whitney_one_hodge_laplacian.h.

References projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::f_.

Referenced by projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::Compute().

◆ SetMesh()

template<typename SCALAR >

void projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::SetMesh ( std::shared_ptr< const lf::mesh::Mesh > mesh_p )

inline

Sets the mesh and creates dof_handler.

Parameters

mesh_p pointer to the mesh

requries all cells in the mesh are triangles requries mesh global dimension to be 3

Definition at line 199 of file whitney_one_hodge_laplacian.h.

References lf::base::RefEl::kTria(), projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::mesh_p_, and lf::base::RefEl::RefEl().

Referenced by projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::Compute().

Member Data Documentation

◆ coo_matrix_

template<typename SCALAR >

lf::assemble::COOMatrix<SCALAR> projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::coo_matrix_

private

Definition at line 259 of file whitney_one_hodge_laplacian.h.

Referenced by projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::Compute(), and projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::GetGalerkinMatrix().

◆ f_

template<typename SCALAR >

std::function<Eigen::Matrix<SCALAR, 3, 1>( const Eigen::Matrix<double, 3, 1> &)> projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::f_

private

Definition at line 258 of file whitney_one_hodge_laplacian.h.

Referenced by projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::Compute(), projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::SetLoadFunction(), and projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::WhitneyOneHodgeLaplace().