Creates and solves the discretised Hodge Laplacian source problems. More...

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

Public Member Functions
	HodgeLaplaciansSourceProblems ()
	Constructor initializes basic mesh (Octaeder with radius 1.0) More...

void	Compute ()
	Computes the Galerkin LSE for all three source problems. More...

void	Solve ()
	solves the linear systems build in Compute More...

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

void	SetLoadFunctions (std::function< SCALAR(const Eigen::Matrix< double, 3, 1 > &)> &f0, std::function< Eigen::Matrix< SCALAR, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)> &f1, std::function< SCALAR(const Eigen::Matrix< double, 3, 1 > &)> &f2)
	Sets the load functions. More...

void	SetK (double k)
	Sets k for the souce problems. More...

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

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

Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 >	GetMuZero ()
	retunrs the basis expansion coefficiants for the solution of the zero form More...

std::tuple< Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 >, Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 > >	GetMuOne ()
	retunrs the basis expansion coefficiants for the solution of the one form More...

std::tuple< Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 >, Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 > >	GetMuTwo ()
	retunrs the basis expansion coefficiants for the solution of the two form More...

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

std::function< SCALAR(const Eigen::Matrix< double, 3, 1 > &)>	f0_

std::function< Eigen::Matrix< SCALAR, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)>	f1_

std::function< SCALAR(const Eigen::Matrix< double, 3, 1 > &)>	f2_

std::vector< lf::assemble::COOMatrix< SCALAR > >	coo_matrix_

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

std::vector< Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 > >	mu_

double	k_

Detailed Description

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

Creates and solves the discretised Hodge Laplacian source problems.

Details regarding the mathematical derivations can be found in the thesis Hodge-Laplacians and Dirac Operators on the Surface of the 3-Sphere section 4.4.

Note: Only triangular meshes are supported

Definition at line 34 of file hodge_laplacians_source_problems.h.

Constructor & Destructor Documentation

◆ HodgeLaplaciansSourceProblems()

template<typename SCALAR >

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

inline

Constructor initializes basic mesh (Octaeder with radius 1.0)

set k to 1

For all three Hodge Laplacians initializes zerovalued functions f

Definition at line 46 of file hodge_laplacians_source_problems.h.

Member Function Documentation

◆ Compute()

template<typename SCALAR >

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

inline

Computes the Galerkin LSE for all three source problems.

\[ - \Delta_l u + k^2 u = f_l \qquad l = 0, 1, 2 \]

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

Definition at line 95 of file hodge_laplacians_source_problems.h.

◆ GetGalerkinMatrix()

template<typename SCALAR >

lf::assemble::COOMatrix< SCALAR > projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::GetGalerkinMatrix ( int index )

inline

returns the Galerkin Matrix

This is the Matrix of the LSE with index index

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

Definition at line 357 of file hodge_laplacians_source_problems.h.

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

◆ GetLoadVector()

template<typename SCALAR >

Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 > projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::GetLoadVector ( int index )

inline

returns the Loadvector

This is the righthandside of LSE with index index

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

Definition at line 344 of file hodge_laplacians_source_problems.h.

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

◆ GetMuOne()

template<typename SCALAR >

std::tuple< Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 >, Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 > > projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::GetMuOne ( )

inline

retunrs the basis expansion coefficiants for the solution of the one form

The first vector of the return value are the coefficiants with respect to whitney one form basis function. They represent an approximation of

\[ u \]

The second vector of the return value are the coefficiants with respect to to the barycentric basis functions. They represent the approximation for

\[ p := \text{div}_{\Gamma}(u) \]

on the mesh.

Returns: basis expansion coefficiants of one form

Note: the methods Compute() and Solve() must be called before the result is available

Definition at line 400 of file hodge_laplacians_source_problems.h.

References projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::mesh_p_, and projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::mu_.

◆ GetMuTwo()

template<typename SCALAR >

std::tuple< Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 >, Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 > > projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::GetMuTwo ( )

inline

retunrs the basis expansion coefficiants for the solution of the two form

The first vector of the return value are the coefficiants with respect to rotated (90 degree colckwise) whitney one form basis function. They represent an approximation of

\[ j = \textbf{grad}_{\Gamma}(u) \]

The second vector of the return value are the coefficiants with respect to to the piecewise constant basis functions. They represent the approximation for

\[ u \]

on the mesh.

Returns: basis expansion coefficiants of two form

Note: the methods Compute() and Solve() must be called before the result is available

Definition at line 433 of file hodge_laplacians_source_problems.h.

References projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::mesh_p_, and projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::mu_.

◆ GetMuZero()

template<typename SCALAR >

Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 > projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::GetMuZero ( )

inline

retunrs the basis expansion coefficiants for the solution of the zero form

The basis expansion coefficiants are with respect to the barycentric basis functions on the mesh.

Returns: basis expansion coefficiants of zero form

Note: the methods Compute() and Solve() must be called before the result is available

Definition at line 374 of file hodge_laplacians_source_problems.h.

References projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::mu_.

◆ SetK()

template<typename SCALAR >

void projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::SetK ( double k )

inline

Sets k for the souce problems.

Parameters

k	real valued parameter scaling the mass matrix

Definition at line 333 of file hodge_laplacians_source_problems.h.

References projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::k_.

◆ SetLoadFunctions()

template<typename SCALAR >

void projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::SetLoadFunctions	(	std::function< SCALAR(const Eigen::Matrix< double, 3, 1 > &)> &	f0,
		std::function< Eigen::Matrix< SCALAR, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)> &	f1,
		std::function< SCALAR(const Eigen::Matrix< double, 3, 1 > &)> &	f2
	)

inline

Sets the load functions.

Parameters

f0	load function in L^2
f1	load functions in L^2_t vector valued
f2	load functions in L^2

Definition at line 318 of file hodge_laplacians_source_problems.h.

References projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::f0_, projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::f1_, and projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::f2_.

Referenced by projects::hldo_sphere::experiments::HodgeLaplacianExperiment< SCALAR >::Compute().

◆ SetMesh()

template<typename SCALAR >

void projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< 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 296 of file hodge_laplacians_source_problems.h.

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

◆ Solve()

template<typename SCALAR >

void projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::Solve ( )

inline

solves the linear systems build in Compute

Uses the Matrices stored in coo_matrix_ and the righthandside vectors stored in phi_ to compute the basis expansion coefficiants mu_ approximating

Note: the method Compute() has to be called prior to calling Solve()

\[ - \Delta_l u + k^2 u = f_l \qquad l = 0, 1, 2 \]

Definition at line 276 of file hodge_laplacians_source_problems.h.

References projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::coo_matrix_, projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::mu_, and projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::phi_.

Member Data Documentation

◆ coo_matrix_

template<typename SCALAR >

std::vector<lf::assemble::COOMatrix<SCALAR> > projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::coo_matrix_

private

Definition at line 448 of file hodge_laplacians_source_problems.h.

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

◆ f0_

template<typename SCALAR >

std::function<SCALAR(const Eigen::Matrix<double, 3, 1> &)> projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::f0_

private

Definition at line 443 of file hodge_laplacians_source_problems.h.

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

◆ f1_

template<typename SCALAR >

std::function<Eigen::Matrix<SCALAR, 3, 1>( const Eigen::Matrix<double, 3, 1> &)> projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::f1_

private

Definition at line 446 of file hodge_laplacians_source_problems.h.

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