projects::hldo_sphere::operators::DiracOperator Class Reference

Computes the Galerkin LSE for the Dirac Operator and the load vector. More...

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

Public Member Functions
	DiracOperator ()
	Constructor creates basic mesh (Octaeder with radius 1.0) and zero valued functions 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	SetLoadFunctions (std::function< complex(const Eigen::Matrix< double, 3, 1 > &)> f0, std::function< Eigen::Matrix< complex, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)> f1, std::function< complex(const Eigen::Matrix< double, 3, 1 > &)> f2)
	Sets the load functions. More...
Eigen::Matrix< complex, Eigen::Dynamic, 1 >	GetLoadVector ()
	returns the Loadvector More...
lf::assemble::COOMatrix< complex >	GetGalerkinMatrix ()
	returns the Galerkin Matrix More...

Private Attributes
std::shared_ptr< const lf::mesh::Mesh >	mesh_p_
std::function< complex(const Eigen::Matrix< double, 3, 1 > &)>	f0_
std::function< Eigen::Matrix< complex, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)>	f1_
std::function< complex(const Eigen::Matrix< double, 3, 1 > &)>	f2_
lf::assemble::COOMatrix< complex >	coo_matrix_
Eigen::Matrix< complex, Eigen::Dynamic, 1 >	phi_

Detailed Description

Computes the Galerkin LSE for the Dirac Operator and the load vector.

\[ \begin{pmatrix} & \int\limits_{\partial \mathbf{S}} \mathbf{u} \cdot \mathbf{grad}_{\Gamma} v \, dS & \\ \int_{\partial \mathbf{S}} \mathbf{grad}_{\Gamma} u \cdot \mathbf{v} \, dS & & \int\limits_{\partial \mathbf{S}} \mu \ \ \text{curl}_{\Gamma} \mathbf{v} \, dS \\ & \int\limits_{\partial \mathbf{S}} \text{curl}_{\Gamma} \mathbf{u} \ \ \nu \, dS & \end{pmatrix} , \begin{pmatrix} \int\limits_{\partial \mathbf{S}} f v \, dS \\ \int\limits_{\partial \mathbf{S}} \mathbf{f} \cdot \mathbf{v} \, dS \\ \int\limits_{\partial \mathbf{S}} \varphi \nu \, dS \end{pmatrix} \]

Details regarding the mathematical derivations can be found in the thesis Hodge-Laplacians and Dirac Operators on the Surface of the 3-Sphere section 4.3.4.

Note

Only triangular meshes are supported

Definition at line 60 of file dirac_operator.h.

Constructor & Destructor Documentation

DiracOperator()

projects::hldo_sphere::operators::DiracOperator::DiracOperator ( )

inline

Constructor creates basic mesh (Octaeder with radius 1.0) and zero valued functions f.

Definition at line 68 of file dirac_operator.h.

References f0_, f1_, f2_, mesh_p_, and projects::hldo_sphere::mesh::SphereTriagMeshBuilder::setRefinementLevel().

Member Function Documentation

Compute()

void projects::hldo_sphere::operators::DiracOperator::Compute

(

)

Computes the Galerkin LSE.

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

Definition at line 7 of file dirac_operator.cc.

References lf::assemble::AssembleVectorLocally(), coo_matrix_, f0_, f1_, f2_, lf::base::RefEl::kPoint(), lf::base::RefEl::kSegment(), lf::base::RefEl::kTria(), mesh_p_, lf::assemble::DofHandler::NumDofs(), phi_, lf::assemble::COOMatrix< SCALAR >::setZero(), and lf::assemble::COOMatrix< SCALAR >::triplets().

Referenced by projects::hldo_sphere::operators::DiracOperatorSourceProblem::Compute().

GetGalerkinMatrix()

lf::assemble::COOMatrix< complex > projects::hldo_sphere::operators::DiracOperator::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 148 of file dirac_operator.h.

References coo_matrix_.

Referenced by projects::hldo_sphere::operators::DiracOperatorSourceProblem::Compute().

GetLoadVector()

Eigen::Matrix< complex, Eigen::Dynamic, 1 > projects::hldo_sphere::operators::DiracOperator::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 137 of file dirac_operator.h.

References phi_.

Referenced by projects::hldo_sphere::operators::DiracOperatorSourceProblem::Compute().

SetLoadFunctions()

void projects::hldo_sphere::operators::DiracOperator::SetLoadFunctions ( std::function< complex(const Eigen::Matrix< double, 3, 1 > &)>  f0, std::function< Eigen::Matrix< complex, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)>  f1, std::function< complex(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 117 of file dirac_operator.h.

References f0_, f1_, and f2_.

Referenced by projects::hldo_sphere::operators::DiracOperatorSourceProblem::Compute().

SetMesh()

void projects::hldo_sphere::operators::DiracOperator::SetMesh

(

std::shared_ptr< const lf::mesh::Mesh >

mesh_p

)

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 131 of file dirac_operator.cc.

References lf::base::RefEl::kTria(), mesh_p_, and lf::base::RefEl::RefEl().

Referenced by projects::hldo_sphere::operators::DiracOperatorSourceProblem::Compute().

Member Data Documentation

coo_matrix_

lf::assemble::COOMatrix<complex> projects::hldo_sphere::operators::DiracOperator::coo_matrix_

private

Definition at line 157 of file dirac_operator.h.

Referenced by Compute(), and GetGalerkinMatrix().

f0_

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

private

Definition at line 152 of file dirac_operator.h.

Referenced by Compute(), DiracOperator(), and SetLoadFunctions().

f1_

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

private

Definition at line 155 of file dirac_operator.h.

Referenced by Compute(), DiracOperator(), and SetLoadFunctions().

f2_

std::function<complex(const Eigen::Matrix<double, 3, 1> &)> projects::hldo_sphere::operators::DiracOperator::f2_

private

Definition at line 156 of file dirac_operator.h.

Referenced by Compute(), DiracOperator(), and SetLoadFunctions().

mesh_p_

std::shared_ptr<const lf::mesh::Mesh> projects::hldo_sphere::operators::DiracOperator::mesh_p_

private

Definition at line 151 of file dirac_operator.h.

Referenced by Compute(), DiracOperator(), and SetMesh().

phi_

Eigen::Matrix<complex, Eigen::Dynamic, 1> projects::hldo_sphere::operators::DiracOperator::phi_

private

Definition at line 158 of file dirac_operator.h.

Referenced by Compute(), and GetLoadVector().

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

• /home/nico/bildung/SemVI/thesis/lehrfempp/projects/hldo_sphere/operators/dirac_operator.h
• /home/nico/bildung/SemVI/thesis/lehrfempp/projects/hldo_sphere/operators/dirac_operator.cc