projects::hldo_sphere::debugging::WhitneyOneCurlTest Class Reference

Tests convergence of the below bilinear form on the Mesh to the analytical solution. More...

#include </home/nico/bildung/SemVI/thesis/lehrfempp/projects/hldo_sphere/debugging/whitney_one_curl_test.h>

Public Member Functions
	WhitneyOneCurlTest ()
	Constructor creates an object with zero testfunctions. More...
void	Compute (int max_ref)
	Computes the error up to the refinemet level 'max_ref'. More...
void	SetAnaSol (double sol)
	Sets the value of the analytical solution \(b(u,v)\). More...
void	SetFunctions (std::function< double(const Eigen::Matrix< double, 3, 1 > &)> v, std::function< Eigen::Matrix< double, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)> u)
	Sets the test functions. More...

Private Attributes
std::function< double(const Eigen::Matrix< double, 3, 1 > &)>	v_
std::function< Eigen::Matrix< double, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)>	u_
double	ana_sol_
Eigen::VectorXd	discrete_sols_
std::vector< std::shared_ptr< const lf::mesh::Mesh > >	meshs_

Detailed Description

Tests convergence of the below bilinear form on the Mesh to the analytical solution.

\[ b(\mathbf{u},v) = \int\limits_{\partial \mathbf{S}} \text{div}\, \mathbf{u} \, v \ dS \]

For this we compute the Galerkin Matrix B and the values at the basis nodes for the analytical solution and then we expect the following quantity to converge to 0 on mesh refinement

\[ | b(u,v) - u^T \, B \, v | \to 0 \]

Definition at line 46 of file whitney_one_curl_test.h.

Constructor & Destructor Documentation

WhitneyOneCurlTest()

projects::hldo_sphere::debugging::WhitneyOneCurlTest::WhitneyOneCurlTest ( )

inline

Constructor creates an object with zero testfunctions.

Definition at line 51 of file whitney_one_curl_test.h.

References discrete_sols_, meshs_, u_, and v_.

Member Function Documentation

Compute()

void projects::hldo_sphere::debugging::WhitneyOneCurlTest::Compute ( int  max_ref )

inline

Computes the error up to the refinemet level 'max_ref'.

Parameters

max_ref

maximal refinement level for which the error is computed

The results are then stored in a csv file under resluts/whitney_one_curl_test_max_ref.csv

Definition at line 72 of file whitney_one_curl_test.h.

References ana_sol_, projects::hldo_sphere::mesh::SphereTriagMeshBuilder::Build(), projects::hldo_sphere::debugging::concat(), lf::geometry::Corners(), discrete_sols_, lf::base::RefEl::kSegment(), lf::base::RefEl::kTria(), lf::assemble::COOMatrix< SCALAR >::makeSparse(), meshs_, lf::assemble::DofHandler::NumDofs(), projects::hldo_sphere::debugging::WhitneyOneBasisExpansionCoeffs::SetMesh(), projects::hldo_sphere::mesh::SphereTriagMeshBuilder::setRadius(), projects::hldo_sphere::mesh::SphereTriagMeshBuilder::setRefinementLevel(), lf::assemble::COOMatrix< SCALAR >::setZero(), u_, v_, and lf::geometry::Volume().

SetAnaSol()

void projects::hldo_sphere::debugging::WhitneyOneCurlTest::SetAnaSol ( double  sol )

inline

Sets the value of the analytical solution \(b(u,v)\).

Parameters

sol	value of the analytical soltion

Note

the solution has to comply with the functions u and v, which are passed as functors

Definition at line 247 of file whitney_one_curl_test.h.

References ana_sol_.

SetFunctions()

void projects::hldo_sphere::debugging::WhitneyOneCurlTest::SetFunctions ( std::function< double(const Eigen::Matrix< double, 3, 1 > &)>  v, std::function< Eigen::Matrix< double, 3, 1 >(const Eigen::Matrix< double, 3, 1 > &)>  u  )

inline

Sets the test functions.

Parameters

v	load function in \( L^2 \)
u	load functions in \( H(\text{curl}_{\Gamma}, \partial \mathbf{S})\) vector valued

Definition at line 255 of file whitney_one_curl_test.h.

References u_, and v_.

Member Data Documentation

ana_sol_

double projects::hldo_sphere::debugging::WhitneyOneCurlTest::ana_sol_

private

Definition at line 269 of file whitney_one_curl_test.h.

Referenced by Compute(), and SetAnaSol().

discrete_sols_

Eigen::VectorXd projects::hldo_sphere::debugging::WhitneyOneCurlTest::discrete_sols_

private

Definition at line 270 of file whitney_one_curl_test.h.

Referenced by Compute(), and WhitneyOneCurlTest().

meshs_

std::vector<std::shared_ptr<const lf::mesh::Mesh> > projects::hldo_sphere::debugging::WhitneyOneCurlTest::meshs_

private

Definition at line 271 of file whitney_one_curl_test.h.

Referenced by Compute(), and WhitneyOneCurlTest().

u_

std::function<Eigen::Matrix<double, 3, 1>( const Eigen::Matrix<double, 3, 1> &)> projects::hldo_sphere::debugging::WhitneyOneCurlTest::u_

private

Definition at line 268 of file whitney_one_curl_test.h.

Referenced by Compute(), SetFunctions(), and WhitneyOneCurlTest().

v_

std::function<double(const Eigen::Matrix<double, 3, 1> &)> projects::hldo_sphere::debugging::WhitneyOneCurlTest::v_

private

Definition at line 265 of file whitney_one_curl_test.h.

Referenced by Compute(), SetFunctions(), and WhitneyOneCurlTest().

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

• /home/nico/bildung/SemVI/thesis/lehrfempp/projects/hldo_sphere/debugging/whitney_one_curl_test.h