Postprocessing such as computing norms and Mesh Functions and plot scripts. More...

Classes
class	MeshFunctionWhitneyOne
	Provides Mesh Function for given basis expansion coefficients. More...

class	MeshFunctionWhitneyTwo
	Provides Mesh Function for Whitney two basis expansion coefficients. More...

class	MeshFunctionWhitneyZero
	Provides Mesh Function for basis expansion coefficients of the zero form. More...

struct	ProblemSolution
	stores solutions for several k and one refinement level More...

struct	ProblemSolutionWrapper
	stores solutions and setupinformation for a list of refinement levels and k values More...

Functions
template<typename MF , typename SQ_F >
std::pair< double, lf::mesh::utils::CodimMeshDataSet< double > >	L2norm (const std::shared_ptr< const lf::mesh::Mesh > &mesh_p, const MF &f, const SQ_F &sq_f, const lf::quad::QuadRule &quadrule)
	Computes the L2Norm of some MeshFunction (type MF) f. More...

template<typename MF , typename SQ_F >
std::pair< double, lf::mesh::utils::CodimMeshDataSet< double > >	SupNorm (const std::shared_ptr< const lf::mesh::Mesh > &mesh_p, const MF &f, const SQ_F &sq_f, const lf::quad::QuadRule &quadrule)
	Computes the supremum norm of the squared values of some MeshFunction (type MF) f. More...

template<typename... Args>
static std::string	concat (Args &&...args)
	Concatenate objects defining an operator<<(std::ostream&) More...

template<typename SCALAR >
void	compare_results (std::string name, ProblemSolutionWrapper< SCALAR > &results_lap, ProblemSolutionWrapper< SCALAR > &results_dirac)
	Generate vtk files containing meshdata and a csv table with results of the comparison of the two given basis expansion coefficients. More...

template<typename U_ZERO , typename U_ONE , typename U_TWO , typename SCALAR >
void	process_results (std::string name, ProblemSolutionWrapper< SCALAR > &results, U_ZERO &u_zero, U_ONE &u_one, U_TWO &u_two, double &k)
	Generate vtk files containing meshdata and a csv table with results. More...

Detailed Description

Postprocessing such as computing norms and Mesh Functions and plot scripts.

Function Documentation

◆ compare_results()

template<typename SCALAR >

void projects::hldo_sphere::post_processing::compare_results	(	std::string	name,
		ProblemSolutionWrapper< SCALAR > &	results_lap,
		ProblemSolutionWrapper< SCALAR > &	results_dirac
	)

Generate vtk files containing meshdata and a csv table with results of the comparison of the two given basis expansion coefficients.

The Table contains for each refinement level, the number of cells, edges and vertices, as well as the global mesh width (the maximum edge length of a triangle). Moreover it contains the l2 norm of the difference of the two functions as well as the approximate orders for every value of k and all three forms.

Template Parameters

SCALAR base type of the result vectors

Parameters

name	identifying the experiment (used to name the outputs)
results_lap	ProblemSolutionWrapper with the results for all levels and ks computed with the Laplace operator
results_dirac	ProblemSolutionWrapper with the results for all levels and ks computed with the Dirac operator

Note: the parameter results_dirac and results_lap must have results for the same list of k values and the same refinement levels.

Definition at line 96 of file results_processing.h.

References concat(), projects::hldo_sphere::post_processing::ProblemSolutionWrapper< SCALAR >::k, lf::base::RefEl::kTria(), L2norm(), projects::hldo_sphere::post_processing::ProblemSolutionWrapper< SCALAR >::levels, lf::quad::make_QuadRule(), projects::hldo_sphere::post_processing::ProblemSolutionWrapper< SCALAR >::mesh, projects::hldo_sphere::post_processing::ProblemSolutionWrapper< SCALAR >::solutions, lf::geometry::Volume(), and lf::io::VtkWriter::WriteCellData().

◆ concat()

template<typename... Args>

static std::string projects::hldo_sphere::post_processing::concat ( Args &&... args )

static

Concatenate objects defining an operator<<(std::ostream&)

Parameters

args	A variadic pack of objects implementing `operator<<(std::ostream&)`

Returns: A string with the objects concatenated

Definition at line 68 of file results_processing.h.

Referenced by compare_results(), and process_results().

◆ L2norm()

template<typename MF , typename SQ_F >

std::pair< double, lf::mesh::utils::CodimMeshDataSet< double > > projects::hldo_sphere::post_processing::L2norm	(	const std::shared_ptr< const lf::mesh::Mesh > &	mesh_p,
		const MF &	f,
		const SQ_F &	sq_f,
		const lf::quad::QuadRule &	quadrule
	)

Computes the L2Norm of some MeshFunction (type MF) f.

Template Parameters

MF	type of the mesh function to take to norm form is required to be defined on the mesh
SQ_F	type of the square function sq_f

Parameters

mesh_p	pointer to the mesh
f	meshfunction to evaluate
sq_f	square function for the output of f \(sq\_f(x) \mapsto \\|x\\|^2\)
quadrule	quadrature rule used for each cell in the mesh

Returns: pair with the norm of the inputfunction f on the mesh and CodimMeshDataSet containing the cellwise integrals over the squared errors

Iterates over all cells in the mesh and compute the squared integral locally, then add up and square

Definition at line 33 of file norms.h.

References lf::quad::QuadRule::NumPoints(), lf::quad::QuadRule::Points(), and lf::quad::QuadRule::Weights().

Referenced by compare_results(), projects::hldo_sphere::debugging::DiracConvergenceTest::Compute(), projects::hldo_sphere::debugging::WhitneyOneBasisExpansionCoeffs::GetL2Error(), and process_results().

◆ process_results()

template<typename U_ZERO , typename U_ONE , typename U_TWO , typename SCALAR >

void projects::hldo_sphere::post_processing::process_results	(	std::string	name,
		ProblemSolutionWrapper< SCALAR > &	results,
		U_ZERO &	u_zero,
		U_ONE &	u_one,
		U_TWO &	u_two,
		double &	k
	)

Generate vtk files containing meshdata and a csv table with results.

The Table contains for each refinement level, the number of cells, edges and vetices, as well as the global mesh width (the maximum edgelenght of a triangle). Moreover it contains the l2 error and the Supremum error as well as the approximate orders for every value of k and all three forms.

Template Parameters

U_ZERO	functor for the analytical solution of the zero form
U_ONE	functor for the analytical solution of the one form
U_TWO	functor for the analytical solution of the two form
SCALAR	base type of the resultvectors

Parameters

name	identifying the experiment (used to name the outputs)
results	ProblemSolutionWrapper with the results for all levels and ks
u_zero	vector with the analytical solutions for u_zero of every k
u_one	vector with the analytical solutions for u_one of every k
u_two	vector with the analytical solutions for u_two of every k
k	reference to the variable used in the functions u_one, u_two, u_zero

Definition at line 302 of file results_processing.h.

References concat(), projects::hldo_sphere::post_processing::ProblemSolutionWrapper< SCALAR >::k, lf::base::RefEl::kTria(), L2norm(), projects::hldo_sphere::post_processing::ProblemSolutionWrapper< SCALAR >::levels, lf::quad::make_QuadRule(), projects::hldo_sphere::post_processing::ProblemSolutionWrapper< SCALAR >::mesh, projects::hldo_sphere::post_processing::ProblemSolutionWrapper< SCALAR >::solutions, SupNorm(), lf::geometry::Volume(), and lf::io::VtkWriter::WriteCellData().

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

◆ SupNorm()

template<typename MF , typename SQ_F >

std::pair< double, lf::mesh::utils::CodimMeshDataSet< double > > projects::hldo_sphere::post_processing::SupNorm	(	const std::shared_ptr< const lf::mesh::Mesh > &	mesh_p,
		const MF &	f,
		const SQ_F &	sq_f,
		const lf::quad::QuadRule &	quadrule
	)

Computes the supremum norm of the squared values of some MeshFunction (type MF) f.

Template Parameters

MF	type of the mesh function to take to norm form
SQ_F	type of the square function sq_f

Parameters

mesh_p	pointer to the mesh
f	meshfunction to evaluate
sq_f	square function for the output of f \( sq\_f(x) \mapsto \\|x\\|^2 \)
quadrule	quadrature rule only used to determine the evalueation points

Returns: pair with the supremum norm of the root of the input function sq_f(f(x)) on the mesh and CodimMeshDataSet containing the cellwise supremums

Definition at line 84 of file norms.h.

References lf::quad::QuadRule::NumPoints(), and lf::quad::QuadRule::Points().

Referenced by process_results().

Classes

Functions

Detailed Description

Function Documentation

◆ compare_results()

◆ concat()

◆ L2norm()

◆ process_results()

◆ SupNorm()