Contains functionality for the implementation of DPG methods. More...

Namespaces
namespace	test

Classes
class	ConvectionElementMatrixProvider
	Class for local quadrature based computations sub element matrices corresponding to convection-like element matrices. More...

class	DiffusionElementMatrixProvider
	Class for local quadrature based computations of sub element matrices corresponding to diffusion element matrices. More...

class	DiscontinuousScalarReferenceFiniteElement
	Decorator class around a ScalarReferenceFiniteElement to represent discontinuous shape functions. More...

class	DpgElementMatrixProvider
	Class to evaluate element matrices for DPG methods. More...

class	DpgElementVectorProvider
	Class to evaluate element vectors of DPG methods. More...

class	FeDiscontinuousO0Quad
	Discontinuous constant finite element on a quadrilateral reference element. More...

class	FeDiscontinuousO0Segment
	Discontinuous constant finite element on a line segment. More...

class	FeDiscontinuousO0Tria
	Discontinuous constant finite element on a triangular reference element. More...

class	FluxElementMatrixProvider
	class for local quadrature based computations of sub element matrices corresponding to element matrices associated to a flux variable in the trial space More...

class	LoadElementVectorProvider
	Class for local quadrature based computations of sub vectors corresponding to load vectors. More...

class	PrescribedSignProvider
	Class which allows evaluation of the \( \text{sgn}_K \) function. More...

class	ProductElementMatrixProvider
	Class providing element matrices associated with bilinear forms between cartesian/product spaces. More...

class	ProductElementMatrixProviderBuilder
	Builder class to build a ProductElementMatrixProvider. More...

class	ProductElementVectorProvider
	Class providing element vectors associated with linear forms on cartesian/product spaces. More...

class	ProductElementVectorProviderBuilder
	Builder class to build a ProductElementVectorProvider. More...

class	ProductUniformFEDofHandler
	Dofhandler for uniform finite element spaces that discretizes a cartesian/product space. More...

class	ProductUniformFESpace
	cartesian/prodcut space of finite element functions on a hybrid 2D mesh. More...

class	ProductUniformFESpaceFactory
	Factory class to build a ProductUniformFESpace. More...

class	ReactionElementMatrixProvider
	Class for local quadrature based computations of sub element matrices corresponding to reaction element matrices. More...

class	SubElementMatrixProvider
	Interface class providing sub element matrices associated with bilinear forms between components of Cartesian product spaces. More...

class	SubElementVectorProvider
	Interface class providing element vectors associated with linear forms of a component of a cartesian/product space. More...

class	TraceElementMatrixProvider
	Class for local quadrature based computations of sub element matrices corresponding to element matrices associated to a trace variable in the trial space. More...

class	TraceScalarReferenceFiniteElement
	Decorator class around a ScalarReferenceFiniteElement to represent traces on the cell boundary. More...

Typedefs
using	gdof_idx_t = lf::uscalfe::gdof_idx_t
	Type for indices into global matrices/vectors. More...

using	ldof_idx_t = lf::uscalfe::ldof_idx_t
	Type for indices referring to entity matrices/vectors. More...

using	size_type = lf::uscalfe::size_type
	Type for vector length/matrix sizes. More...

using	dim_t = lf::uscalfe::dim_t
	Tpe for (co)-dimensions. More...

using	glb_idx_t = lf::uscalfe::glb_idx_t
	Type for global index of entities. More...

using	sub_idx_t = lf::uscalfe::sub_idx_t
	Type for indexing of sub-entities. More...

using	quad_rule_collection_t = lf::uscalfe::quad_rule_collection_t
	data structure for passing collections of quadrature rules, see lf::uscalfe for more information. More...

using	dof_map_t = lf::assemble::UniformFEDofHandler::dof_map_t
	see lf::assemble More...

Functions
template<class PTR >
	DpgElementMatrixProvider (PTR stiffness_provider, PTR gramianProvider) -> DpgElementMatrixProvider< typename PTR::element_type::SCALAR >

template<class PTR1 , class PTR2 >
	DpgElementVectorProvider (PTR1 eLoadVectorProvider, PTR2 eStiffnessProvider, PTR2 gramianProvider) -> DpgElementVectorProvider< typename PTR1::element_type::SCALAR >

std::vector< lf::quad::QuadRule >	BoundaryQuadRule (lf::base::RefEl ref_el, const lf::quad::QuadRule &qr)
	Constructs a quadrature rule on the boundary of a reference element. More...

Eigen::MatrixXd	OuterNormals (const lf::geometry::Geometry &geometry)
	Compute the outer normals of a geometry object. More...

template<typename CONVECTION_COEFF >
lf::mesh::utils::CodimMeshDataSet< bool >	flagEntitiesOnInflowBoundary (const std::shared_ptr< const lf::mesh::Mesh > &mesh_p, CONVECTION_COEFF beta)
	flag all edges located on the inflow boundary More...

template<typename CONVECTION_COEFF >
lf::mesh::utils::CodimMeshDataSet< bool >	flagEntitiesOnOutflowBoundary (const std::shared_ptr< const lf::mesh::Mesh > &mesh_p, CONVECTION_COEFF beta)
	flag all edges located on the outflow boundary More...

template<typename SCALAR , typename EDGESELECTOR_DIRICHLET , typename EDGESELECTOR_NEUMANN , typename FUNCTION_G , typename FUNCTION_H >
std::vector< std::pair< bool, SCALAR > >	InitEssentialConditionsFromFunctions (const ProductUniformFESpace< SCALAR > &fes, size_type trace_component, size_type flux_component, EDGESELECTOR_DIRICHLET &&dirichletcondflag, EDGESELECTOR_NEUMANN &&neumanncondflag, FUNCTION_G &&g, FUNCTION_H &&h)
	Initialization of flags/values for dofs of fluxes and traces of a on a product finite element space whose values are imposed by two specified functions on two specified parts of the boundary. More...

template<typename SCALAR >
lf::mesh::utils::CodimMeshDataSet< SCALAR >	ElementErrorEstimators (const ProductUniformFEDofHandler &trial_dofh, std::shared_ptr< ProductElementMatrixProvider< SCALAR > > stiffness_provider, std::shared_ptr< ProductElementMatrixProvider< SCALAR > > gramian_provider, std::shared_ptr< ProductElementVectorProvider< SCALAR > > load_provider, const Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 > &sol_vec)
	Evaluation of the local DPG error estimators on a mesh. More...

template<typename SCALAR >
SCALAR	EvalPosteriorError (const std::shared_ptr< const lf::mesh::Mesh > &mesh_p, const lf::mesh::utils::CodimMeshDataSet< SCALAR > &local_errors)
	Evaluation of the DPG error estimator. More...

template<class PTR , class DIFF_COEFF >
	DiffusionElementMatrixProvider (PTR fe_space_trial, PTR fe_space_test, size_type trial_component, size_type test_component, DIFF_COEFF alpha) -> DiffusionElementMatrixProvider< typename PTR::element_type::SCALAR, DIFF_COEFF >

template<class PTR , class REACTION_COEFF >
	ReactionElementMatrixProvider (PTR fe_trial, PTR fe_test, size_type trial_component, size_type test_component, REACTION_COEFF gamma) -> ReactionElementMatrixProvider< typename PTR::element_type::SCALAR, REACTION_COEFF >

template<class PTR , typename CONVECTION_COEFF_1 , typename CONVECTION_COEFF_2 >
	ConvectionElementMatrixProvider (PTR fe_trial, PTR fe_test, size_type trial_component, size_type test_component, CONVECTION_COEFF_1 beta_1, CONVECTION_COEFF_2 beta_2) -> ConvectionElementMatrixProvider< typename PTR::element_type::SCALAR, CONVECTION_COEFF_1, CONVECTION_COEFF_2 >

template<class PTR , class DIFF_COEFF >
	FluxElementMatrixProvider (PTR fe_space_trial, PTR fe_space_test, size_type trial_component, size_type test_component, DIFF_COEFF alpha) -> FluxElementMatrixProvider< typename PTR::element_type::SCALAR, DIFF_COEFF >

template<class PTR , class COEFF >
	TraceElementMatrixProvider (PTR fe_space_trial, PTR fe_space_test, size_type trial_component, size_type test_component, COEFF alpha) -> TraceElementMatrixProvider< typename PTR::element_type::SCALAR, COEFF >

template<class PTR , class FUNCTOR >
	LoadElementVectorProvider (PTR fe_space_test, size_type test_component, FUNCTOR f) -> LoadElementVectorProvider< typename PTR::element_type::SCALAR, FUNCTOR >

template<typename ptr , typename vector >
	ProductElementMatrixProvider (ptr fe_space_tiral, ptr fe_space_test, vector subproviders) -> ProductElementMatrixProvider< typename ptr::element_type::SCALAR >

template<typename PTR , typename vector >
	ProductElementVectorProvider (PTR fe_space_test, vector subproviders) -> ProductElementVectorProvider< typename PTR::element_type::SCALAR >

Detailed Description

Contains functionality for the implementation of DPG methods.

Typedef Documentation

◆ dim_t

using projects::dpg::dim_t = typedef lf::uscalfe::dim_t

Tpe for (co)-dimensions.

Definition at line 20 of file dpg.h.

◆ dof_map_t

using projects::dpg::dof_map_t = typedef lf::assemble::UniformFEDofHandler::dof_map_t

see lf::assemble

Definition at line 22 of file product_dofhandler.h.

◆ gdof_idx_t

using projects::dpg::gdof_idx_t = typedef lf::uscalfe::gdof_idx_t

Type for indices into global matrices/vectors.

Definition at line 11 of file dpg.h.

◆ glb_idx_t

using projects::dpg::glb_idx_t = typedef lf::uscalfe::glb_idx_t

Type for global index of entities.

Definition at line 23 of file dpg.h.

◆ ldof_idx_t

using projects::dpg::ldof_idx_t = typedef lf::uscalfe::ldof_idx_t

Type for indices referring to entity matrices/vectors.

Definition at line 14 of file dpg.h.

◆ quad_rule_collection_t

using projects::dpg::quad_rule_collection_t = typedef lf::uscalfe::quad_rule_collection_t

data structure for passing collections of quadrature rules, see lf::uscalfe for more information.

Definition at line 31 of file loc_comp_dpg.h.

◆ size_type

typedef lf::uscalfe::size_type projects::dpg::size_type

Type for vector length/matrix sizes.

type for vector length/matrix sizes

Definition at line 17 of file dpg.h.

◆ sub_idx_t

using projects::dpg::sub_idx_t = typedef lf::uscalfe::sub_idx_t

Type for indexing of sub-entities.

Definition at line 26 of file dpg.h.

Function Documentation

◆ BoundaryQuadRule()

std::vector< lf::quad::QuadRule > projects::dpg::BoundaryQuadRule	(	lf::base::RefEl	ref_el,
		const lf::quad::QuadRule &	qr
	)

Constructs a quadrature rule on the boundary of a reference element.

Parameters

ref_el	The reference element on whose boundary a quadrule should be constructed (triangle or quadrilateral).
qr	a quadrule on the reference line segment.

Returns: a vector x s.t. x[i] is a valid quadrule on edge i of the referene element ref_el

This function constructs a quadrature rule on the boundary of a reference element based on another quadrature rule on the reference line segment which is transformed to all edges of the reference element.

Definition at line 13 of file dpg_tools.cc.

References lf::base::RefEl::kQuad(), lf::base::RefEl::kTria(), lf::base::RefEl::NumSubEntities(), lf::quad::QuadRule::Points(), and lf::quad::QuadRule::Weights().

Referenced by projects::dpg::FluxElementMatrixProvider< SCALAR, DIFF_COEFF >::FluxElementMatrixProvider(), and projects::dpg::TraceElementMatrixProvider< SCALAR, COEFF >::TraceElementMatrixProvider().

◆ ConvectionElementMatrixProvider()

template<class PTR , typename CONVECTION_COEFF_1 , typename CONVECTION_COEFF_2 >

projects::dpg::ConvectionElementMatrixProvider	(	PTR	fe_trial,
		PTR	fe_test,
		size_type	trial_component,
		size_type	test_component,
		CONVECTION_COEFF_1	beta_1,
		CONVECTION_COEFF_2	beta_2
	)		-> ConvectionElementMatrixProvider< typename PTR::element_type::SCALAR, CONVECTION_COEFF_1, CONVECTION_COEFF_2 >

◆ DiffusionElementMatrixProvider()

template<class PTR , class DIFF_COEFF >

projects::dpg::DiffusionElementMatrixProvider	(	PTR	fe_space_trial,
		PTR	fe_space_test,
		size_type	trial_component,
		size_type	test_component,
		DIFF_COEFF	alpha
	)		-> DiffusionElementMatrixProvider< typename PTR::element_type::SCALAR, DIFF_COEFF >

◆ DpgElementMatrixProvider()

template<class PTR >

projects::dpg::DpgElementMatrixProvider	(	PTR	stiffness_provider,
		PTR	gramianProvider
	)		-> DpgElementMatrixProvider< typename PTR::element_type::SCALAR >

◆ DpgElementVectorProvider()

template<class PTR1 , class PTR2 >

projects::dpg::DpgElementVectorProvider	(	PTR1	eLoadVectorProvider,
		PTR2	eStiffnessProvider,
		PTR2	gramianProvider
	)		-> DpgElementVectorProvider< typename PTR1::element_type::SCALAR >

◆ ElementErrorEstimators()

template<typename SCALAR >

lf::mesh::utils::CodimMeshDataSet< SCALAR > projects::dpg::ElementErrorEstimators	(	const ProductUniformFEDofHandler &	trial_dofh,
		std::shared_ptr< ProductElementMatrixProvider< SCALAR > >	stiffness_provider,
		std::shared_ptr< ProductElementMatrixProvider< SCALAR > >	gramian_provider,
		std::shared_ptr< ProductElementVectorProvider< SCALAR > >	load_provider,
		const Eigen::Matrix< SCALAR, Eigen::Dynamic, 1 > &	sol_vec
	)

Evaluation of the local DPG error estimators on a mesh.

Parameters

trial_dofh	local-to-global index mapping for the trial space of the DPG method
stiffness_provider	evaluates the extended element stiffness matrix \( B \)
gramian_provider	evaluates the local Gramian matrix \( G \)
load_provider	evaluates the extended element load vector \( l \)
sol_vec	finite element vector of a function in the trial space

Returns: A datastructure of scalar values, which for each cell contains the loacl DPG error estimate for the function represented by sol_vec.

Template Parameters

SCALAR a scalar type like 'double'

Definition at line 327 of file dpg_tools.h.

References ElementErrorEstimators(), projects::dpg::ProductUniformFEDofHandler::GlobalDofIndices(), projects::dpg::ProductUniformFEDofHandler::Mesh(), and projects::dpg::ProductUniformFEDofHandler::NumLocalDofs().

Referenced by ElementErrorEstimators(), projects::dpg::test::TestConververgencePrimalDPGAdaptedNormConvectionDiffusionDirichletBVP(), and projects::dpg::test::TestConververgencePrimalDPGConvectionDiffusionDirichletBVP().

◆ EvalPosteriorError()

template<typename SCALAR >

SCALAR projects::dpg::EvalPosteriorError	(	const std::shared_ptr< const lf::mesh::Mesh > &	mesh_p,
		const lf::mesh::utils::CodimMeshDataSet< SCALAR > &	local_errors
	)

Evaluation of the DPG error estimator.

Parameters

mesh_p	the underlying mesh
local_errors	data structure containing the local DPG error estimator for each cell of the mesh

Returns: The global DPG error estimator.

Template Parameters

Scalar a scalar type like 'double'

Definition at line 374 of file dpg_tools.h.

References EvalPosteriorError().

Referenced by EvalPosteriorError(), projects::dpg::test::TestConververgencePrimalDPGAdaptedNormConvectionDiffusionDirichletBVP(), and projects::dpg::test::TestConververgencePrimalDPGConvectionDiffusionDirichletBVP().

◆ flagEntitiesOnInflowBoundary()

template<typename CONVECTION_COEFF >

lf::mesh::utils::CodimMeshDataSet< bool > projects::dpg::flagEntitiesOnInflowBoundary	(	const std::shared_ptr< const lf::mesh::Mesh > &	mesh_p,
		CONVECTION_COEFF	beta
	)

flag all edges located on the inflow boundary

Parameters

mesh_p	the underlying mesh
beta	the prescribed convection field \( \beta \) .

Returns: a datastructure of boolean values which specifies for each edge, if it lies on the inflow boundary or not.

An edge is located on the inflow boundary, if it is located on the boundary \( \partial \Omega \) and if it holds that \( \beta \cdot n_{\Omega} \) < 0 on that edge.

Note: For non constant convection fields this condition may or may not hold on the whole edge, so we only check this condition in the midpoint of the edge.

Definition at line 155 of file dpg_tools.h.

References lf::mesh::utils::flagEntitiesOnBoundary(), and OuterNormals().

Referenced by flagEntitiesOnOutflowBoundary().

◆ flagEntitiesOnOutflowBoundary()

template<typename CONVECTION_COEFF >

lf::mesh::utils::CodimMeshDataSet< bool > projects::dpg::flagEntitiesOnOutflowBoundary	(	const std::shared_ptr< const lf::mesh::Mesh > &	mesh_p,
		CONVECTION_COEFF	beta
	)

flag all edges located on the outflow boundary

Parameters

mesh_p	the underlying mesh
beta	the prescribed convection field \( \beta \)

Returns: a datastructure of boolean values, which specifies for each edge, if it lies on the outflow boundary or not

An edge is located on the outflow boundary, if it is located on the boundary \( \partial \Omega \) and if it holds that \( \beta \cdot n_{\Omega} \geq 0 \) on that edge.

Note: For non constant convection fields this condition may or may not hold on the whole edge, so we only check this condition in the midpoint of the edge.

Definition at line 204 of file dpg_tools.h.

References lf::mesh::utils::flagEntitiesOnBoundary(), and flagEntitiesOnInflowBoundary().

◆ FluxElementMatrixProvider()

template<class PTR , class DIFF_COEFF >

projects::dpg::FluxElementMatrixProvider	(	PTR	fe_space_trial,
		PTR	fe_space_test,
		size_type	trial_component,
		size_type	test_component,
		DIFF_COEFF	alpha
	)		-> FluxElementMatrixProvider< typename PTR::element_type::SCALAR, DIFF_COEFF >

◆ InitEssentialConditionsFromFunctions()

template<typename SCALAR , typename EDGESELECTOR_DIRICHLET , typename EDGESELECTOR_NEUMANN , typename FUNCTION_G , typename FUNCTION_H >

std::vector< std::pair< bool, SCALAR > > projects::dpg::InitEssentialConditionsFromFunctions	(	const ProductUniformFESpace< SCALAR > &	fes,
		size_type	trace_component,
		size_type	flux_component,
		EDGESELECTOR_DIRICHLET &&	dirichletcondflag,
		EDGESELECTOR_NEUMANN &&	neumanncondflag,
		FUNCTION_G &&	g,
		FUNCTION_H &&	h
	)

Initialization of flags/values for dofs of fluxes and traces of a on a product finite element space whose values are imposed by two specified functions on two specified parts of the boundary.

Template Parameters

SCALAR	scalar type like 'double'
EDGESELECTOR_DIRICHLET	and EDGESELECTOR_NEUMANN predicates returning true for edges with fixed dofs
FUNCTION_G	and FUNCTION_H MeshFunction which define the imposed values on the edges

InitEssentialConditionsFromFunctions

Parameters

dofh	the local_to-global index mapping of the product space
fe_spec_edge_trace	description of the local shape functions for a 'kSegment' type entity for the trace component
fe_spec_edge_flux	description of the local shape functions for a 'kSegment' type entity for the flux component
dirichletcondflag	predicate object whose evaluation operator returns true for all edges on which the degrees of freedom for the trace component should be set to a fixed value
neumanncondflag	predicate object whose evaluation operator returns true for all edges on which the degrees of freedom for the flux component should be set to a fixed value.
g	functor providing the evaluation of the essential conditions for the trace component (dirichlet data)
h	functor providing the evalutation of the essential conditions for the flux component (neumann data)
trace_component	the index of the trace component in the product space
flux_component	the index of the flux component in the product space

Returns: a vector of flag-value pairs, a 'true' first component indicates a fixed dof, the second component provides the value in this case.

The dpg formulation usually involves variables, which represent fluxes or traces. This allows us to impose both Dirichlet and Neumann boundary conditions as essential boundary conditions on the corresponding components and is a generalization of the lehrfempp function lf::fe::InitEssentialConditionFromFunction to product spaces.

This function is meant to supply information for the elimination of essential dofs by means of the function lf::assembl::fix_flagged_solution_components().

Definition at line 272 of file dpg_tools.h.

References projects::dpg::ProductUniformFESpace< SCALAR >::ComponentFESpace(), lf::fe::InitEssentialConditionFromFunction(), projects::dpg::ProductUniformFESpace< SCALAR >::LocGlobMap(), projects::dpg::ProductUniformFEDofHandler::NumDofs(), and projects::dpg::ProductUniformFEDofHandler::Offset().

◆ LoadElementVectorProvider()

template<class PTR , class FUNCTOR >

projects::dpg::LoadElementVectorProvider	(	PTR	fe_space_test,
		size_type	test_component,
		FUNCTOR	f
	)		-> LoadElementVectorProvider< typename PTR::element_type::SCALAR, FUNCTOR >

◆ OuterNormals()

Eigen::MatrixXd projects::dpg::OuterNormals ( const lf::geometry::Geometry & geometry )

Compute the outer normals of a geometry object.

Parameters

geometry The geometry of the cell for which the outer normals are computed. Should be either a triangle or quadrilateral

Returns: The outer normals, packed into the columns of a 2xn matrix, where n is the number of edges of the geometry .

Definition at line 49 of file dpg_tools.cc.

References lf::geometry::Corners(), lf::geometry::Geometry::Jacobian(), lf::base::RefEl::kQuad(), lf::base::RefEl::kTria(), lf::base::RefEl::NodeCoords(), lf::geometry::Geometry::RefEl(), and lf::base::RefEl::SubSubEntity2SubEntity().

Referenced by projects::dpg::TraceElementMatrixProvider< SCALAR, COEFF >::Eval(), and flagEntitiesOnInflowBoundary().

◆ ProductElementMatrixProvider()

template<typename ptr , typename vector >

projects::dpg::ProductElementMatrixProvider	(	ptr	fe_space_tiral,
		ptr	fe_space_test,
		vector	subproviders
	)		-> ProductElementMatrixProvider< typename ptr::element_type::SCALAR >

◆ ProductElementVectorProvider()

template<typename PTR , typename vector >

projects::dpg::ProductElementVectorProvider	(	PTR	fe_space_test,
		vector	subproviders
	)		-> ProductElementVectorProvider< typename PTR::element_type::SCALAR >

◆ ReactionElementMatrixProvider()

template<class PTR , class REACTION_COEFF >

projects::dpg::ReactionElementMatrixProvider	(	PTR	fe_trial,
		PTR	fe_test,
		size_type	trial_component,
		size_type	test_component,
		REACTION_COEFF	gamma
	)		-> ReactionElementMatrixProvider< typename PTR::element_type::SCALAR, REACTION_COEFF >

◆ TraceElementMatrixProvider()

template<class PTR , class COEFF >

projects::dpg::TraceElementMatrixProvider	(	PTR	fe_space_trial,
		PTR	fe_space_test,
		size_type	trial_component,
		size_type	test_component,
		COEFF	alpha
	)		-> TraceElementMatrixProvider< typename PTR::element_type::SCALAR, COEFF >

Namespaces

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ dim_t

◆ dof_map_t

◆ gdof_idx_t

◆ glb_idx_t

◆ ldof_idx_t

◆ quad_rule_collection_t

◆ size_type

◆ sub_idx_t

Function Documentation

◆ BoundaryQuadRule()

◆ ConvectionElementMatrixProvider()

◆ DiffusionElementMatrixProvider()

◆ DpgElementMatrixProvider()

◆ DpgElementVectorProvider()

◆ ElementErrorEstimators()

◆ EvalPosteriorError()

◆ flagEntitiesOnInflowBoundary()

◆ flagEntitiesOnOutflowBoundary()

◆ FluxElementMatrixProvider()

◆ InitEssentialConditionsFromFunctions()

◆ LoadElementVectorProvider()

◆ OuterNormals()

◆ ProductElementMatrixProvider()

◆ ProductElementVectorProvider()

◆ ReactionElementMatrixProvider()

◆ TraceElementMatrixProvider()