Combine local solver and global information for elliptic problems. More...

#include <elliptic.hxx>

Collaboration diagram for GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >:

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Public Member Functions
	Elliptic (const typename TopologyT::constructor_value_type &construct_topo, const typename GeometryT::constructor_value_type &construct_geom, const typename LocalSolverT::constructor_value_type &construct_loc_sol)
	Abstract problem constructor. More...

	Elliptic (const typename TopologyT::constructor_value_type &construct_topo, const typename LocalSolverT::constructor_value_type &construct_loc_sol)
	Abstract problem constructor. More...

	Elliptic (const typename TopologyT::constructor_value_type &construct_topo)
	Abstract problem constructor. More...

void	read_dirichlet_indices (const std::vector< unsigned int > &indices)
	Read indices of Dirichlet type hypernodes/faces. More...

LargeVecT	zero_vector () const
	Returns vector of appropriate size for the predefined problem. More...

template<typename hyNode_index_t = dof_index_t>
LargeVecT	trace_to_flux (const LargeVecT &x_vec, const dof_value_t time=0.)
	Evaluate condensed matrix-vector product. More...

template<typename hyNode_index_t = dof_index_t>
LargeVecT	residual_flux (const LargeVecT &x_vec, const dof_value_t time=0.)
	Evaluate condensed matrix-vector product containing data. More...

template<typename hyNode_index_t = dof_index_t>
std::vector< dof_value_t >	errors (const LargeVecT &x_vec, const dof_value_t time=0.)
	Calculate L2 error of approximated function. More...

dof_index_t	size_of_system () const
	Determine size of condensed system for the skeletal unknowns. More...

std::string	plot_option (const std::string &option, std::string value="")
	Set plot option and return old plot option. More...

void	plot_solution (const LargeVecT &lambda, const dof_value_t time=0.)
	Plot solution in vtu format. More...

unsigned int	get_refinement ()
	Return refinement level. More...

void	set_refinement (unsigned int level)
	Set refinement level. More...

Private Types
using	dof_value_t = typename LargeVecT::value_type
	Floating type is determined by floating type of large vector's entries. More...

Private Member Functions
	HAS_MEMBER_FUNCTION (trace_to_flux, has_trace_to_flux)
	Prepare struct to check for function to exist (cf. compile_time_tricks.hxx). More...

	HAS_MEMBER_FUNCTION (residual_flux, has_residual_flux)
	Prepare struct to check for function to exist (cf. compile_time_tricks.hxx). More...

	HAS_MEMBER_FUNCTION (errors, has_errors)
	Prepare struct to check for function to exist (cf. compile_time_tricks.hxx). More...

Private Attributes
HDGHyperGraph< LocalSolverT::n_glob_dofs_per_node(), TopologyT, GeometryT, NodeDescriptorT, typename LocalSolverT::data_type >	hyper_graph_
	Instantiation of a hypergraph. More...

std::vector< dof_index_t >	dirichlet_indices_
	Vector containing the indices of Dirichlet type nodes. More...

const LocalSolverT	local_solver_
	Instantiation of a local solver. More...

PlotOptions	plot_options
	Struct encoding the options for plotting. More...

Static Private Attributes
static constexpr unsigned int	hyEdge_dim = TopologyT::hyEdge_dim()
	Some constant variable that might be helpful. More...

static constexpr unsigned int	n_dofs_per_node = LocalSolverT::n_glob_dofs_per_node()
	Some constant variable that might be helpful. More...

Detailed Description

template<class TopologyT, class GeometryT, class NodeDescriptorT, class LocalSolverT, typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>
class GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >

Combine local solver and global information for elliptic problems.

Template Parameters

TopologyT	Class type containing topological information.
GeometryT	Class type containing geometrical information.
NodeDescriptorT	Class type containing the information of nodes of hyperedges.
LocalSolverT	Class type of the local solver.
LargeVecT	Clas type of large, global vector.
dof_index_t	Index type of hyperedges. Default is `unsigned` `int`.

Authors: Guido Kanschat, Heidelberg University, 2019–2020.; Andreas Rupp, Heidelberg University, 2019–2020.

Member Typedef Documentation

◆ dof_value_t

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

using GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::dof_value_t = typename LargeVecT::value_type

private

Floating type is determined by floating type of large vector's entries.

Constructor & Destructor Documentation

◆ Elliptic() [1/3]

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::Elliptic	(	const typename TopologyT::constructor_value_type &	construct_topo,
		const typename GeometryT::constructor_value_type &	construct_geom,
		const typename LocalSolverT::constructor_value_type &	construct_loc_sol
	)

inline

Abstract problem constructor.

Constructor for class containing a HyperGraph and a local solver that solve a PDE on a hyperedge.

Parameters

construct_topo	Information to construct a topology.
construct_geom	Information to construct a geometry.
construct_loc_sol	Information to construct a local solver.

◆ Elliptic() [2/3]

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::Elliptic	(	const typename TopologyT::constructor_value_type &	construct_topo,
		const typename LocalSolverT::constructor_value_type &	construct_loc_sol
	)

inline

Abstract problem constructor.

Constructor for class containing a HyperGraph and a local solver that solve a PDE on a hyperedge.

Parameters

construct_topo	Information to construct a topology.
construct_loc_sol	Information to construct a local solver.

◆ Elliptic() [3/3]

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::Elliptic ( const typename TopologyT::constructor_value_type & construct_topo )

inline

Abstract problem constructor.

Constructor for class containing a HyperGraph and a local solver that solve a PDE on a hyperedge.

Parameters

construct_topo Information to construct a topology.

Member Function Documentation

◆ errors()

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

template<typename hyNode_index_t = dof_index_t>

std::vector<dof_value_t> GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::errors	(	const LargeVecT &	x_vec,
		const dof_value_t	time = `0.`
	)

inline

Calculate L2 error of approximated function.

Template Parameters

hyNode_index_t Typename of the hypernode index. Defaults to unsigned int.

Parameters

x_vec	A vector containing the input vector \(x\).
time	Time at which analytical functions will be evaluated.

Return values

error A vector containing the errors.

◆ get_refinement()

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

unsigned int GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::get_refinement ( )

inline

Return refinement level.

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◆ HAS_MEMBER_FUNCTION() [1/3]

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::HAS_MEMBER_FUNCTION	(	errors	,
		has_errors
	)

private

Prepare struct to check for function to exist (cf. compile_time_tricks.hxx).

◆ HAS_MEMBER_FUNCTION() [2/3]

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::HAS_MEMBER_FUNCTION	(	residual_flux	,
		has_residual_flux
	)

private

Prepare struct to check for function to exist (cf. compile_time_tricks.hxx).

◆ HAS_MEMBER_FUNCTION() [3/3]

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::HAS_MEMBER_FUNCTION	(	trace_to_flux	,
		has_trace_to_flux
	)

private

Prepare struct to check for function to exist (cf. compile_time_tricks.hxx).

◆ plot_option()

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

std::string GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::plot_option	(	const std::string &	option,
		std::string	value = `""`
	)

inline

Set plot option and return old plot option.

Function to set and / or read the current plot option.

Parameters

option	A `std::string` containing the plot option to be considered.
value	A `std::string` containing the new value of the considered option. If empty, the old value is kept.

Return values

opt_value A std::string containing the value of the plot option.

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◆ plot_solution()

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

void GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::plot_solution	(	const LargeVecT &	lambda,
		const dof_value_t	time = `0.`
	)

inline

Plot solution in vtu format.

Function that plots the solution of the problem to a predefined file.

Parameters

lambda	A vector of unknowns containing the data vector.
time	Time at which analytical functions are evaluated.

Return values

file	A file in the output directory.

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◆ read_dirichlet_indices()

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

void GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::read_dirichlet_indices ( const std::vector< unsigned int > & indices )

inline

Read indices of Dirichlet type hypernodes/faces.

Read the indices ot the hypernodes/faces that are of Dirichlet type and therefore do not contain degrees of freedom that are allowed to change within iterations of the iterative solver and other processes. In contrast, these degrees of freedom are set by the user.

The user creates a vector that contains the coefficients of the corresponding degrees of freedom (read by this function) and defines the Dirichlet values by this choice. The remaining elements of the global vector of unknowns (which is not the vector indices are supposed to be zero).

Parameters

indices A vector containing the (global) indices of Dirichlet type hypernodes.

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◆ residual_flux()

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

template<typename hyNode_index_t = dof_index_t>

LargeVecT GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::residual_flux	(	const LargeVecT &	x_vec,
		const dof_value_t	time = `0.`
	)

inline

Evaluate condensed matrix-vector product containing data.

Function that evaluates the condensed, matrix-free version of the matrix-vector product \(A x - f = y\), where \(A\) is the condensed matrix of the LDG-H method, \(x\) is the vector of parameters to define the skeletal variable \(\lambda\), \(f\) is the right-hand side of the problem and \(y\) is the resulting vector, which has the same size as the input vector \(x\).

Template Parameters

hyNode_index_t Typename of the hypernode index. Defaults to unsigned int.

Parameters

x_vec	A vector containing the input vector \(x\).
time	Time at which analytical functions will be evaluated.

Return values

y_vec A vector containing the product \(y = Ax\).

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◆ set_refinement()

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

void GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::set_refinement ( unsigned int level )

inline

Set refinement level.

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◆ size_of_system()

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

dof_index_t GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::size_of_system ( ) const

inline

Determine size of condensed system for the skeletal unknowns.

Function that returns the size \(n\) of the \(n \times n\) linear, sparse system \(Ax = b\) that is solved by the program in a matrix-free fashion.

This function is needed to define a LinearOperator from Python's scipy.sparse.linalg package which can be used to define iterative solvers for sparse systems.

Return values

n	Size of the condensed (square) system of equations.

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◆ trace_to_flux()

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

template<typename hyNode_index_t = dof_index_t>

LargeVecT GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::trace_to_flux	(	const LargeVecT &	x_vec,
		const dof_value_t	time = `0.`
	)

inline

Evaluate condensed matrix-vector product.

Function that evaluates the condensed, matrix-free version of the matrix-vector product \(A x = y\), where \(A\) is the condensed matrix of the LDG-H method, \(x\) is the vector of parameters to define the skeletal variable \(\lambda\), and \(y\) is the resulting vector, which has the same size as the input vector \(x\).

Template Parameters

hyNode_index_t Typename of the hypernode index. Defaults to unsigned int.

Parameters

x_vec	A vector containing the input vector \(x\).
time	Time at which given analyitic functions will be evaluated.

Return values

y_vec A vector containing the product \(y = Ax\).

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◆ zero_vector()

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

LargeVecT GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::zero_vector ( ) const

inline

Returns vector of appropriate size for the predefined problem.

Returns a vector containing only the value zero, but of the size \(n\) which is also the number which is returned if size_of_system() is evaluated.

Return values

zero	A vector of the correct size for the unknowns of the given problem.

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Member Data Documentation

◆ dirichlet_indices_

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

std::vector<dof_index_t> GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::dirichlet_indices_

private

Vector containing the indices of Dirichlet type nodes.

◆ hyEdge_dim

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

constexpr unsigned int GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::hyEdge_dim = TopologyT::hyEdge_dim()

staticconstexprprivate

Some constant variable that might be helpful.

◆ hyper_graph_

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

HDGHyperGraph<LocalSolverT::n_glob_dofs_per_node(), TopologyT, GeometryT, NodeDescriptorT, typename LocalSolverT::data_type> GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::hyper_graph_

private

Instantiation of a hypergraph.

◆ local_solver_

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

const LocalSolverT GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::local_solver_

private

Instantiation of a local solver.

◆ n_dofs_per_node

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

constexpr unsigned int GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::n_dofs_per_node = LocalSolverT::n_glob_dofs_per_node()

staticconstexprprivate

Some constant variable that might be helpful.

◆ plot_options

template<class TopologyT , class GeometryT , class NodeDescriptorT , class LocalSolverT , typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>

PlotOptions GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::plot_options

private

Struct encoding the options for plotting.

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

/home/runner/work/HyperHDG/HyperHDG/include/HyperHDG/global_loop/elliptic.hxx

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

template<class TopologyT, class GeometryT, class NodeDescriptorT, class LocalSolverT, typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int> class GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >

Member Typedef Documentation

◆ dof_value_t

Constructor & Destructor Documentation

◆ Elliptic() [1/3]

◆ Elliptic() [2/3]

◆ Elliptic() [3/3]

Member Function Documentation

◆ errors()

◆ get_refinement()

◆ HAS_MEMBER_FUNCTION() [1/3]

◆ HAS_MEMBER_FUNCTION() [2/3]

◆ HAS_MEMBER_FUNCTION() [3/3]

◆ plot_option()

◆ plot_solution()

◆ read_dirichlet_indices()

◆ residual_flux()

◆ set_refinement()

◆ size_of_system()

◆ trace_to_flux()

◆ zero_vector()

Member Data Documentation

◆ dirichlet_indices_

◆ hyEdge_dim

◆ hyper_graph_

◆ local_solver_

◆ n_dofs_per_node

◆ plot_options

template<class TopologyT, class GeometryT, class NodeDescriptorT, class LocalSolverT, typename LargeVecT = std::vector<double>, typename dof_index_t = unsigned int>
class GlobalLoop::Elliptic< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >