Combine local solver and global information for nonlinear eigenvalue problems. More...

#include <nonlinear_eigenvalue.hxx>

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

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Public Member Functions
	NonlinearEigenvalue (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...

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

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

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

template<typename hyNode_index_t = dof_index_t>
LargeVecT	jacobian_of_trace_to_flux (const LargeVecT &x_vec, const dof_value_t eig, const LargeVecT &x_val, const dof_value_t eig_val)
	Evaluate condensed matrix-vector product. More...

template<typename hyNode_index_t = dof_index_t>
LargeVecT	make_initial (const LargeVecT &x_vec, const dof_value_t eig=0.)
	Create initial starting value for Newton's methods. 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 std::vector< dof_value_t > &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 (jacobian_of_trace_to_flux, has_jacobian_of_trace_to_flux)
	Prepare struct to check for function to exist (cf. compile_time_tricks.hxx). More...

	HAS_MEMBER_FUNCTION (make_initial, has_make_initial)
	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...

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

PlotOptions	plot_options
	Struct encoding the options for plotting. 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::NonlinearEigenvalue< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >

Combine local solver and global information for nonlinear eigenvalue 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::NonlinearEigenvalue< 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

◆ NonlinearEigenvalue() [1/3]

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

GlobalLoop::NonlinearEigenvalue< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::NonlinearEigenvalue	(	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.

◆ NonlinearEigenvalue() [2/3]

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

GlobalLoop::NonlinearEigenvalue< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::NonlinearEigenvalue	(	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.

◆ NonlinearEigenvalue() [3/3]

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

GlobalLoop::NonlinearEigenvalue< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::NonlinearEigenvalue ( 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

◆ 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::NonlinearEigenvalue< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::get_refinement ( )

inline

Return refinement level.

◆ 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::NonlinearEigenvalue< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::HAS_MEMBER_FUNCTION	(	jacobian_of_trace_to_flux	,
		has_jacobian_of_trace_to_flux
	)

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::NonlinearEigenvalue< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::HAS_MEMBER_FUNCTION	(	make_initial	,
		has_make_initial
	)

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::NonlinearEigenvalue< 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).

◆ jacobian_of_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::NonlinearEigenvalue< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::jacobian_of_trace_to_flux	(	const LargeVecT &	x_vec,
		const dof_value_t	eig,
		const LargeVecT &	x_val,
		const dof_value_t	eig_val
	)

inline

Evaluate condensed matrix-vector product.

This function corresponds to evaluating the Jacobian at point x_val, eig_val in direction x_vec, eig.

Parameters

x_vec	Direction in which Jacobian is evaluated.
eig	Direction in which Jacobian is evaluated.
x_val	Point at which Jacobian is evaluated.
eig_val	Point at which Jacobian is evaluated.

Return values

y_vec Corresponds to directional derivative.

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◆ make_initial()

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::NonlinearEigenvalue< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::make_initial	(	const LargeVecT &	x_vec,
		const dof_value_t	eig = `0.`
	)

inline

Create initial starting value for Newton's methods.

Parameters

x_vec	A vector containing the input vector \(x\) which should be zero.
eig	Eigenvalue (approximation).

Return values

y_vec A vector containing initial flux vector.

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◆ 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::NonlinearEigenvalue< 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::NonlinearEigenvalue< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::plot_solution	(	const std::vector< dof_value_t > &	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.

Return values

file	A file in the output directory.

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

inline

Set refinement level.

◆ 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::NonlinearEigenvalue< 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	An `int` which Python needs and actually is a parsed `unsigned` `int`.

◆ 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::NonlinearEigenvalue< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::trace_to_flux	(	const LargeVecT &	x_vec,
		const dof_value_t	eig = `0.`
	)

inline

Evaluate condensed matrix-vector product.

This function corresponds to the evaluation of the residual. Here, the vector contains the eigenfunction representation, while the floating point is the eigenvalue.

Parameters

x_vec	A vector containing the input vector.
eig	Eigenvalue.

Return values

y_vec A vector containing the residual.

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Member Data Documentation

◆ 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::NonlinearEigenvalue< 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::NonlinearEigenvalue< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >::local_solver_

private

Instantiation of a local solver.

◆ plot_options

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

PlotOptions GlobalLoop::NonlinearEigenvalue< 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/nonlinear_eigenvalue.hxx

Public Member Functions

Private Types

Private Member Functions

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::NonlinearEigenvalue< TopologyT, GeometryT, NodeDescriptorT, LocalSolverT, LargeVecT, dof_index_t >

Member Typedef Documentation

◆ dof_value_t

Constructor & Destructor Documentation

◆ NonlinearEigenvalue() [1/3]

◆ NonlinearEigenvalue() [2/3]

◆ NonlinearEigenvalue() [3/3]

Member Function Documentation

◆ get_refinement()

◆ HAS_MEMBER_FUNCTION() [1/3]

◆ HAS_MEMBER_FUNCTION() [2/3]

◆ HAS_MEMBER_FUNCTION() [3/3]

◆ jacobian_of_trace_to_flux()

◆ make_initial()

◆ plot_option()

◆ plot_solution()

◆ set_refinement()

◆ size_of_system()

◆ trace_to_flux()

Member Data Documentation

◆ hyper_graph_

◆ local_solver_

◆ plot_options

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