Local solver for the equation that governs the bending of an elastic Bernoulli beam. More...

#include <bernoulli_beams.hxx>

Collaboration diagram for LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_t >:

[legend]

Classes
struct	data_type
	Define type of (hyperedge related) data that is stored in HyDataContainer. More...

struct	error_def
	Define how errors are evaluated. More...

struct	node_element
	Define type of node elements, especially with respect to nodal shape functions. More...

Public Types
typedef lSol_float_t	constructor_value_type
	Class is constructed using a single double indicating the penalty parameter. More...

Public Member Functions
	BernoulliBendingBeam (const constructor_value_type &tau=1.)
	Constructor for local solver. More...

template<class hyEdgeT , typename SmallMatInT , typename SmallMatOutT >
SmallMatOutT &	trace_to_flux (const SmallMatInT &lambda_values_in, SmallMatOutT &lambda_values_out, hyEdgeT &hyper_edge, const lSol_float_t time=0.) const
	Evaluate local contribution to matrix–vector multiplication. More...

template<class hyEdgeT , typename SmallMatInT , typename SmallMatOutT >
SmallMatOutT &	residual_flux (const SmallMatInT &lambda_values_in, SmallMatOutT &lambda_values_out, hyEdgeT &hyper_edge, const lSol_float_t time=0.) const
	Evaluate local contribution to residual. More...

template<class hyEdgeT >
std::array< lSol_float_t, 1U >	errors (const std::array< std::array< lSol_float_t, n_glob_dofs_per_node()>, 2 *hyEdge_dimT > &lambda_values, hyEdgeT &hyper_edge, const lSol_float_t time=0.) const
	Local squared contribution to the L2 error. More...

template<typename abscissa_float_t , std::size_t sizeT, class input_array_t , class hyEdgeT >
std::array< std::array< lSol_float_t, Hypercube< hyEdge_dimT >::pow(sizeT)>, BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t >::system_dimension()>	bulk_values (const std::array< abscissa_float_t, sizeT > &abscissas, const input_array_t &lambda_values, hyEdgeT &hyper_edge, const lSol_float_t time=0.) const
	Evaluate local local reconstruction at tensorial products of abscissas. More...

Static Public Member Functions
static constexpr unsigned int	hyEdge_dim ()
	Return template parameter `hyEdge_dimT`. More...

static constexpr unsigned int	n_glob_dofs_per_node ()
	Evaluate amount of global degrees of freedom per hypernode. More...

static constexpr unsigned int	system_dimension ()
	Dimension of of the solution evaluated with respect to a hyperedge. More...

static constexpr unsigned int	node_system_dimension ()
	Dimension of of the solution evaluated with respect to a hypernode. 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...

template<class hyEdgeT , typename SmallMatT >
std::array< std::array< double, bilaplacian_sol_t::n_glob_dofs_per_node()>, 2 *hyEdge_dimT >	node_dof_to_edge_dof (const SmallMatT &lambda, hyEdgeT &hyper_edge, const unsigned int outer_index) const
	Do the preprocessing to transfer global to local dofs. More...

template<class hyEdgeT , typename SmallMatT >
SmallMatT &	edge_dof_to_node_dof (const std::array< std::array< double, bilaplacian_sol_t::n_glob_dofs_per_node()>, 2 *hyEdge_dimT > &lambda, SmallMatT &lambda_values_out, hyEdgeT &hyper_edge, const unsigned int outer_index) const
	Do the postprocessing to transfer local to global dofs. More...

Private Attributes
const bilaplacian_sol_t	bilaplacian_solver
	The bilaplacian solver that solves the locally defined PDE. More...

Detailed Description

template<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>
class LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_t >

Local solver for the equation that governs the bending of an elastic Bernoulli beam.

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

Member Typedef Documentation

◆ constructor_value_type

template<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

typedef lSol_float_t LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_t >::constructor_value_type

Class is constructed using a single double indicating the penalty parameter.

Constructor & Destructor Documentation

◆ BernoulliBendingBeam()

template<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_t >::BernoulliBendingBeam ( const constructor_value_type & tau = 1. )

inline

Constructor for local solver.

Parameters

tau	Penalty parameter of HDG scheme.

Member Function Documentation

◆ bulk_values()

template<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

template<typename abscissa_float_t , std::size_t sizeT, class input_array_t , class hyEdgeT >

std::array<std::array<lSol_float_t, Hypercube<hyEdge_dimT>::pow(sizeT)>, BernoulliBendingBeam<hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t>:: system_dimension()> LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_t >::bulk_values	(	const std::array< abscissa_float_t, sizeT > &	abscissas,
		const input_array_t &	lambda_values,
		hyEdgeT &	hyper_edge,
		const lSol_float_t	time = `0.`
	)		const

inline

Evaluate local local reconstruction at tensorial products of abscissas.

Template Parameters

absc_float_t	Floating type for the abscissa values.
abscissas_sizeT	Size of the array of array of abscissas.
input_array_t	Type of input array.
hyEdgeT	The geometry type / typename of the considered hyEdge's geometry.

Parameters

abscissas	Abscissas of the supporting points.
lambda_values	The values of the skeletal variable's coefficients.
hyper_edge	The geometry of the considered hyperedge (of typename GeomT).
time	Time.

Return values

func_values Function values at tensorial points.

◆ edge_dof_to_node_dof()

template<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

template<class hyEdgeT , typename SmallMatT >

SmallMatT& LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_t >::edge_dof_to_node_dof	(	const std::array< std::array< double, bilaplacian_sol_t::n_glob_dofs_per_node()>, 2 *hyEdge_dimT > &	lambda,
		SmallMatT &	lambda_values_out,
		hyEdgeT &	hyper_edge,
		const unsigned int	outer_index
	)		const

inlineprivate

Do the postprocessing to transfer local to global dofs.

◆ errors()

template<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

template<class hyEdgeT >

std::array<lSol_float_t, 1U> LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_t >::errors	(	const std::array< std::array< lSol_float_t, n_glob_dofs_per_node()>, 2 *hyEdge_dimT > &	lambda_values,
		hyEdgeT &	hyper_edge,
		const lSol_float_t	time = `0.`
	)		const

inline

Local squared contribution to the L2 error.

Template Parameters

hyEdgeT The geometry type / typename of the considered hyEdge's geometry.

Parameters

lambda_values	The values of the skeletal variable's coefficients.
hyper_edge	The geometry of the considered hyperedge (of typename GeomT).
time	Time at which analytic functions are evaluated.

Return values

vec_b Local part of vector b.

◆ HAS_MEMBER_FUNCTION() [1/3]

template<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_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<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_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<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_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).

◆ hyEdge_dim()

template<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

static constexpr unsigned int LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_t >::hyEdge_dim ( )

inlinestaticconstexpr

Return template parameter hyEdge_dimT.

Return values

hyEdge_dimT Dimension of hypergraph's hyperedges.

◆ n_glob_dofs_per_node()

template<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

static constexpr unsigned int LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_t >::n_glob_dofs_per_node ( )

inlinestaticconstexpr

Evaluate amount of global degrees of freedom per hypernode.

This number must be equal to HyperNodeFactory::n_glob_dofs_per_node()() of the HyperNodeFactory cooperating with this object.

Return values

n_dofs Number of global degrees of freedom per hypernode.

◆ node_dof_to_edge_dof()

template<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

template<class hyEdgeT , typename SmallMatT >

std::array<std::array<double, bilaplacian_sol_t::n_glob_dofs_per_node()>, 2 * hyEdge_dimT> LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_t >::node_dof_to_edge_dof	(	const SmallMatT &	lambda,
		hyEdgeT &	hyper_edge,
		const unsigned int	outer_index
	)		const

inlineprivate

Do the preprocessing to transfer global to local dofs.

◆ node_system_dimension()

template<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

static constexpr unsigned int LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_t >::node_system_dimension ( )

inlinestaticconstexpr

Dimension of of the solution evaluated with respect to a hypernode.

◆ residual_flux()

template<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

template<class hyEdgeT , typename SmallMatInT , typename SmallMatOutT >

SmallMatOutT& LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_t >::residual_flux	(	const SmallMatInT &	lambda_values_in,
		SmallMatOutT &	lambda_values_out,
		hyEdgeT &	hyper_edge,
		const lSol_float_t	time = `0.`
	)		const

inline

Evaluate local contribution to residual.

◆ system_dimension()

template<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

static constexpr unsigned int LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_t >::system_dimension ( )

inlinestaticconstexpr

Dimension of of the solution evaluated with respect to a hyperedge.

◆ trace_to_flux()

template<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

template<class hyEdgeT , typename SmallMatInT , typename SmallMatOutT >

SmallMatOutT& LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_t >::trace_to_flux	(	const SmallMatInT &	lambda_values_in,
		SmallMatOutT &	lambda_values_out,
		hyEdgeT &	hyper_edge,
		const lSol_float_t	time = `0.`
	)		const

inline

Evaluate local contribution to matrix–vector multiplication.

Template Parameters

hyEdgeT	The geometry type / typename of the considered hyEdge's geometry.
SmallMatInT	Data type of `lambda_values_in`.
SmallMatOutT	Data type of `lambda_values_out`.

Parameters

lambda_values_in	Local part of vector x.
lambda_values_out	Local part that will be added to A * x.
hyper_edge	HyperEdge that is considered.
time	Time at which analytic functions are evaluated.

Return values

vecAx Local part of vector A * x.

Member Data Documentation

◆ bilaplacian_solver

template<unsigned int hyEdge_dimT, unsigned int space_dim, unsigned int poly_deg, unsigned int quad_deg, typename lSol_float_t = double, typename bilaplacian_sol_t = BilaplacianUniform<hyEdge_dimT, poly_deg, quad_deg, lSol_float_t>>

const bilaplacian_sol_t LocalSolver::BernoulliBendingBeam< hyEdge_dimT, space_dim, poly_deg, quad_deg, lSol_float_t, bilaplacian_sol_t >::bilaplacian_solver

private

The bilaplacian solver that solves the locally defined PDE.

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

/home/runner/work/HyperHDG/HyperHDG/include/HyperHDG/local_solver/bernoulli_beams.hxx

Classes

Public Types

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ constructor_value_type

Constructor & Destructor Documentation

◆ BernoulliBendingBeam()

Member Function Documentation

◆ bulk_values()

◆ edge_dof_to_node_dof()

◆ errors()

◆ HAS_MEMBER_FUNCTION() [1/3]

◆ HAS_MEMBER_FUNCTION() [2/3]

◆ HAS_MEMBER_FUNCTION() [3/3]

◆ hyEdge_dim()

◆ n_glob_dofs_per_node()

◆ node_dof_to_edge_dof()

◆ node_system_dimension()

◆ residual_flux()

◆ system_dimension()

◆ trace_to_flux()

Member Data Documentation

◆ bilaplacian_solver