HHO2D

Class providing helper methods and assemble and solve routines for general 2D HHO schemes. More...

Classes
class	HHO2D

Typedefs
typedef std::function< Eigen::MatrixXd(Cell *, ElementQuad &)>	MatrixFType
	type for the global operator as a function of a Cell and an ElementQuad
typedef std::function< Eigen::VectorXd(Cell *, ElementQuad &)>	VectorFType
	type for the load vector as a function of a Cell and an ElementQuad

Functions
	HHO2D::HHO2D (HybridCore &, const size_t, const size_t, const bool use_threads=true, size_t doeT=0, size_t doeF=0)
	Class constructor: initialises the model by providing a HybridCore object, and the exact solution and boundary conditions of the model.
void	HHO2D::assemble ()
	A general assemble routine that calculates the statically condensed matrices required by solve.
UVector	HHO2D::solve ()
	Solves the statically condensed system.
UVector	HHO2D::neumann_solve ()
	Solves the system when the model is ill posed (not yet running)
double	HHO2D::energy_norm (const UVector)
	Returns the energy norm of a given UVector.
void	HHO2D::set_global_operator (const MatrixFType &)
	Set the global operator.
void	HHO2D::set_load_vector (const VectorFType &)
	Set the load vector.
void	HHO2D::plot (const std::string, const UVector &, const FType< double > &)
	Plot the numerical and exact solutions.
VectorFType	HHO2D::standard_load_vector (const CellFType< double > &)
	Returns the standard load vector (f, v_T)_T with no Neumann boundary conditions.
VectorFType	HHO2D::standard_load_vector (const CellFType< double > &, const CellFType< VectorRd > &, const BoundaryConditions &)
	Returns the standard load vector (f, v_T)_T.
VectorFType	HHO2D::standard_load_vector (const CellFType< double > &, const FType< double > &, const BoundaryConditions &)
	Returns the standard load vector (f, v_T)_T.
void	HHO2D::set_dirichlet (const FType< double > &, const size_t)
	Set the Dirichlet boundary conditions.
void	HHO2D::set_dirichlet (const size_t)
	Set the Dirichlet boundary condition to zero.
Eigen::SparseMatrix< double >	HHO2D::get_SysMat ()
	Return the (statically condensed) matrix system.
double	HHO2D::get_assembly_time () const
	CPU time to assemble the scheme.
double	HHO2D::get_solving_time () const
	CPU time to solve the scheme.
double	HHO2D::get_solving_error () const
	Residual after solving the scheme.

Detailed Description

Class providing helper methods and assemble and solve routines for general 2D HHO schemes.

The HHO2D class contains methods applicable to a general 2D HHO model. It contains assemble and solve routines usable by any scheme. The global operator and load vector are passed to the model through setters and are then accessible by assemble and solve. The class also contains helper methods for writing HHO schemes.

Typedef Documentation

MatrixFType

typedef std::function<Eigen::MatrixXd(Cell *, ElementQuad &)> MatrixFType

type for the global operator as a function of a Cell and an ElementQuad

VectorFType

typedef std::function<Eigen::VectorXd(Cell *, ElementQuad &)> VectorFType

type for the load vector as a function of a Cell and an ElementQuad

Function Documentation

assemble()

void HHO2D::assemble

(

)

A general assemble routine that calculates the statically condensed matrices required by solve.

energy_norm()

double HHO2D::energy_norm

(

const UVector

Xh

)

Returns the energy norm of a given UVector.

get_assembly_time()

double HHO2D::get_assembly_time ( ) const

inline

CPU time to assemble the scheme.

get_solving_error()

double HHO2D::get_solving_error ( ) const

inline

Residual after solving the scheme.

get_solving_time()

double HHO2D::get_solving_time ( ) const

inline

CPU time to solve the scheme.

get_SysMat()

Eigen::SparseMatrix< double > HHO2D::get_SysMat ( )

inline

Return the (statically condensed) matrix system.

HHO2D()

HHO2D::HHO2D	(	HybridCore &	hho,
		const size_t	L,
		const size_t	K,
		const bool	use_threads = true,
		size_t	doeT = 0,
		size_t	doeF = 0
	)

Class constructor: initialises the model by providing a HybridCore object, and the exact solution and boundary conditions of the model.

Parameters

hho	A reference to the HybridCore object containing mesh data
L	Cell polynomial degree
K	Edge polynomial degree
use_threads	Optional argument to indicate if threads should be used
doeT	Optional argument to set cell quadrature degree. Default is L + K + 1
doeF	Optional argument to set edge quadrature degree. Default is 2 * K + 1

neumann_solve()

UVector HHO2D::neumann_solve

(

)

Solves the system when the model is ill posed (not yet running)

plot()

void HHO2D::plot	(	const std::string	plot_file,
		const UVector &	sol,
		const FType< double > &	exact_sol
	)

Plot the numerical and exact solutions.

Parameters

plot_file	Plot file
sol	Numerical solution
exact_sol	Exact solution

set_dirichlet() [1/2]

void HHO2D::set_dirichlet	(	const FType< double > &	f,
		const size_t	n_dir_edges
	)

Set the Dirichlet boundary conditions.

Parameters

f	Function on the Dirichlet BC edges
n_dir_edges	Number of Dirichlet edges

set_dirichlet() [2/2]

void HHO2D::set_dirichlet

(

const size_t

n_dir_edges

)

Set the Dirichlet boundary condition to zero.

Parameters

n_dir_edges

Number of Dirichlet edges

set_global_operator()

void HHO2D::set_global_operator

(

const MatrixFType &

AT

)

Set the global operator.

set_load_vector()

void HHO2D::set_load_vector

(

const VectorFType &

bT

)

Set the load vector.

solve()

UVector HHO2D::solve

(

)

Solves the statically condensed system.

standard_load_vector() [1/3]

VectorFType HHO2D::standard_load_vector

(

const CellFType< double > &

source

)

Returns the standard load vector (f, v_T)_T with no Neumann boundary conditions.

Parameters

source

Source term

standard_load_vector() [2/3]

VectorFType HHO2D::standard_load_vector	(	const CellFType< double > &	source,
		const CellFType< VectorRd > &	f,
		const BoundaryConditions &	BC
	)

Returns the standard load vector (f, v_T)_T.

Parameters

source	Source term
f	Gradient to be dotted with the normal vector on each Neumann edge
BC	A reference to the BC to determine Neumann edges

standard_load_vector() [3/3]

VectorFType HHO2D::standard_load_vector	(	const CellFType< double > &	source,
		const FType< double > &	f,
		const BoundaryConditions &	BC
	)

Returns the standard load vector (f, v_T)_T.

Parameters

source	Source term
f	Function on the Neumann BC edges
BC	A reference to the BC to determine Neumann edges