HHO_Diffusion

HHO scheme for diffusion equation \(-div(K\nabla u)=f\), with \(K\) piecewise constant. More...

Classes
class	HArDCore2D::HHO_Diffusion
	The HHO_Diffusion class provides tools to implement the HHO method for the diffusion problem. More...

Functions
	HArDCore2D::HHO_Diffusion::HHO_Diffusion (HybridCore &hho, size_t K, int L, CellFType< MatrixRd > kappa, CellFType< double > source, BoundaryConditions BC, FType< double > exact_solution, CellFType< VectorRd > grad_exact_solution, std::string solver_type, bool use_threads, std::ostream &output=std::cout)
	Constructor of the class.
void	HArDCore2D::HHO_Diffusion::assemble (HybridCore &hho)
	Assemble and solve the scheme.
UVector	HArDCore2D::HHO_Diffusion::solve (HybridCore &hho)
double	HArDCore2D::HHO_Diffusion::EnergyNorm (HybridCore &hho, const UVector Xh)
	Discrete energy norm (associated to the diffusion operator) of an hybrid function.
Eigen::SparseMatrix< double >	HArDCore2D::HHO_Diffusion::get_SysMat ()
	Return the (statically condensed) matrix system.
double	HArDCore2D::HHO_Diffusion::get_assembly_time () const
	cpu time to assemble the scheme
double	HArDCore2D::HHO_Diffusion::get_solving_time () const
	cpu time to solve the scheme
double	HArDCore2D::HHO_Diffusion::get_solving_error () const
	residual after solving the scheme
double	HArDCore2D::HHO_Diffusion::get_itime (size_t idx) const
	various intermediate assembly times
const size_t	HArDCore2D::HHO_Diffusion::get_nlocal_cell_dofs ()
	Number of DOFs in each cell.
const size_t	HArDCore2D::HHO_Diffusion::get_nlocal_edge_dofs ()
	Number of DOFs on each edge.
const size_t	HArDCore2D::HHO_Diffusion::get_nhighorder_dofs ()
	Number of DOFs per cell for high-order (K+1) polynomials.
const size_t	HArDCore2D::HHO_Diffusion::get_ntotal_cell_dofs ()
	Total number of cell DOFs over the entire mesh.
const size_t	HArDCore2D::HHO_Diffusion::get_ntotal_edge_dofs ()
	Total number of edge DOFs over the entire mesh.
const size_t	HArDCore2D::HHO_Diffusion::get_ndir_edge_dofs ()
	Total number of edge DOFs for Dirichlet edges.
const size_t	HArDCore2D::HHO_Diffusion::get_ntotal_dofs ()
	Total number of degrees of freedom over the entire mesh.

Detailed Description

HHO scheme for diffusion equation \(-div(K\nabla u)=f\), with \(K\) piecewise constant.

Function Documentation

assemble()

void HArDCore2D::HHO_Diffusion::assemble

(

HybridCore &

hho

)

Assemble and solve the scheme.

EnergyNorm()

double HArDCore2D::HHO_Diffusion::EnergyNorm	(	HybridCore &	hho,
		const UVector	Xh
	)

Discrete energy norm (associated to the diffusion operator) of an hybrid function.

get_assembly_time()

double HArDCore2D::HHO_Diffusion::get_assembly_time ( ) const

inline

cpu time to assemble the scheme

get_itime()

double HArDCore2D::HHO_Diffusion::get_itime ( size_t  idx ) const

inline

various intermediate assembly times

get_ndir_edge_dofs()

const size_t HArDCore2D::HHO_Diffusion::get_ndir_edge_dofs ( )

inline

Total number of edge DOFs for Dirichlet edges.

get_nhighorder_dofs()

const size_t HArDCore2D::HHO_Diffusion::get_nhighorder_dofs ( )

inline

Number of DOFs per cell for high-order (K+1) polynomials.

get_nlocal_cell_dofs()

const size_t HArDCore2D::HHO_Diffusion::get_nlocal_cell_dofs ( )

inline

Number of DOFs in each cell.

get_nlocal_edge_dofs()

const size_t HArDCore2D::HHO_Diffusion::get_nlocal_edge_dofs ( )

inline

Number of DOFs on each edge.

get_ntotal_cell_dofs()

const size_t HArDCore2D::HHO_Diffusion::get_ntotal_cell_dofs ( )

inline

Total number of cell DOFs over the entire mesh.

get_ntotal_dofs()

const size_t HArDCore2D::HHO_Diffusion::get_ntotal_dofs ( )

inline

Total number of degrees of freedom over the entire mesh.

get_ntotal_edge_dofs()

const size_t HArDCore2D::HHO_Diffusion::get_ntotal_edge_dofs ( )

inline

Total number of edge DOFs over the entire mesh.

get_solving_error()

double HArDCore2D::HHO_Diffusion::get_solving_error ( ) const

inline

residual after solving the scheme

get_solving_time()

double HArDCore2D::HHO_Diffusion::get_solving_time ( ) const

inline

cpu time to solve the scheme

get_SysMat()

Eigen::SparseMatrix< double > HArDCore2D::HHO_Diffusion::get_SysMat ( )

inline

Return the (statically condensed) matrix system.

HHO_Diffusion()

HArDCore2D::HHO_Diffusion::HHO_Diffusion	(	HybridCore &	hho,
		size_t	K,
		int	L,
		CellFType< MatrixRd >	kappa,
		CellFType< double >	source,
		BoundaryConditions	BC,
		FType< double >	exact_solution,
		CellFType< VectorRd >	grad_exact_solution,
		std::string	solver_type,
		bool	use_threads,
		std::ostream &	output = std::cout
	)

Constructor of the class.

Parameters

hho	reference to the mesh
K	degree of polynomials on edges
L	degree of polynomials in cells
kappa	diffusion tensor
source	source term
BC	type of boundary conditions
exact_solution	exact solution
grad_exact_solution	gradient of the exact solution
solver_type	type of solver to use for the global system (bicgstab at the moment)
use_threads	optional argument determining if local parallelisation is to be used
output	optional argument for output of messages

solve()

UVector HArDCore2D::HHO_Diffusion::solve

(

HybridCore &

hho

)