Build discrete stiffness matrices and handled boundary conditions for diffusion term in CDO vertex-based and vertex+cell schemes. More...

#include "cs_defs.h"
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <math.h>
#include <bft_mem.h>
#include <bft_printf.h>
#include "cs_cdo_scheme_geometry.h"
#include "cs_math.h"
#include "cs_property.h"
#include "cs_cdo_diffusion.h"

Include dependency graph for cs_cdo_diffusion.c:

Functions
static cs_locmat_t *	_compute_wbs_stiffness (const cs_cdo_quantities_t quant, const cs_cell_mesh_t cm, const cs_real_3_t tensor, cs_cdo_diff_t diff)
	Compute the stiffness matrix on this cell using a Whitney Barycentric Subdivision (WBS) algo. More...

static cs_locmat_t *	_compute_vcb_stiffness (const cs_cdo_quantities_t quant, const cs_cell_mesh_t cm, const cs_real_3_t tensor, cs_cdo_diff_t diff)
	Compute the stiffness matrix on the current cell using a Whitney Barycentric Subdivision (WBS) algo and a V+C CDO scheme. More...

static void	_ntrgrd_cost_algo (short int f, const cs_cell_mesh_t cm, const cs_real_3_t mnu, double beta, cs_cdo_diff_t diff, cs_locmat_t *ntrgrd)
	Compute the normal trace operator for a given border face when a COST algo. is used for reconstructing the degrees of freedom. More...

static void	_ntrgrd_wbs_algo (const cs_face_mesh_t fm, const cs_cell_mesh_t cm, const cs_real_3_t pty_nuf, cs_cdo_diff_t diff, cs_locmat_t ntrgrd)
	Compute the normal trace operator for a given border face when a WBS algo. is used for reconstructing the degrees of freedom. More...

static void	_ntrgrd_vcb_algo (const cs_face_mesh_t fm, const cs_cell_mesh_t cm, const cs_real_3_t pty_nuf, cs_cdo_diff_t diff, cs_locmat_t ntrgrd)
	Compute the normal trace operator for a given border face when a WBS algo. and a V+C scheme is considered. More...

cs_cdo_diff_t *	cs_cdo_diffusion_builder_init (const cs_cdo_connect_t *connect, cs_space_scheme_t space_scheme, bool is_uniform, const cs_param_hodge_t h_info, const cs_param_bc_enforce_t bc_enforce)
	Initialize a builder structure used to build the stiffness matrix. More...

cs_cdo_diff_t *	cs_cdo_diffusion_builder_free (cs_cdo_diff_t *diff)
	Free a cs_cdo_diff_t structure. More...

cs_hodge_builder_t *	cs_cdo_diffusion_get_hodge_builder (cs_cdo_diff_t *diff)
	Get the related Hodge builder structure. More...

void	cs_cdo_diffusion_get_tmp_buffers (const cs_cdo_diff_t diff, cs_real_3_t tmp_vec, cs_real_t *tmp_sca)
	Get temporary buffers attached to a cs_cdo_diff_t structure. More...

void	cs_cdo_diffusion_build_c2bcbf (const cs_cdo_connect_t connect, const cs_cdo_bc_list_t dir_face, cs_lnum_t p_c2bcbf_idx[], cs_lnum_t p_c2bcbf_ids[])
	Define a cell –> Dirichlet boundary faces connectivity. More...

cs_locmat_t *	cs_cdo_diffusion_build_local (const cs_cdo_quantities_t quant, const cs_cell_mesh_t cm, const cs_real_3_t tensor, cs_cdo_diff_t diff)
	Define the local (cellwise) stiffness matrix. More...

void	cs_cdo_diffusion_weak_bc (cs_lnum_t f_id, const cs_cell_mesh_t cm, const cs_real_t matpty[3][3], cs_cdo_diff_t diff, cs_cdo_locsys_t *csys)
	Define the local (cellwise) "normal trace gradient" matrix taking into account Dirichlet BCs by a weak enforcement using Nitsche technique (symmetrized or not) More...

void	cs_cdo_diffusion_cellwise_flux (const cs_cell_mesh_t cm, const cs_dface_t dface, const cs_real_t pty_tens[3][3], const double p_v, const double p_c, cs_cdo_diff_t diff, double *c_flux)
	Compute the diffusive flux across dual faces for a given cell The computation takes into account a subdivision into tetrahedra of the current cell based on p_{ef,c}. More...

double	cs_cdo_diffusion_face_flux (const cs_face_mesh_t fm, const cs_real_t pty_tens[3][3], const double p_v, const double p_f, const double p_c, cs_cdo_diff_t *diff)
	Compute the diffusive flux across a face (based on a subdivision into tetrahedra of the volume p_{f,c}) More...

Detailed Description

Build discrete stiffness matrices and handled boundary conditions for diffusion term in CDO vertex-based and vertex+cell schemes.

Function Documentation

◆ _compute_vcb_stiffness()

static cs_locmat_t* _compute_vcb_stiffness	(	const cs_cdo_quantities_t *	quant,
		const cs_cell_mesh_t *	cm,
		const cs_real_3_t *	tensor,
		cs_cdo_diff_t *	diff
	)

static

Compute the stiffness matrix on the current cell using a Whitney Barycentric Subdivision (WBS) algo and a V+C CDO scheme.

Parameters

[in]	quant	pointer to a cs_cdo_quantities_t struct.
[in]	cm	pointer to a cs_cell_mesh_t struct.
[in]	tensor	3x3 matrix attached to the diffusion property
[in,out]	diff	auxiliary structure used to build the diff. term

Returns: a pointer to a local stiffness matrix

◆ _compute_wbs_stiffness()

static cs_locmat_t* _compute_wbs_stiffness	(	const cs_cdo_quantities_t *	quant,
		const cs_cell_mesh_t *	cm,
		const cs_real_3_t *	tensor,
		cs_cdo_diff_t *	diff
	)

static

Compute the stiffness matrix on this cell using a Whitney Barycentric Subdivision (WBS) algo.

(end ignore by Doxygen)

Parameters

[in]	quant	pointer to a cs_cdo_quantities_t struct.
[in]	cm	pointer to a cs_cell_mesh_t struct.
[in]	tensor	3x3 matrix attached to the diffusion property
[in,out]	diff	auxiliary structure used to build the diff. term

Returns: a pointer to a local stiffness matrix

◆ _ntrgrd_cost_algo()

static void _ntrgrd_cost_algo	(	short int	f,
		const cs_cell_mesh_t *	cm,
		const cs_real_3_t	mnu,
		double	beta,
		cs_cdo_diff_t *	diff,
		cs_locmat_t *	ntrgrd
	)

static

Compute the normal trace operator for a given border face when a COST algo. is used for reconstructing the degrees of freedom.

Parameters

[in]	f	face id in the cellwise numbering
[in]	cm	pointer to a cs_cell_mesh_t structure
[in]	mnu	property tensor times the face normal
[in]	beta	value of the stabilizarion coef. related to reco.
[in,out]	diff	pointer to a builder structure
[in,out]	ntrgrd	local matrix related to the normal trace op.

◆ _ntrgrd_vcb_algo()

static void _ntrgrd_vcb_algo	(	const cs_face_mesh_t *	fm,
		const cs_cell_mesh_t *	cm,
		const cs_real_3_t	pty_nuf,
		cs_cdo_diff_t *	diff,
		cs_locmat_t *	ntrgrd
	)

static

Compute the normal trace operator for a given border face when a WBS algo. and a V+C scheme is considered.

Parameters

[in]	fm	pointer to a cs_face_mesh_t structure
[in]	cm	pointer to a cs_cell_mesh_t structure
[in]	pty_nuf	property tensor times the face normal
[in,out]	diff	pointer to a builder structure
[in,out]	ntrgrd	local matrix related to the normal trace op.

◆ _ntrgrd_wbs_algo()

static void _ntrgrd_wbs_algo	(	const cs_face_mesh_t *	fm,
		const cs_cell_mesh_t *	cm,
		const cs_real_3_t	pty_nuf,
		cs_cdo_diff_t *	diff,
		cs_locmat_t *	ntrgrd
	)

static

Compute the normal trace operator for a given border face when a WBS algo. is used for reconstructing the degrees of freedom.

Parameters

[in]	fm	pointer to a cs_face_mesh_t structure
[in]	cm	pointer to a cs_cell_mesh_t structure
[in]	pty_nuf	property tensor times the face normal
[in,out]	diff	pointer to a builder structure
[in,out]	ntrgrd	local matrix related to the normal trace op.

◆ cs_cdo_diffusion_build_c2bcbf()

void cs_cdo_diffusion_build_c2bcbf	(	const cs_cdo_connect_t *	connect,
		const cs_cdo_bc_list_t *	dir_face,
		cs_lnum_t *	p_c2bcbf_idx[],
		cs_lnum_t *	p_c2bcbf_ids[]
	)

Define a cell –> Dirichlet boundary faces connectivity.

Parameters

[in]	connect	pointer to a cs_cdo_connect_t structure
[in]	dir_face	pointer to a cs_cdo_bc_list_t structure
[in,out]	c2bcbf_idx	pointer to the index to build
[in,out]	c2bcbf_ids	pointer to the list of ids to build

◆ cs_cdo_diffusion_build_local()

cs_locmat_t* cs_cdo_diffusion_build_local	(	const cs_cdo_quantities_t *	quant,
		const cs_cell_mesh_t *	cm,
		const cs_real_3_t *	tensor,
		cs_cdo_diff_t *	diff
	)

Define the local (cellwise) stiffness matrix.

Parameters

[in]	quant	pointer to a cs_cdo_quantities_t struct.
[in]	cm	cell-wise connectivity and quantitites
[in]	tensor	3x3 matrix attached to the diffusion property
[in,out]	diff	auxiliary structure used to build the diff. term

Returns: a pointer to a local stiffness matrix

◆ cs_cdo_diffusion_builder_free()

cs_cdo_diff_t* cs_cdo_diffusion_builder_free ( cs_cdo_diff_t * diff )

Free a cs_cdo_diff_t structure.

Parameters

[in,out] diff pointer to a cs_cdo_diff_t struc.

Returns: NULL

◆ cs_cdo_diffusion_builder_init()

cs_cdo_diff_t* cs_cdo_diffusion_builder_init	(	const cs_cdo_connect_t *	connect,
		cs_space_scheme_t	space_scheme,
		bool	is_uniform,
		const cs_param_hodge_t	h_info,
		const cs_param_bc_enforce_t	bc_enforce
	)

Initialize a builder structure used to build the stiffness matrix.

Parameters

[in]	connect	pointer to a cs_cdo_connect_t structure
[in]	space_scheme	scheme used for discretizing in space
[in]	is_uniform	diffusion tensor is uniform ? (true or false)
[in]	h_info	cs_param_hodge_t structure
[in]	bc_enforce	type of boundary enforcement for Dirichlet values

Returns: a pointer to a new allocated cs_cdo_diff_t structure

◆ cs_cdo_diffusion_cellwise_flux()

void cs_cdo_diffusion_cellwise_flux	(	const cs_cell_mesh_t *	cm,
		const cs_dface_t *	dface,
		const cs_real_t	pty_tens[3][3],
		const double *	p_v,
		const double	p_c,
		cs_cdo_diff_t *	diff,
		double *	c_flux
	)

Compute the diffusive flux across dual faces for a given cell The computation takes into account a subdivision into tetrahedra of the current cell based on p_{ef,c}.

Parameters

[in]	cm	pointer to a cs_face_mesh_t structure
[in]	dface	pointer to the dual faces related to cell edges
[in]	pty_tens	3x3 matrix related to the diffusion property
[in]	p_v	array of values attached to face vertices
[in]	p_c	value attached to the cell
[in,out]	diff	auxiliary structure dedicated to diffusion
[in,out]	c_flux	flux across dual faces inside this cell

◆ cs_cdo_diffusion_face_flux()

double cs_cdo_diffusion_face_flux	(	const cs_face_mesh_t *	fm,
		const cs_real_t	pty_tens[3][3],
		const double *	p_v,
		const double	p_f,
		const double	p_c,
		cs_cdo_diff_t *	diff
	)

Compute the diffusive flux across a face (based on a subdivision into tetrahedra of the volume p_{f,c})

Parameters

[in]	fm	pointer to a cs_face_mesh_t structure
[in]	pty_tens	3x3 matrix related to the diffusion property
[in]	p_v	array of values attached to face vertices
[in]	p_f	value attached to the face
[in]	p_c	value attached to the cell
[in,out]	diff	auxiliary structure dedicated to diffusion

Returns: the value of the diffusive flux across the current face

◆ cs_cdo_diffusion_get_hodge_builder()

cs_hodge_builder_t* cs_cdo_diffusion_get_hodge_builder ( cs_cdo_diff_t * diff )

Get the related Hodge builder structure.

Parameters

[in] diff pointer to a cs_cdo_diff_t structure

Returns: a pointer to a cs_hodge_builder_t structure

◆ cs_cdo_diffusion_get_tmp_buffers()

void cs_cdo_diffusion_get_tmp_buffers	(	const cs_cdo_diff_t *	diff,
		cs_real_3_t **	tmp_vec,
		cs_real_t **	tmp_sca
	)

Get temporary buffers attached to a cs_cdo_diff_t structure.

Parameters

[in]	diff	pointer to a cs_cdo_diff_t structure
[in,out]	tmp_vec	pointer to a buffer of cs_real_3_t
[in,out]	tmp_sca	pointer to a buffer of cs_real_t

◆ cs_cdo_diffusion_weak_bc()

void cs_cdo_diffusion_weak_bc	(	cs_lnum_t	f_id,
		const cs_cell_mesh_t *	cm,
		const cs_real_t	matpty[3][3],
		cs_cdo_diff_t *	diff,
		cs_cdo_locsys_t *	csys
	)

Define the local (cellwise) "normal trace gradient" matrix taking into account Dirichlet BCs by a weak enforcement using Nitsche technique (symmetrized or not)

Parameters

[in]	f_id	face id (a border face attached to a Dir. BC)
[in]	cm	pointer to a cs_cell_mesh_t struct.
[in]	matpty	3x3 matrix related to the diffusion property
[in,out]	diff	auxiliary structure used to build the diff. term
[in,out]	csys	structure storing the cell-wise system

Functions

Detailed Description

Function Documentation

◆ _compute_vcb_stiffness()

◆ _compute_wbs_stiffness()

◆ _ntrgrd_cost_algo()

◆ _ntrgrd_vcb_algo()

◆ _ntrgrd_wbs_algo()

◆ cs_cdo_diffusion_build_c2bcbf()

◆ cs_cdo_diffusion_build_local()

◆ cs_cdo_diffusion_builder_free()

◆ cs_cdo_diffusion_builder_init()

◆ cs_cdo_diffusion_cellwise_flux()

◆ cs_cdo_diffusion_face_flux()

◆ cs_cdo_diffusion_get_hodge_builder()

◆ cs_cdo_diffusion_get_tmp_buffers()

◆ cs_cdo_diffusion_weak_bc()