cs_quadrature.h File Reference

#include <bft_error.h>
#include "cs_base.h"
#include "cs_defs.h"
#include "cs_math.h"
#include "cs_param.h"

Include dependency graph for cs_quadrature.h:

Go to the source code of this file.

Typedefs
typedef void()	cs_quadrature_edge_t(const cs_real_3_t v1, const cs_real_3_t v2, double len, cs_real_3_t gpts[], double *weights)
	Generic function pointer to compute the quadrature points for an edge from v1 -> v2. More...
typedef void()	cs_quadrature_tria_t(const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_real_3_t gpts[], double *weights)
	Generic functoin pointer to compute the quadrature points for a triangle. More...
typedef void()	cs_quadrature_tet_t(const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_real_3_t gpts[], double weights[])
	Generic function to compute the quadrature points in a tetrehedra. More...
typedef void()	cs_quadrature_edge_integral_t(double tcur, const cs_real_3_t v1, const cs_real_3_t v2, double len, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over an edge based on a specified quadrature rule and add it to results. More...
typedef void()	cs_quadrature_tria_integral_t(double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a triangle based on a specified quadrature rule and add it to results. More...
typedef void()	cs_quadrature_tetra_integral_t(double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a tetrahedron based on a specified quadrature rule and add it to results. More...

Enumerations
enum	cs_quadrature_type_t {   CS_QUADRATURE_NONE, CS_QUADRATURE_BARY, CS_QUADRATURE_BARY_SUBDIV, CS_QUADRATURE_HIGHER,   CS_QUADRATURE_HIGHEST, CS_QUADRATURE_N_TYPES }

Functions
void	cs_quadrature_setup (void)
	Compute constant weights for all quadratures used. More...
const char *	cs_quadrature_get_type_name (const cs_quadrature_type_t type)
	Return th name associated to a type of quadrature. More...
static void	cs_quadrature_edge_1pt (const cs_real_3_t v1, const cs_real_3_t v2, double len, cs_real_3_t gpts[], double *w)
	Compute quadrature points for an edge from v1 -> v2 (2 points) Exact for polynomial function up to order 1. More...
void	cs_quadrature_edge_2pts (const cs_real_3_t v1, const cs_real_3_t v2, double len, cs_real_3_t gpts[], double *w)
	Compute quadrature points for an edge from v1 -> v2 (2 points) Exact for polynomial function up to order 3. More...
void	cs_quadrature_edge_3pts (const cs_real_3_t v1, const cs_real_3_t v2, double len, cs_real_3_t gpts[], double w[])
	Compute quadrature points for an edge from v1 -> v2 (3 points) Exact for polynomial function up to order 5. More...
static void	cs_quadrature_tria_1pt (const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_real_3_t gpts[], double *w)
	Compute quadrature points for a triangle (1 point) Exact for polynomial function up to order 1 (barycentric approx.) More...
void	cs_quadrature_tria_3pts (const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_real_3_t gpts[], double *w)
	Compute quadrature points for a triangle (3 points) Exact for polynomial function up to order 2. More...
void	cs_quadrature_tria_4pts (const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_real_3_t gpts[], double w[])
	Compute quadrature points for a triangle (4 points) Exact for polynomial function up to order 3. More...
void	cs_quadrature_tria_7pts (const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_real_3_t gpts[], double w[])
	Compute quadrature points for a triangle (7 points) Exact for polynomial function up to order 5. More...
static void	cs_quadrature_tet_1pt (const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_real_3_t gpts[], double weight[])
	Compute the quadrature in a tetrehedra. Exact for 1st order polynomials (order 2). More...
void	cs_quadrature_tet_4pts (const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_real_3_t gpts[], double weights[])
	Compute the quadrature in a tetrehedra. Exact for 2nd order polynomials (order 3). More...
void	cs_quadrature_tet_5pts (const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_real_3_t gpts[], double weights[])
	Compute the quadrature in a tetrehedra. Exact for 3rd order polynomials (order 4). More...
void	cs_quadrature_tet_15pts (const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_real_3_t gpts[], double weights[])
	Compute the quadrature in a tetrehedra. Exact for 5th order polynomials (order 6). More...
static void	cs_quadrature_edge_1pt_scal (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, double len, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over an edge with the mid-point rule and add it to results Case of a scalar-valued function. More...
static void	cs_quadrature_edge_2pts_scal (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, double len, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over an edge with a quadrature rule using 2 Gauss points and a unique weight and add it to results Case of a scalar-valued function. More...
static void	cs_quadrature_edge_3pts_scal (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, double len, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over an edge with a quadrature rule using 3 Gauss points and weights and add it to results Case of a scalar-valued function. More...
static void	cs_quadrature_tria_1pt_scal (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a triangle using a barycentric quadrature rule and add it to results Case of a scalar-valued function. More...
static void	cs_quadrature_tria_3pts_scal (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a triangle with a quadrature rule using 3 Gauss points and a unique weight and add it to results Case of a scalar-valued function. More...
static void	cs_quadrature_tria_4pts_scal (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a triangle with a quadrature rule using 4 Gauss points and 4 weights and add it to results Case of a scalar-valued function. More...
static void	cs_quadrature_tria_1pt_vect (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a triangle using a barycentric quadrature rule and add it to results Case of a vector-valued function. More...
static void	cs_quadrature_tria_3pts_vect (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a triangle with a quadrature rule using 3 Gauss points and a unique weight and add it to results Case of a vector-valued function. More...
static void	cs_quadrature_tria_4pts_vect (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a triangle with a quadrature rule using 4 Gauss points and 4 weights and add it to results. Case of a vector-valued function. More...
static void	cs_quadrature_tria_1pt_tens (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a triangle using a barycentric quadrature rule and add it to results. Case of a tensor-valued function. More...
static void	cs_quadrature_tria_3pts_tens (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a triangle with a quadrature rule using 3 Gauss points and a unique weight and add it to results. Case of a tensor-valued function. More...
static void	cs_quadrature_tria_4pts_tens (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a triangle with a quadrature rule using 4 Gauss points and 4 weights and add it to results. Case of a tensor-valued function. More...
static void	cs_quadrature_tet_1pt_scal (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a tetrahedron using a barycentric quadrature rule and add it to results. Case of a scalar-valued function. More...
static void	cs_quadrature_tet_4pts_scal (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a tetrahedron with a quadrature rule using 4 Gauss points and a unique weight and add it to results. Case of a scalar-valued function. More...
static void	cs_quadrature_tet_5pts_scal (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a tetrahedron with a quadrature rule using 5 Gauss points and 5 weights and add it to results. Case of a scalar-valued function. More...
static void	cs_quadrature_tet_1pt_vect (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a tetrahedron using a barycentric quadrature rule and add it to results. Case of a vector-valued function. More...
static void	cs_quadrature_tet_4pts_vect (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a tetrahedron with a quadrature rule using 4 Gauss points and a unique weight and add it to results. Case of a vector-valued function. More...
static void	cs_quadrature_tet_5pts_vect (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a tetrahedron with a quadrature rule using 5 Gauss points and 5 weights and add it to results. Case of a vector-valued function. More...
static void	cs_quadrature_tet_1pt_tens (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a tetrahedron using a barycentric quadrature rule and add it to results. Case of a tensor-valued function. More...
static void	cs_quadrature_tet_4pts_tens (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a tetrahedron with a quadrature rule using 4 Gauss points and a unique weight and add it to results. Case of a tensor-valued function. More...
static void	cs_quadrature_tet_5pts_tens (double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_analytic_func_t *ana, void *input, double results[])
	Compute the integral over a tetrahedron with a quadrature rule using 5 Gauss points and 5 weights and add it to results Case of a tensor-valued function. More...
static cs_quadrature_tria_integral_t *	cs_quadrature_get_tria_integral (int dim, cs_quadrature_type_t qtype)
	Retrieve the integral function according to the quadrature type and the stride provided. More...
static cs_quadrature_tetra_integral_t *	cs_quadrature_get_tetra_integral (int dim, cs_quadrature_type_t qtype)
	Retrieve the integral function according to the quadrature type and the stride provided. More...
cs_flag_t	cs_quadrature_get_flag (const cs_quadrature_type_t qtype, const cs_flag_t loc)
	Get the flags adapted to the given quadrature type qtype and the location on which the quadrature should be performed. More...

Typedef Documentation

cs_quadrature_edge_integral_t

typedef void() cs_quadrature_edge_integral_t(double tcur, const cs_real_3_t v1, const cs_real_3_t v2, double len, cs_analytic_func_t *ana, void *input, double results[])

Compute the integral over an edge based on a specified quadrature rule and add it to results.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the edge
[in]	v2	second point of the edge
[in]	len	length of the edge
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_edge_t

typedef void() cs_quadrature_edge_t(const cs_real_3_t v1, const cs_real_3_t v2, double len, cs_real_3_t gpts[], double *weights)

Generic function pointer to compute the quadrature points for an edge from v1 -> v2.

Parameters

[in]	v1	first vertex
[in]	v2	second vertex
[in]	len	length of edge [v1, v2]
[in,out]	gpts	gauss points
[in,out]	w	weight (same weight for the two points)

cs_quadrature_tet_t

typedef void() cs_quadrature_tet_t(const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_real_3_t gpts[], double weights[])

Generic function to compute the quadrature points in a tetrehedra.

Parameters

[in]	v1	first vertex
[in]	v2	second vertex
[in]	v3	third vertex
[in]	v4	fourth vertex
[in]	vol	volume of tetrahedron {v1, v2, v3, v4}
[in,out]	gpts	Gauss points
[in,out]	weights	weigths related to each Gauss point

cs_quadrature_tetra_integral_t

typedef void() cs_quadrature_tetra_integral_t(double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, const cs_real_3_t v4, double vol, cs_analytic_func_t *ana, void *input, double results[])

Compute the integral over a tetrahedron based on a specified quadrature rule and add it to results.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the tetrahedron
[in]	v2	second point of the tetrahedron
[in]	v3	third point of the tetrahedron
[in]	v4	fourth point of the tetrahedron
[in]	vol	volume of the tetrahedron
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tria_integral_t

typedef void() cs_quadrature_tria_integral_t(double tcur, const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_analytic_func_t *ana, void *input, double results[])

Compute the integral over a triangle based on a specified quadrature rule and add it to results.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the triangle
[in]	v2	second point of the triangle
[in]	v3	third point of the triangle
[in]	area	area of the triangle
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tria_t

typedef void() cs_quadrature_tria_t(const cs_real_3_t v1, const cs_real_3_t v2, const cs_real_3_t v3, double area, cs_real_3_t gpts[], double *weights)

Generic functoin pointer to compute the quadrature points for a triangle.

Parameters

[in]	v1	first vertex
[in]	v2	second vertex
[in]	v3	third vertex
[in]	area	area of triangle {v1, v2, v3}
[in,out]	gpts	Gauss points
[in,out]	weights	weights values

Enumeration Type Documentation

cs_quadrature_type_t

enum cs_quadrature_type_t

Enumerator
CS_QUADRATURE_NONE
CS_QUADRATURE_BARY
CS_QUADRATURE_BARY_SUBDIV
CS_QUADRATURE_HIGHER
CS_QUADRATURE_HIGHEST
CS_QUADRATURE_N_TYPES

Function Documentation

cs_quadrature_edge_1pt()

static void cs_quadrature_edge_1pt ( const cs_real_3_t  v1, const cs_real_3_t  v2, double  len, cs_real_3_t  gpts[], double *  w  )

inlinestatic

Compute quadrature points for an edge from v1 -> v2 (2 points) Exact for polynomial function up to order 1.

Parameters

[in]	v1	first vertex
[in]	v2	second vertex
[in]	len	length of edge [v1, v2]
[in,out]	gpts	gauss points
[in,out]	w	weight (same weight for the two points)

cs_quadrature_edge_1pt_scal()

static void cs_quadrature_edge_1pt_scal ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, double  len, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over an edge with the mid-point rule and add it to results Case of a scalar-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the edge
[in]	v2	second point of the edge
[in]	len	length of the edge
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_edge_2pts()

void cs_quadrature_edge_2pts	(	const cs_real_3_t	v1,
		const cs_real_3_t	v2,
		double	len,
		cs_real_3_t	gpts[],
		double *	w
	)

Compute quadrature points for an edge from v1 -> v2 (2 points) Exact for polynomial function up to order 3.

Parameters

[in]	v1	first vertex
[in]	v2	second vertex
[in]	len	length of edge [v1, v2]
[in,out]	gpts	gauss points
[in,out]	w	weight (same weight for the two points)

cs_quadrature_edge_2pts_scal()

static void cs_quadrature_edge_2pts_scal ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, double  len, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over an edge with a quadrature rule using 2 Gauss points and a unique weight and add it to results Case of a scalar-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the edge
[in]	v2	second point of the edge
[in]	len	length of the edge
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_edge_3pts()

void cs_quadrature_edge_3pts	(	const cs_real_3_t	v1,
		const cs_real_3_t	v2,
		double	len,
		cs_real_3_t	gpts[],
		double	w[]
	)

Compute quadrature points for an edge from v1 -> v2 (3 points) Exact for polynomial function up to order 5.

Parameters

[in]	v1	first vertex
[in]	v2	second vertex
[in]	len	length of edge [v1, v2]
[in,out]	gpts	gauss points
[in,out]	w	weights
[in]	v1	first vertex
[in]	v2	second vertex
[in]	len	length of edge [v1, v2]
[in,out]	gpts	gauss points
[in,out]	w	weights

cs_quadrature_edge_3pts_scal()

static void cs_quadrature_edge_3pts_scal ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, double  len, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over an edge with a quadrature rule using 3 Gauss points and weights and add it to results Case of a scalar-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the edge
[in]	v2	second point of the edge
[in]	len	length of the edge
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_get_flag()

cs_flag_t cs_quadrature_get_flag	(	const cs_quadrature_type_t	qtype,
		const cs_flag_t	loc
	)

Get the flags adapted to the given quadrature type qtype and the location on which the quadrature should be performed.

Parameters

[in]	qtype	cs_quadrature_type_t
[in]	loc	It could be CS_FLAG_CELL, CS_FLAG_FACE or CS_FLAG_EDGE plus CS_FLAG_PRIMAL or CS_FLAG_DUAL

Returns

metadata stored in a cs_flag_t to build a cs_cell_mesh_t

cs_quadrature_get_tetra_integral()

static cs_quadrature_tetra_integral_t* cs_quadrature_get_tetra_integral ( int  dim, cs_quadrature_type_t  qtype  )

inlinestatic

Retrieve the integral function according to the quadrature type and the stride provided.

Parameters

[in]	dim	dimension of the function to integrate
[in]	qtype	quadrature type

Returns

a pointer to the integral function

cs_quadrature_get_tria_integral()

static cs_quadrature_tria_integral_t* cs_quadrature_get_tria_integral ( int  dim, cs_quadrature_type_t  qtype  )

inlinestatic

Retrieve the integral function according to the quadrature type and the stride provided.

Parameters

[in]	dim	dimension of the function to integrate
[in]	qtype	quadrature type

Returns

a pointer to the integral function

cs_quadrature_get_type_name()

const char* cs_quadrature_get_type_name

(

const cs_quadrature_type_t

type

)

Return th name associated to a type of quadrature.

Parameters

[in]

type

cs_quadrature_type_t

Returns

the name associated to a given type of quadrature

cs_quadrature_setup()

void cs_quadrature_setup

(

void

)

Compute constant weights for all quadratures used.

cs_quadrature_tet_15pts()

void cs_quadrature_tet_15pts	(	const cs_real_3_t	v1,
		const cs_real_3_t	v2,
		const cs_real_3_t	v3,
		const cs_real_3_t	v4,
		double	vol,
		cs_real_3_t	gpts[],
		double	weights[]
	)

Compute the quadrature in a tetrehedra. Exact for 5th order polynomials (order 6).

Parameters

[in]	v1	first vertex
[in]	v2	second vertex
[in]	v3	third vertex
[in]	v4	fourth vertex
[in]	vol	volume of tetrahedron {v1, v2, v3, v4}
[in,out]	gpts	15 Gauss points (size = 3*15)
[in,out]	weights	15 weigths related to each Gauss point

cs_quadrature_tet_1pt()

static void cs_quadrature_tet_1pt ( const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, const cs_real_3_t  v4, double  vol, cs_real_3_t  gpts[], double  weight[]  )

inlinestatic

Compute the quadrature in a tetrehedra. Exact for 1st order polynomials (order 2).

Parameters

[in]	v1	first vertex
[in]	v2	second vertex
[in]	v3	third vertex
[in]	v4	fourth vertex
[in]	vol	volume of tetrahedron
[in,out]	gpts	1 Gauss point
[in,out]	weight	weight related to this point (= volume)

cs_quadrature_tet_1pt_scal()

static void cs_quadrature_tet_1pt_scal ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, const cs_real_3_t  v4, double  vol, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a tetrahedron using a barycentric quadrature rule and add it to results. Case of a scalar-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the tetrahedron
[in]	v2	second point of the tetrahedron
[in]	v3	third point of the tetrahedron
[in]	v4	fourth point of the tetrahedron
[in]	vol	volume of the tetrahedron
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tet_1pt_tens()

static void cs_quadrature_tet_1pt_tens ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, const cs_real_3_t  v4, double  vol, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a tetrahedron using a barycentric quadrature rule and add it to results. Case of a tensor-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the tetrahedron
[in]	v2	second point of the tetrahedron
[in]	v3	third point of the tetrahedron
[in]	v4	fourth point of the tetrahedron
[in]	vol	volume of the tetrahedron
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tet_1pt_vect()

static void cs_quadrature_tet_1pt_vect ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, const cs_real_3_t  v4, double  vol, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a tetrahedron using a barycentric quadrature rule and add it to results. Case of a vector-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the tetrahedron
[in]	v2	second point of the tetrahedron
[in]	v3	third point of the tetrahedron
[in]	v4	fourth point of the tetrahedron
[in]	vol	volume of the tetrahedron
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tet_4pts()

void cs_quadrature_tet_4pts	(	const cs_real_3_t	v1,
		const cs_real_3_t	v2,
		const cs_real_3_t	v3,
		const cs_real_3_t	v4,
		double	vol,
		cs_real_3_t	gpts[],
		double	weights[]
	)

Compute the quadrature in a tetrehedra. Exact for 2nd order polynomials (order 3).

Parameters

[in]	v1	first vertex
[in]	v2	second vertex
[in]	v3	third vertex
[in]	v4	fourth vertex
[in]	vol	volume of tetrahedron {v1, v2, v3, v4}
[in,out]	gpts	4 Gauss points (size = 3*4)
[in,out]	weights	weight (same value for all points)

cs_quadrature_tet_4pts_scal()

static void cs_quadrature_tet_4pts_scal ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, const cs_real_3_t  v4, double  vol, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a tetrahedron with a quadrature rule using 4 Gauss points and a unique weight and add it to results. Case of a scalar-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the tetrahedron
[in]	v2	second point of the tetrahedron
[in]	v3	third point of the tetrahedron
[in]	v4	fourth point of the tetrahedron
[in]	vol	volume of the tetrahedron
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tet_4pts_tens()

static void cs_quadrature_tet_4pts_tens ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, const cs_real_3_t  v4, double  vol, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a tetrahedron with a quadrature rule using 4 Gauss points and a unique weight and add it to results. Case of a tensor-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the tetrahedron
[in]	v2	second point of the tetrahedron
[in]	v3	third point of the tetrahedron
[in]	v4	fourth point of the tetrahedron
[in]	vol	volume of the tetrahedron
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tet_4pts_vect()

static void cs_quadrature_tet_4pts_vect ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, const cs_real_3_t  v4, double  vol, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a tetrahedron with a quadrature rule using 4 Gauss points and a unique weight and add it to results. Case of a vector-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the tetrahedron
[in]	v2	second point of the tetrahedron
[in]	v3	third point of the tetrahedron
[in]	v4	fourth point of the tetrahedron
[in]	vol	volume of the tetrahedron
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tet_5pts()

void cs_quadrature_tet_5pts	(	const cs_real_3_t	v1,
		const cs_real_3_t	v2,
		const cs_real_3_t	v3,
		const cs_real_3_t	v4,
		double	vol,
		cs_real_3_t	gpts[],
		double	weights[]
	)

Compute the quadrature in a tetrehedra. Exact for 3rd order polynomials (order 4).

Parameters

[in]	v1	first vertex
[in]	v2	second vertex
[in]	v3	third vertex
[in]	v4	fourth vertex
[in]	vol	volume of tetrahedron {v1, v2, v3, v4}
[in,out]	gpts	5 Gauss points (size = 3*5)
[in,out]	weights	5 weigths related to each Gauss point

cs_quadrature_tet_5pts_scal()

static void cs_quadrature_tet_5pts_scal ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, const cs_real_3_t  v4, double  vol, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a tetrahedron with a quadrature rule using 5 Gauss points and 5 weights and add it to results. Case of a scalar-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the tetrahedron
[in]	v2	second point of the tetrahedron
[in]	v3	third point of the tetrahedron
[in]	v4	fourth point of the tetrahedron
[in]	vol	volume of the tetrahedron
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tet_5pts_tens()

static void cs_quadrature_tet_5pts_tens ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, const cs_real_3_t  v4, double  vol, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a tetrahedron with a quadrature rule using 5 Gauss points and 5 weights and add it to results Case of a tensor-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the tetrahedron
[in]	v2	second point of the tetrahedron
[in]	v3	third point of the tetrahedron
[in]	v4	fourth point of the tetrahedron
[in]	vol	volume of the tetrahedron
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tet_5pts_vect()

static void cs_quadrature_tet_5pts_vect ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, const cs_real_3_t  v4, double  vol, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a tetrahedron with a quadrature rule using 5 Gauss points and 5 weights and add it to results. Case of a vector-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the tetrahedron
[in]	v2	second point of the tetrahedron
[in]	v3	third point of the tetrahedron
[in]	v4	fourth point of the tetrahedron
[in]	vol	volume of the tetrahedron
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tria_1pt()

static void cs_quadrature_tria_1pt ( const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, double  area, cs_real_3_t  gpts[], double *  w  )

inlinestatic

Compute quadrature points for a triangle (1 point) Exact for polynomial function up to order 1 (barycentric approx.)

Parameters

[in]	v1	first vertex
[in]	v2	second vertex
[in]	v3	third vertex
[in]	area	area of triangle {v1, v2, v3}
[in,out]	gpts	gauss points
[in,out]	w	weight

cs_quadrature_tria_1pt_scal()

static void cs_quadrature_tria_1pt_scal ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, double  area, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a triangle using a barycentric quadrature rule and add it to results Case of a scalar-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the triangle
[in]	v2	second point of the triangle
[in]	v3	third point of the triangle
[in]	area	area of the triangle
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tria_1pt_tens()

static void cs_quadrature_tria_1pt_tens ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, double  area, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a triangle using a barycentric quadrature rule and add it to results. Case of a tensor-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the triangle
[in]	v2	second point of the triangle
[in]	v3	third point of the triangle
[in]	area	area of the triangle
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tria_1pt_vect()

static void cs_quadrature_tria_1pt_vect ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, double  area, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a triangle using a barycentric quadrature rule and add it to results Case of a vector-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	1st point of the triangle
[in]	v2	2nd point of the triangle
[in]	v3	3rd point of the triangle
[in]	area	area of the triangle
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tria_3pts()

void cs_quadrature_tria_3pts	(	const cs_real_3_t	v1,
		const cs_real_3_t	v2,
		const cs_real_3_t	v3,
		double	area,
		cs_real_3_t	gpts[],
		double *	w
	)

Compute quadrature points for a triangle (3 points) Exact for polynomial function up to order 2.

Parameters

[in]	v1	first vertex
[in]	v2	second vertex
[in]	v3	third vertex
[in]	area	area of triangle {v1, v2, v3}
[in,out]	gpts	gauss points
[in,out]	w	weight (same weight for the three points)

cs_quadrature_tria_3pts_scal()

static void cs_quadrature_tria_3pts_scal ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, double  area, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a triangle with a quadrature rule using 3 Gauss points and a unique weight and add it to results Case of a scalar-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the triangle
[in]	v2	second point of the triangle
[in]	v3	third point of the triangle
[in]	area	area of the triangle
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tria_3pts_tens()

static void cs_quadrature_tria_3pts_tens ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, double  area, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a triangle with a quadrature rule using 3 Gauss points and a unique weight and add it to results. Case of a tensor-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the triangle
[in]	v2	second point of the triangle
[in]	v3	third point of the triangle
[in]	area	area of the triangle
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tria_3pts_vect()

static void cs_quadrature_tria_3pts_vect ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, double  area, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a triangle with a quadrature rule using 3 Gauss points and a unique weight and add it to results Case of a vector-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the triangle
[in]	v2	second point of the triangle
[in]	v3	third point of the triangle
[in]	area	area of the triangle
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tria_4pts()

void cs_quadrature_tria_4pts	(	const cs_real_3_t	v1,
		const cs_real_3_t	v2,
		const cs_real_3_t	v3,
		double	area,
		cs_real_3_t	gpts[],
		double	w[]
	)

Compute quadrature points for a triangle (4 points) Exact for polynomial function up to order 3.

Parameters

[in]	v1	first vertex
[in]	v2	second vertex
[in]	v3	third vertex
[in]	area	area of triangle {v1, v2, v3}
[in,out]	gpts	gauss points
[in,out]	w	weights

cs_quadrature_tria_4pts_scal()

static void cs_quadrature_tria_4pts_scal ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, double  area, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a triangle with a quadrature rule using 4 Gauss points and 4 weights and add it to results Case of a scalar-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the triangle
[in]	v2	second point of the triangle
[in]	v3	third point of the triangle
[in]	area	area of the triangle
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tria_4pts_tens()

static void cs_quadrature_tria_4pts_tens ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, double  area, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a triangle with a quadrature rule using 4 Gauss points and 4 weights and add it to results. Case of a tensor-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the triangle
[in]	v2	second point of the triangle
[in]	v3	third point of the triangle
[in]	area	area of the triangle
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tria_4pts_vect()

static void cs_quadrature_tria_4pts_vect ( double  tcur, const cs_real_3_t  v1, const cs_real_3_t  v2, const cs_real_3_t  v3, double  area, cs_analytic_func_t *  ana, void *  input, double  results[]  )

inlinestatic

Compute the integral over a triangle with a quadrature rule using 4 Gauss points and 4 weights and add it to results. Case of a vector-valued function.

Parameters

[in]	tcur	current physical time of the simulation
[in]	v1	first point of the triangle
[in]	v2	second point of the triangle
[in]	v3	third point of the triangle
[in]	area	area of the triangle
[in]	ana	pointer to the analytic function
[in]	input	NULL or pointer to a structure cast on-the-fly
[in,out]	results	array of double

cs_quadrature_tria_7pts()

void cs_quadrature_tria_7pts	(	const cs_real_3_t	v1,
		const cs_real_3_t	v2,
		const cs_real_3_t	v3,
		double	area,
		cs_real_3_t	gpts[],
		double	w[]
	)

Compute quadrature points for a triangle (7 points) Exact for polynomial function up to order 5.

Parameters

[in]	v1	first vertex
[in]	v2	second vertex
[in]	v3	third vertex
[in]	area	area of triangle {v1, v2, v3}
[in,out]	gpts	gauss points
[in,out]	w	weights