Description

Class to perform Gauss-Legendre quadrature, in 1D, 2D, 3D.

It integrates a function on a nD domain using the Gauss quadrature; this is mostly useful in the case that the integrand is polynomial, because the result is exact if the order of quadrature is greater or equal to the degree of the polynomial. Integrate() functions are static; no need to allocate an instance of this class.

#include <ChQuadrature.h>

Static Public Member Functions
template<class T >
static void	Integrate1D (T &result, ChIntegrable1D< T > &integrand, const double a, const double b, const int order)
	Integrate the integrand T = f(x) over the 1D interval [xA, xB], with desired order of quadrature. More...

template<class T >
static void	Integrate2D (T &result, ChIntegrable2D< T > &integrand, const double Xa, const double Xb, const double Ya, const double Yb, const int order)
	Integrate the integrand T = f(x,y) over the 2D interval [xA, xB][yA, yB], with desired order of quadrature. More...

template<class T >
static void	Integrate3D (T &result, ChIntegrable3D< T > &integrand, const double Xa, const double Xb, const double Ya, const double Yb, const double Za, const double Zb, const int order)
	Integrate the integrand T = f(x,y,z) over the 3D interval [xA, xB][yA, yB][zA, zB], with desired order of quadrature. More...

template<class T >
static void	Integrate2Dtriangle (T &result, ChIntegrable2D< T > &integrand, const int order)
	Special case of 2D integration: integrate the integrand T = f(u,v) over a triangle, with desired order of quadrature. More...

template<class T >
static void	Integrate3Dtetrahedron (T &result, ChIntegrable3D< T > &integrand, const int order)
	Special case of 3D integration: integrate the integrand T = f(u,v,w) over a tetrahedron, with desired order of quadrature. More...

static ChQuadratureTables *	GetStaticTables ()
	Access a statically-allocated set of tables, from 0 to a 10th order, with precomputed tables.

static ChQuadratureTablesTriangle *	GetStaticTablesTriangle ()
	Access a statically-allocated set of tables for tetrahedron quadrature, with 5 precomputed tables. More...

static ChQuadratureTablesTetrahedron *	GetStaticTablesTetrahedron ()
	Access a statically-allocated set of tables for tetrahedron quadrature, with 5 precomputed tables. More...

Member Function Documentation

◆ GetStaticTablesTetrahedron()

ChQuadratureTablesTetrahedron * chrono::ChQuadrature::GetStaticTablesTetrahedron ( )

static

Access a statically-allocated set of tables for tetrahedron quadrature, with 5 precomputed tables.

Use Dunavant theory.

◆ GetStaticTablesTriangle()

ChQuadratureTablesTriangle * chrono::ChQuadrature::GetStaticTablesTriangle ( )

static

Access a statically-allocated set of tables for tetrahedron quadrature, with 5 precomputed tables.

◆ Integrate1D()

template<class T >

static void chrono::ChQuadrature::Integrate1D	(	T &	result,
		ChIntegrable1D< T > &	integrand,
		const double	a,
		const double	b,
		const int	order
	)

inlinestatic

Integrate the integrand T = f(x) over the 1D interval [xA, xB], with desired order of quadrature.

Best if integrand is polynomial. For order in 1..10, precomputed polynomial coefficients are used for max speed.

Parameters

result	result is returned here
integrand	this is the integrand
a	min limit for x domain
b	min limit for x domain
order	order of integration

◆ Integrate2D()

template<class T >

static void chrono::ChQuadrature::Integrate2D	(	T &	result,
		ChIntegrable2D< T > &	integrand,
		const double	Xa,
		const double	Xb,
		const double	Ya,
		const double	Yb,
		const int	order
	)

inlinestatic

Integrate the integrand T = f(x,y) over the 2D interval [xA, xB][yA, yB], with desired order of quadrature.

Best if integrand is polynomial. For order in 1..10, precomputed polynomial coefficients are used for max speed.

Parameters

result	result is returned here
integrand	this is the integrand
Xa	min limit for x domain
Xb	min limit for x domain
Ya	min limit for y domain
Yb	min limit for y domain
order	order of integration

◆ Integrate2Dtriangle()

template<class T >

static void chrono::ChQuadrature::Integrate2Dtriangle	(	T &	result,
		ChIntegrable2D< T > &	integrand,
		const int	order
	)

inlinestatic

Special case of 2D integration: integrate the integrand T = f(u,v) over a triangle, with desired order of quadrature.

Best if integrand is polynomial. Two triangle coordinates are assumed to be 'area' coordinates u,v in [0...1]. The third is assumed 1-u-v.
For order in 1..5. Use precomputed polynomial coefficients for max speed.

Parameters

result	result is returned here
integrand	this is the integrand
order	order of integration

◆ Integrate3D()

template<class T >

static void chrono::ChQuadrature::Integrate3D	(	T &	result,
		ChIntegrable3D< T > &	integrand,
		const double	Xa,
		const double	Xb,
		const double	Ya,
		const double	Yb,
		const double	Za,
		const double	Zb,
		const int	order
	)

inlinestatic

Integrate the integrand T = f(x,y,z) over the 3D interval [xA, xB][yA, yB][zA, zB], with desired order of quadrature.

Best if integrand is polynomial. For order in 1..10, precomputed polynomial coefficients are used for max speed.

Parameters

result	result is returned here
integrand	this is the integrand
Xa	min limit for x domain
Xb	min limit for x domain
Ya	min limit for y domain
Yb	min limit for y domain
Za	min limit for z domain
Zb	min limit for z domain
order	order of integration

◆ Integrate3Dtetrahedron()

template<class T >

static void chrono::ChQuadrature::Integrate3Dtetrahedron	(	T &	result,
		ChIntegrable3D< T > &	integrand,
		const int	order
	)

inlinestatic

Special case of 3D integration: integrate the integrand T = f(u,v,w) over a tetrahedron, with desired order of quadrature.

Best if integrand is polynomial. Three tetrahedron coordinates are assumed to be 'volume' coordinates u,v,w in [0...1]. The 4th is assumed 1-u-v-w.
For order in 1..5. Use precomputed polynomial coefficients for max speed.

Parameters

result	result is returned here
integrand	this is the integrand
order	order of integration

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

/builds/uwsbel/chrono/src/chrono/core/ChQuadrature.h
/builds/uwsbel/chrono/src/chrono/core/ChQuadrature.cpp

Description

Static Public Member Functions

Member Function Documentation

◆ GetStaticTablesTetrahedron()

◆ GetStaticTablesTriangle()

◆ Integrate1D()

◆ Integrate2D()

◆ Integrate2Dtriangle()

◆ Integrate3D()

◆ Integrate3Dtetrahedron()