Description

Gauss-Legendre quadrature in 1D, 2D, or 3D.

This class provides methods to integrate a function (the integrand) on a domain using the Gauss quadrature. This method is most useful for polynomial integrands, in which case the result is exact if the order of quadrature is greater or equal to the degree of the polynomial.

#include <ChQuadrature.h>

Static Public Member Functions
template<class T >
static void	Integrate1D (T &result, ChIntegrand1D< T > &integrand, const double x_min, const double x_max, const int order)
	Integrate the integrand T = f(x) over the 1D interval [xA, xB], with specified order of quadrature. More...

template<class T >
static void	Integrate2D (T &result, ChIntegrand2D< T > &integrand, const double x_min, const double x_max, const double y_min, const double y_max, 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, ChIntegrand3D< T > &integrand, const double x_min, const double x_max, const double y_min, const double y_max, const double z_min, const double z_max, 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, ChIntegrand2D< T > &integrand, const int order)
	Integrate the 2D integrand T = f(u,v) over a triangle, with desired order of quadrature. More...

template<class T >
static void	Integrate3Dtetrahedron (T &result, ChIntegrand3D< T > &integrand, const int order)
	Integrate the 3D 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 10th order, with precomputed tables.

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

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.

◆ Integrate1D()

template<class T >

static void chrono::ChQuadrature::Integrate1D	(	T &	result,
		ChIntegrand1D< T > &	integrand,
		const double	x_min,
		const double	x_max,
		const int	order
	)

inlinestatic

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

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

Parameters

result	result is returned here
integrand	this is the integrand
x_min	min limit for x domain
x_max	min limit for x domain
order	order of integration

◆ Integrate2D()

template<class T >

static void chrono::ChQuadrature::Integrate2D	(	T &	result,
		ChIntegrand2D< T > &	integrand,
		const double	x_min,
		const double	x_max,
		const double	y_min,
		const double	y_max,
		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.

Parameters

result	result is returned here
integrand	this is the integrand
x_min	min limit for x domain
x_max	min limit for x domain
y_min	min limit for y domain
y_max	min limit for y domain
order	order of integration

◆ Integrate2Dtriangle()

template<class T >

static void chrono::ChQuadrature::Integrate2Dtriangle	(	T &	result,
		ChIntegrand2D< T > &	integrand,
		const int	order
	)

inlinestatic

Integrate the 2D 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 and v in [0...1], with the 3rd assumed to be 1-u-v. For order between 1 and 5, use precomputed polynomial coefficients.

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,
		ChIntegrand3D< T > &	integrand,
		const double	x_min,
		const double	x_max,
		const double	y_min,
		const double	y_max,
		const double	z_min,
		const double	z_max,
		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.

Parameters

result	result is returned here
integrand	this is the integrand
x_min	min limit for x domain
x_max	min limit for x domain
y_min	min limit for y domain
y_max	min limit for y domain
z_min	min limit for z domain
z_max	min limit for z domain
order	order of integration

◆ Integrate3Dtetrahedron()

template<class T >

static void chrono::ChQuadrature::Integrate3Dtetrahedron	(	T &	result,
		ChIntegrand3D< T > &	integrand,
		const int	order
	)

inlinestatic

Integrate the 3D 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, and w in [0...1], with the 4th assumed to be1-u-v-w. For order between 1 and 5 use precomputed polynomial coefficients.

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()

◆ Integrate1D()

◆ Integrate2D()

◆ Integrate2Dtriangle()

◆ Integrate3D()

◆ Integrate3Dtetrahedron()