ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType > Class Template Reference

This is class represents the Gauss-Jacobi quadrature rule on a reference element. More...

#include <GaussJacobiQuadrature.h>

Inheritance diagram for ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >:

Collaboration diagram for ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >:

Public Types
using	scalar_t = double

Public Member Functions
	GaussJacobiQuadrature (const ElementType &ref_element, const T &alpha, const T &beta, const size_t &max_newton_itersations=10, const size_t &min_newton_iterations=1)
	Construct a new Gauss Jacobi Quadrature rule object.
void	computeNodesAndWeights () override
scalar_t	getChebyshevNodes (const size_t &i) const
	Returns the i-th Chebyshev node, used as initial guess for the Newton iterations.
Public Member Functions inherited from ippl::Quadrature< T, NumNodes1D, ElementType >
	Quadrature (const ElementType &ref_element)
	Construct a new Quadrature object.
size_t	getOrder () const
	Returns the order of the quadrature rule. (order = degree + 1)
size_t	getDegree () const
	Returns the degree of exactness of the quadrature rule.
Vector< T, numElementNodes >	getWeightsForRefElement () const
	Get the quadrature weights for the reference element.
Vector< Vector< T, dim >, numElementNodes >	getIntegrationNodesForRefElement () const
	Get the integration (quadrature) nodes for the reference element.
Vector< T, NumNodes1D >	getIntegrationNodes1D (const T &a, const T &b) const
	Get the quadrature nodes for one dimension. (With respect to the given domain [a, b])
Vector< T, NumNodes1D >	getWeights1D (const T &a, const T &b) const
	Get the quadrature weights for one dimension. (With respect to the given domain [a, b])

Additional Inherited Members
Static Public Attributes inherited from ippl::Quadrature< T, NumNodes1D, ElementType >
static constexpr unsigned	numNodes1D = NumNodes1D
static constexpr unsigned	dim = ElementType::dim
static constexpr unsigned	numElementNodes
Protected Attributes inherited from ippl::Quadrature< T, NumNodes1D, ElementType >
unsigned	degree_m
const ElementType &	ref_element_m
Vector< T, NumNodes1D >	integration_nodes_m
Vector< T, NumNodes1D >	weights_m
T	a_m
T	b_m

Detailed Description

template<typename T, unsigned NumNodes1D, typename ElementType>
class ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >

This is class represents the Gauss-Jacobi quadrature rule on a reference element.

Template Parameters

T	floating point number type of the quadrature nodes and weights
NumNodes1D	number of quadrature nodes for one dimension
ElementType	element type for which the quadrature rule is defined

Constructor & Destructor Documentation

GaussJacobiQuadrature()

template<typename T , unsigned NumNodes1D, typename ElementType >

ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::GaussJacobiQuadrature	(	const ElementType &	ref_element,
		const T &	alpha,
		const T &	beta,
		const size_t &	max_newton_itersations = 10,
		const size_t &	min_newton_iterations = 1
	)

Construct a new Gauss Jacobi Quadrature rule object.

Parameters

ref_element	reference element to compute the quadrature nodes on
alpha	first Jacobi parameter alpha
beta	second Jacobi parameter beta
max_newton_itersations	maximum number of Newton iterations (default 10)
min_newton_iterations	minimum number of Newton iterations (default 1)

Member Function Documentation

computeNodesAndWeights()

template<typename T , unsigned NumNodes1D, typename ElementType >

void ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::computeNodesAndWeights ( )

overridevirtual

Computes the quadrature nodes and weights and stores them in the quadrature nodes and weights arrays.

the following algorithm for computing the roots and weights for the Gauss-Jacobi quadrature has been taken from LehrFEM++ (MIT License) https://craffael.github.io/lehrfempp/gauss__quadrature_8cc_source.html

Implements ippl::Quadrature< T, NumNodes1D, ElementType >.

getChebyshevNodes()

template<typename T , unsigned NumNodes1D, typename ElementType >

GaussJacobiQuadrature< T, NumNodes1D, ElementType >::scalar_t ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::getChebyshevNodes

(

const size_t &

i

)

const

Returns the i-th Chebyshev node, used as initial guess for the Newton iterations.

Parameters

i	index of the Chebyshev node

Returns

scalar_t - i-th Chebyshev node

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

• ippl-src/src/FEM/Quadrature/GaussJacobiQuadrature.h
• ippl-src/src/FEM/Quadrature/GaussJacobiQuadrature.hpp