This is class represents the Gauss-Legendre quadrature rule. It is a special case of the Gauss-Jacobi quadrature rule with alpha = beta = 0.0. More...

#include <GaussJacobiQuadrature.h>

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

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

Public Types
using	scalar_t = double

Public Member Functions
	GaussLegendreQuadrature (const ElementType &ref_element, const size_t &max_newton_itersations=10, const size_t &min_newton_iterations=1)
	Construct a new Gauss Legendre 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.
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]).

Static Public Attributes
static constexpr unsigned	numNodes1D = NumNodes1D
static constexpr unsigned	dim = ElementType::dim
static constexpr unsigned	numElementNodes

Protected Attributes
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

Private Member Functions
scalar_t	getLehrFEMInitialGuess (const size_t &i, const Vector< scalar_t, NumNodes1D > &integration_nodes) const
	Computes the initial guess for the Newton iterations, the way they are computed in the implementation from LehrFEM++.

Private Attributes
const T	alpha_m
const T	beta_m
const size_t	max_newton_iterations_m
const size_t	min_newton_iterations_m

Detailed Description

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

This is class represents the Gauss-Legendre quadrature rule. It is a special case of the Gauss-Jacobi quadrature rule with alpha = beta = 0.0.

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

Definition at line 90 of file GaussJacobiQuadrature.h.

Member Typedef Documentation

◆ scalar_t

template<typename T, unsigned NumNodes1D, typename ElementType>

using ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::scalar_t = double

inherited

Definition at line 31 of file GaussJacobiQuadrature.h.

Constructor & Destructor Documentation

◆ GaussLegendreQuadrature()

template<typename T, unsigned NumNodes1D, typename ElementType>

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

inline

Construct a new Gauss Legendre Quadrature rule object.

Parameters

ref_element	reference element to compute the quadrature nodes on
max_newton_itersations	maximum number of Newton iterations (default 10)
min_newton_iterations	minimum number of Newton iterations (default 1)

Definition at line 99 of file GaussJacobiQuadrature.h.

References ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::GaussJacobiQuadrature().

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Member Function Documentation

◆ computeNodesAndWeights()

template<typename T, unsigned NumNodes1D, typename ElementType>

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

overridevirtualinherited

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 >.

Definition at line 91 of file GaussJacobiQuadrature.hpp.

References alpha_m, beta_m, ippl::Chebyshev, getChebyshevNodes(), getLehrFEMInitialGuess(), ippl::Quadrature< T, NumNodes1D, ElementType >::integration_nodes_m, ippl::LehrFEM, max_newton_iterations_m, min_newton_iterations_m, and ippl::Quadrature< T, NumNodes1D, ElementType >::weights_m.

Referenced by GaussJacobiQuadrature().

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◆ 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

inherited

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

Definition at line 34 of file GaussJacobiQuadrature.hpp.

Referenced by computeNodesAndWeights().

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◆ getDegree()

template<typename T, unsigned NumNodes1D, typename ElementType>

size_t ippl::Quadrature< T, NumNodes1D, ElementType >::getDegree ( ) const

inherited

Returns the degree of exactness of the quadrature rule.

Returns: unsigned - degree

Definition at line 13 of file Quadrature.hpp.

References degree_m.

◆ getIntegrationNodes1D()

template<typename T, unsigned NumNodes1D, typename ElementType>

Vector< T, NumNodes1D > ippl::Quadrature< T, NumNodes1D, ElementType >::getIntegrationNodes1D	(	const T &	a,
		const T &	b ) const

inherited

Get the quadrature nodes for one dimension. (With respect to the given domain [a, b]).

Parameters

a	local domain start
b	local domain end

Returns: Vector<T, NumNodes1D>

Definition at line 72 of file Quadrature.hpp.

Referenced by getIntegrationNodesForRefElement().

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◆ getIntegrationNodesForRefElement()

template<typename T, unsigned NumNodes1D, typename ElementType>

Vector< Vector< T, Quadrature< T, NumNodes1D, ElementType >::dim >, Quadrature< T, NumNodes1D, ElementType >::numElementNodes > ippl::Quadrature< T, NumNodes1D, ElementType >::getIntegrationNodesForRefElement ( ) const

inherited

Get the integration (quadrature) nodes for the reference element.

Returns: Vector<Vector<T, Dim>, numElementNodes>

Definition at line 47 of file Quadrature.hpp.

References getIntegrationNodes1D(), and numElementNodes.

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◆ getLehrFEMInitialGuess()

template<typename T, unsigned NumNodes1D, typename ElementType>

GaussJacobiQuadrature< T, NumNodes1D, ElementType >::scalar_t ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::getLehrFEMInitialGuess	(	const size_t &	i,
		const Vector< scalar_t, NumNodes1D > &	integration_nodes ) const

privateinherited

Computes the initial guess for the Newton iterations, the way they are computed in the implementation from LehrFEM++.

Parameters

i	index of the initial guess (corresponding to the i-th quadrature node)
integration_nodes	the integration nodes

Returns: scalar_t - initial guess

Definition at line 41 of file GaussJacobiQuadrature.hpp.

References alpha_m, and beta_m.

Referenced by computeNodesAndWeights().

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◆ getOrder()

template<typename T, unsigned NumNodes1D, typename ElementType>

size_t ippl::Quadrature< T, NumNodes1D, ElementType >::getOrder ( ) const

inherited

Returns the order of the quadrature rule. (order = degree + 1).

Returns: unsigned - order

Definition at line 8 of file Quadrature.hpp.

References degree_m.

◆ getWeights1D()

template<typename T, unsigned NumNodes1D, typename ElementType>

Vector< T, NumNodes1D > ippl::Quadrature< T, NumNodes1D, ElementType >::getWeights1D	(	const T &	a,
		const T &	b ) const

inherited

Get the quadrature weights for one dimension. (With respect to the given domain [a, b]).

Parameters

a	local domain start
b	local domain end

Returns: Vector<T, NumNodes1D>

Definition at line 81 of file Quadrature.hpp.

References a_m, b_m, and weights_m.

Referenced by getWeightsForRefElement().

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◆ getWeightsForRefElement()

template<typename T, unsigned NumNodes1D, typename ElementType>

Vector< T, Quadrature< T, NumNodes1D, ElementType >::numElementNodes > ippl::Quadrature< T, NumNodes1D, ElementType >::getWeightsForRefElement ( ) const

inherited

Get the quadrature weights for the reference element.

Returns: Vector<T, numElementNodes>

Definition at line 19 of file Quadrature.hpp.

References getWeights1D(), and numElementNodes.

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Member Data Documentation

◆ a_m

template<typename T, unsigned NumNodes1D, typename ElementType>

T ippl::Quadrature< T, NumNodes1D, ElementType >::a_m

protectedinherited

Definition at line 117 of file Quadrature.h.

Referenced by ippl::MidpointQuadrature< T, NumNodes1D, ElementType >::computeNodesAndWeights(), ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::GaussJacobiQuadrature(), getWeights1D(), and ippl::MidpointQuadrature< T, NumNodes1D, ElementType >::MidpointQuadrature().

◆ alpha_m

template<typename T, unsigned NumNodes1D, typename ElementType>

const T ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::alpha_m

privateinherited

Definition at line 74 of file GaussJacobiQuadrature.h.

Referenced by computeNodesAndWeights(), GaussJacobiQuadrature(), and getLehrFEMInitialGuess().

◆ b_m

template<typename T, unsigned NumNodes1D, typename ElementType>

T ippl::Quadrature< T, NumNodes1D, ElementType >::b_m

protectedinherited

Definition at line 119 of file Quadrature.h.

Referenced by ippl::MidpointQuadrature< T, NumNodes1D, ElementType >::computeNodesAndWeights(), ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::GaussJacobiQuadrature(), getWeights1D(), and ippl::MidpointQuadrature< T, NumNodes1D, ElementType >::MidpointQuadrature().

◆ beta_m

template<typename T, unsigned NumNodes1D, typename ElementType>

const T ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::beta_m

privateinherited

Definition at line 75 of file GaussJacobiQuadrature.h.

Referenced by computeNodesAndWeights(), GaussJacobiQuadrature(), and getLehrFEMInitialGuess().

◆ degree_m

template<typename T, unsigned NumNodes1D, typename ElementType>

unsigned ippl::Quadrature< T, NumNodes1D, ElementType >::degree_m

protectedinherited

Definition at line 111 of file Quadrature.h.

Referenced by ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::GaussJacobiQuadrature(), getDegree(), getOrder(), and ippl::MidpointQuadrature< T, NumNodes1D, ElementType >::MidpointQuadrature().

◆ dim

template<typename T, unsigned NumNodes1D, typename ElementType>

unsigned ippl::Quadrature< T, NumNodes1D, ElementType >::dim = ElementType::dim

staticconstexprinherited

Definition at line 41 of file Quadrature.h.

◆ integration_nodes_m

template<typename T, unsigned NumNodes1D, typename ElementType>

Vector<T, NumNodes1D> ippl::Quadrature< T, NumNodes1D, ElementType >::integration_nodes_m

protectedinherited

Definition at line 113 of file Quadrature.h.

Referenced by ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::computeNodesAndWeights(), ippl::MidpointQuadrature< T, NumNodes1D, ElementType >::computeNodesAndWeights(), and ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::GaussJacobiQuadrature().

◆ max_newton_iterations_m

template<typename T, unsigned NumNodes1D, typename ElementType>

const size_t ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::max_newton_iterations_m

privateinherited

Definition at line 77 of file GaussJacobiQuadrature.h.

Referenced by computeNodesAndWeights(), and GaussJacobiQuadrature().

◆ min_newton_iterations_m

template<typename T, unsigned NumNodes1D, typename ElementType>

const size_t ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::min_newton_iterations_m

privateinherited

Definition at line 78 of file GaussJacobiQuadrature.h.

Referenced by computeNodesAndWeights(), and GaussJacobiQuadrature().

◆ numElementNodes

template<typename T, unsigned NumNodes1D, typename ElementType>

unsigned ippl::Quadrature< T, NumNodes1D, ElementType >::numElementNodes

staticconstexprinherited

Initial value:

Definition at line 44 of file Quadrature.h.

Referenced by getIntegrationNodesForRefElement(), and getWeightsForRefElement().

◆ numNodes1D

template<typename T, unsigned NumNodes1D, typename ElementType>

unsigned ippl::Quadrature< T, NumNodes1D, ElementType >::numNodes1D = NumNodes1D

staticconstexprinherited

Definition at line 38 of file Quadrature.h.

◆ ref_element_m

template<typename T, unsigned NumNodes1D, typename ElementType>

const ElementType& ippl::Quadrature< T, NumNodes1D, ElementType >::ref_element_m

protectedinherited

Definition at line 112 of file Quadrature.h.

Referenced by Quadrature().

◆ weights_m

template<typename T, unsigned NumNodes1D, typename ElementType>

Vector<T, NumNodes1D> ippl::Quadrature< T, NumNodes1D, ElementType >::weights_m

protectedinherited

Definition at line 114 of file Quadrature.h.

Referenced by ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::computeNodesAndWeights(), ippl::MidpointQuadrature< T, NumNodes1D, ElementType >::computeNodesAndWeights(), ippl::GaussJacobiQuadrature< T, NumNodes1D, ElementType >::GaussJacobiQuadrature(), and getWeights1D().

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

GaussJacobiQuadrature.h

Public Types

Public Member Functions

Static Public Attributes

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ scalar_t

Constructor & Destructor Documentation

◆ GaussLegendreQuadrature()

Member Function Documentation

◆ computeNodesAndWeights()

◆ getChebyshevNodes()

◆ getDegree()

◆ getIntegrationNodes1D()

◆ getIntegrationNodesForRefElement()

◆ getLehrFEMInitialGuess()

◆ getOrder()

◆ getWeights1D()

◆ getWeightsForRefElement()

Member Data Documentation

◆ a_m

◆ alpha_m

◆ b_m

◆ beta_m

◆ degree_m

◆ dim

◆ integration_nodes_m

◆ max_newton_iterations_m

◆ min_newton_iterations_m

◆ numElementNodes

◆ numNodes1D

◆ ref_element_m

◆ weights_m