#include <LagrangeBasis2.hpp>

Classes
class	TensorProduct2D

class	TensorProduct3D

Static Public Member Functions
GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64	weight (const int q)
	The value of the weight for the given support point. More...

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64	parentSupportCoord (const localIndex supportPointIndex)
	Calculate the parent coordinates for the xi0 direction, given the linear index of a support point. More...

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64	value (const int index, const real64 xi)
	The value of the basis function for a support point evaluated at a point along the axes. More...

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64	value0 (const real64 xi)
	The value of the basis function for support point 0. More...

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64	value1 (const real64 xi)
	The value of the basis function for support point 1. More...

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64	value2 (const real64 xi)
	The value of the basis function for support point 2. More...

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64	gradient0 (const real64 xi)
	The gradient of the basis function for support point 0 evaluated at a point along the axes. More...

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64	gradient1 (const real64 xi)
	The gradient of the basis function for support point 1 evaluated at a point along the axes. More...

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64	gradient2 (const real64 xi)
	The gradient of the basis function for support point 1 evaluated at a point along the axes. More...

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64	gradient (const int index, const real64 xi)
	The gradient of the basis function for a support point evaluated at a point along the axes. More...

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64	gradientAt (const int q, const int p)
	The gradient of the basis function for a support point evaluated at a given support point. By symmetry, p is assumed to be in 0, ..., (N-1)/2. More...

Static Public Attributes
constexpr static localIndex	numSupportPoints = 3
	The number of support points for the basis.

Detailed Description

This class contains the implementation for a second order (quadratic) Lagrange polynomial basis. The parent space is defined by:

            o-------------o-------------o  ---> xi

Index: 0 1 2 Coordinate: -1 0 1

Definition at line 38 of file LagrangeBasis2.hpp.

Member Function Documentation

◆ gradient()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis2::gradient	(	const int	index,
		const real64	xi
	)

inlinestaticconstexpr

The gradient of the basis function for a support point evaluated at a point along the axes.

Parameters

index	The index of the support point.
xi	The coordinate at which to evaluate the basis.

Returns: The value of basis function.

Definition at line 197 of file LagrangeBasis2.hpp.

◆ gradient0()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis2::gradient0 ( const real64 xi )

inlinestaticconstexpr

The gradient of the basis function for support point 0 evaluated at a point along the axes.

Parameters

xi	The coordinate at which to evaluate the gradient.

Returns: The gradient of basis function

Definition at line 157 of file LagrangeBasis2.hpp.

◆ gradient1()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis2::gradient1 ( const real64 xi )

inlinestaticconstexpr

The gradient of the basis function for support point 1 evaluated at a point along the axes.

Parameters

xi	The coordinate at which to evaluate the gradient.

Returns: The gradient of basis function

Definition at line 170 of file LagrangeBasis2.hpp.

◆ gradient2()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis2::gradient2 ( const real64 xi )

inlinestaticconstexpr

The gradient of the basis function for support point 1 evaluated at a point along the axes.

Parameters

xi	The coordinate at which to evaluate the gradient.

Returns: The gradient of basis function

Definition at line 183 of file LagrangeBasis2.hpp.

◆ gradientAt()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis2::gradientAt	(	const int	q,
		const int	p
	)

inlinestaticconstexpr

The gradient of the basis function for a support point evaluated at a given support point. By symmetry, p is assumed to be in 0, ..., (N-1)/2.

Parameters

q	The index of the basis function
p	The index of the support point

Returns: The gradient of basis function.

Definition at line 221 of file LagrangeBasis2.hpp.

◆ parentSupportCoord()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis2::parentSupportCoord ( const localIndex supportPointIndex )

inlinestaticconstexpr

Calculate the parent coordinates for the xi0 direction, given the linear index of a support point.

Parameters

supportPointIndex The linear index of support point

Returns: parent coordinate in the xi0 direction.

Definition at line 71 of file LagrangeBasis2.hpp.

◆ value()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis2::value	(	const int	index,
		const real64	xi
	)

inlinestaticconstexpr

The value of the basis function for a support point evaluated at a point along the axes.

Parameters

index	The index of the support point.
xi	The coordinate at which to evaluate the basis.

Returns: The value of basis function.

Definition at line 95 of file LagrangeBasis2.hpp.

◆ value0()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis2::value0 ( const real64 xi )

inlinestaticconstexpr

The value of the basis function for support point 0.

Parameters

xi	The coordinate at which to evaluate the basis.

Returns: The value of the basis.

Definition at line 118 of file LagrangeBasis2.hpp.

◆ value1()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis2::value1 ( const real64 xi )

inlinestaticconstexpr

The value of the basis function for support point 1.

Parameters

xi	The coordinate at which to evaluate the basis.

Returns: The value of the basis.

Definition at line 131 of file LagrangeBasis2.hpp.

◆ value2()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis2::value2 ( const real64 xi )

inlinestaticconstexpr

The value of the basis function for support point 2.

Parameters

xi	The coordinate at which to evaluate the basis.

Returns: The value of the basis.

Definition at line 143 of file LagrangeBasis2.hpp.

◆ weight()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis2::weight ( const int q )

inlinestaticconstexpr

The value of the weight for the given support point.

Parameters

q	The index of the support point

Returns: The value of the weight

Definition at line 51 of file LagrangeBasis2.hpp.

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

coreComponents/finiteElement/elementFormulations/LagrangeBasis2.hpp

Classes

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Function Documentation

◆ gradient()

◆ gradient0()

◆ gradient1()

◆ gradient2()

◆ gradientAt()

◆ parentSupportCoord()

◆ value()

◆ value0()

◆ value1()

◆ value2()

◆ weight()