#include <LagrangeBasis1.hpp>

Classes
struct	TensorProduct2D

struct	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 the 0 support point. More...

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

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

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64	gradientAt (const int q, const int)
	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. in the case of the first-order basis, this value is independent of p. More...

Static Public Attributes
constexpr static localIndex	numSupportPoints = 2
	The number of support points for the basis.

Detailed Description

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

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

Index: 0 1 Coordinate: -1 1

Definition at line 39 of file LagrangeBasis1.hpp.

Member Function Documentation

◆ gradient()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis1::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 associated with the basis function.
xi	The coordinate at which to evaluate the gradient.

Returns: The gradient of basis function.

Definition at line 134 of file LagrangeBasis1.hpp.

◆ gradient0()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis1::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 (-0.5)

Definition at line 149 of file LagrangeBasis1.hpp.

◆ gradient1()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis1::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 (0.5)

Definition at line 163 of file LagrangeBasis1.hpp.

◆ gradientAt()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis1::gradientAt	(	const int	q,
		const int
	)

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. in the case of the first-order basis, this value is independent of p.

Parameters

q	The index of the basis function

Returns: The gradient of basis function.

Definition at line 191 of file LagrangeBasis1.hpp.

◆ gradientBubble()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis1::gradientBubble ( const real64 xi )

inlinestaticconstexpr

The gradient of the bubble 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 177 of file LagrangeBasis1.hpp.

◆ parentSupportCoord()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis1::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 66 of file LagrangeBasis1.hpp.

◆ value()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis1::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 80 of file LagrangeBasis1.hpp.

◆ value0()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis1::value0 ( const real64 xi )

inlinestaticconstexpr

The value of the basis function for the 0 support point.

Parameters

xi	The coordinate at which to evaluate the basis.

Returns: The value of the basis.

Definition at line 94 of file LagrangeBasis1.hpp.

◆ value1()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis1::value1 ( const real64 xi )

inlinestaticconstexpr

The value of the basis function for the 1 support point.

Parameters

xi	The coordinate at which to evaluate the basis.

Returns: The value of the basis.

Definition at line 106 of file LagrangeBasis1.hpp.

◆ valueBubble()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis1::valueBubble ( const real64 xi )

inlinestaticconstexpr

The value of the bubble basis function.

Parameters

xi	The coordinate at which to evaluate the basis.

Returns: The value of the basis.

Definition at line 118 of file LagrangeBasis1.hpp.

◆ weight()

GEOS_HOST_DEVICE constexpr static GEOS_FORCE_INLINE real64 geos::finiteElement::LagrangeBasis1::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 52 of file LagrangeBasis1.hpp.

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

coreComponents/finiteElement/elementFormulations/LagrangeBasis1.hpp

Classes

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Function Documentation

◆ gradient()

◆ gradient0()

◆ gradient1()

◆ gradientAt()

◆ gradientBubble()

◆ parentSupportCoord()

◆ value()

◆ value0()

◆ value1()

◆ valueBubble()

◆ weight()