#include <Helper.hpp>

Public Types
enum	VarType { Deriv0 = 0 , Deriv1 = 1 }
	Order of derivative of a function. More...

typedef double	SC

Static Public Member Functions
static void	computeSurfaceNormal (int dim, vec2D_dbl_ptr_Type pointsRep, vec_int_Type nodeList, vec_dbl_Type &v_E, double &norm_v_E)
	Compute surface normal of corresponding surface.

static void	buildTransformation (const vec_int_Type &element, vec2D_dbl_ptr_Type pointsRep, SmallMatrix< SC > &B, std::string FEType="P")
	Build transformation of element to reference element depending on FEType.

static void	buildTransformation (const vec_int_Type &element, vec2D_dbl_ptr_Type pointsRep, SmallMatrix< SC > &B, vec_dbl_Type &b, std::string FEType="P")
	Build transformation of element to reference element depending on FEType.

static void	buildTransformationSurface (const vec_int_Type &element, vec2D_dbl_ptr_Type pointsRep, SmallMatrix< SC > &B, vec_dbl_Type &b, std::string FEType="P")
	Transformation of a surface to the reference element.

static void	gradPhi (int Dimension, int intFE, int i, vec_dbl_Type &QuadPts, vec_dbl_ptr_Type &value)
	Returning gradient of phi evaluated at the quadrature points.

static void	getQuadratureValues (int Dimension, int Degree, vec2D_dbl_ptr_Type &QuadPts, vec_dbl_ptr_Type &QuadW, std::string FEType)
	Get quadrature formula.

static vec2D_dbl_Type	getQuadratureValuesOnSurface (int dim, std::string FEType, vec_dbl_Type &QuadW, vec_LO_Type surfaceIDs, vec2D_dbl_ptr_Type points)
	Returns quadrature formula on surface element.

static int	getDPhi (vec3D_dbl_ptr_Type &DPhi, vec_dbl_ptr_Type &weightsDPhi, int Dimension, std::string FEType, int Degree)
	Full matrix representation of gradient of a basis function for each quadrature point.

static void	getDPhiAtCM (vec3D_dbl_ptr_Type &DPhi, int dim, std::string FEType)

static void	applyBTinv (vec3D_dbl_ptr_Type &dPhiIn, vec3D_dbl_Type &dPhiOut, const SmallMatrix< SC > &Binv)
	Applying the transformation matriX B to the gradient of phi, as is done in when transforming the gradient of phi to the reference element.

static UN	determineDegree (UN dim, std::string FEType, VarType orderOfDerivative)
	Determine polynomial degree of a finite element basis function or its gradient that is required to select the correct quadrature formula for exact integration.

static int	getPhi (vec2D_dbl_ptr_Type &Phi, vec_dbl_ptr_Type &weightsPhi, int dim, std::string FEType, int Degree, std::string FETypeQuadPoints="")
	Get basisfunction phi per quadrature point.

static int	getFuncAtQuadNodes (vec_dbl_ptr_Type &funcVals, RhsFunc_Type &rhsFunc, int dim, std::string FEType, int Degree, std::string FETypeQuadPoints="")

static void	phi (int dim, int intFE, int i, vec_dbl_Type &p, double *value)
	Get phi i.

static int	getPhiGlobal (vec2D_dbl_ptr_Type &Phi, vec_dbl_ptr_Type &weightsPhi, int dim, std::string FEType, int Degree)

Detailed Description

Helper class of static functions that contains rudimental finite element components. It contains basis functions, quadrature rules, transformation functions, and other stuff.

Member Enumeration Documentation

◆ VarType

enum FEDD::Helper::VarType

Order of derivative of a function.

Enumerator
Deriv0	order 0, f(x)
Deriv1	order 1, gradient(f(x))

Member Function Documentation

◆ applyBTinv()

void FEDD::Helper::applyBTinv	(	vec3D_dbl_ptr_Type &	dPhiIn,
		vec3D_dbl_Type &	dPhiOut,
		const SmallMatrix< SC > &	Binv )

static

Applying the transformation matriX B to the gradient of phi, as is done in when transforming the gradient of phi to the reference element.

Parameters

dPhiIn
dPhiOut
Binv

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◆ buildTransformation() [1/2]

void FEDD::Helper::buildTransformation	(	const vec_int_Type &	element,
		vec2D_dbl_ptr_Type	pointsRep,
		SmallMatrix< SC > &	B,
		std::string	FEType = "P" )

static

Build transformation of element to reference element depending on FEType.

Parameters

[in]	element	Finite element
[in]	pointsRep	List of repeated points
[out]	B	Resulting transformation matrix
[in]	FEType	FE Discretization

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◆ buildTransformation() [2/2]

void FEDD::Helper::buildTransformation	(	const vec_int_Type &	element,
		vec2D_dbl_ptr_Type	pointsRep,
		SmallMatrix< SC > &	B,
		vec_dbl_Type &	b,
		std::string	FEType = "P" )

static

Build transformation of element to reference element depending on FEType.

Parameters

[in]	element	Finite element
[in]	pointsRep	List of repeated points
[out]	B	Resulting transformation matrix
[in]	b	Point to transform from
[in]	FEType	FE Discretization

◆ buildTransformationSurface()

void FEDD::Helper::buildTransformationSurface	(	const vec_int_Type &	element,
		vec2D_dbl_ptr_Type	pointsRep,
		SmallMatrix< SC > &	B,
		vec_dbl_Type &	b,
		std::string	FEType = "P" )

static

Transformation of a surface to the reference element.

Parameters

[in]	element	Finite element
[in]	pointsRep	List of repeated points
[out]	B	Resulting transformation matrix
[in]	b	Point to transform from
[in]	FEType	FE Discretization

◆ computeSurfaceNormal()

void FEDD::Helper::computeSurfaceNormal	(	int	dim,
		vec2D_dbl_ptr_Type	pointsRep,
		vec_int_Type	nodeList,
		vec_dbl_Type &	v_E,
		double &	norm_v_E )

static

Compute surface normal of corresponding surface.

Parameters

[in]	dim	Dimension
[in]	pointsRep	List of all repeated nodes
[in]	nodeList	Ids of local surface points
[out]	v_E	normal vector
[out]	norm_v_E	Normal vector length

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◆ determineDegree()

UN FEDD::Helper::determineDegree	(	UN	dim,
		std::string	FEType,
		VarType	orderOfDerivative )

static

Determine polynomial degree of a finite element basis function or its gradient that is required to select the correct quadrature formula for exact integration.

This is a wrapper. See Helper::requiredQuadratureDegreeForBasisfunction for details in case the degree is required for a basis function. See Helper::requiredQuadratureDegreeForGradientOfBasisfunction for details in case the degree is required for the gradient of a basis function.

Parameters

[in]	dim	Dimension of the domain.
[in]	FEType	Finite element type, e.g., "P1", "Q2" etc.
[in]	orderOfDerivative	{Deriv0,Deriv1} Order of the derivative: order=0 (type=Deriv0) is the original function, order=1 (type=Deriv1) is the gradient, i.e., the first derivative.

Returns: a polynomial degree for a finite element basis function or its gradient

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◆ getDPhi()

int FEDD::Helper::getDPhi	(	vec3D_dbl_ptr_Type &	DPhi,
		vec_dbl_ptr_Type &	weightsDPhi,
		int	Dimension,
		std::string	FEType,
		int	Degree )

static

Full matrix representation of gradient of a basis function for each quadrature point.

Parameters

DPhi	grad Phi per quadpoint dim:(quadpoint,i,j)
weightsDPhi	Quadrature weights
Dimension	Dimension
FEType	Finite Element Type
Degree	Integration degree

Returns

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◆ getDPhiAtCM()

void FEDD::Helper::getDPhiAtCM	(	vec3D_dbl_ptr_Type &	DPhi,
		int	dim,
		std::string	FEType )

static

Parameters

DPhi	grad Phi p
Dimension	Dimension
FEType	Finite Element Type

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◆ getPhi()

int FEDD::Helper::getPhi	(	vec2D_dbl_ptr_Type &	Phi,
		vec_dbl_ptr_Type &	weightsPhi,
		int	dim,
		std::string	FEType,
		int	Degree,
		std::string	FETypeQuadPoints = "" )

static

Get basisfunction phi per quadrature point.

Parameters

Phi	Basisfunction phi per quad point with (quadpoint,i)
weightsPhi	Quadrature weights
dim	dimension
FEType	Finite element discretization
Degree	Integration degree
FETypeQuadPoints

Returns

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◆ getQuadratureValues()

void FEDD::Helper::getQuadratureValues	(	int	Dimension,
		int	Degree,
		vec2D_dbl_ptr_Type &	QuadPts,
		vec_dbl_ptr_Type &	QuadW,
		std::string	FEType )

static

Get quadrature formula.

A quadrature formula is used to integrate approximate an integral of f(x) over the domain Omega, i.e., integral_Omega f(x) dx, via the following sum: sum_i f(xi)*wi, where xi is a quadrature point, and wi a quadrature weight.

Source of the formulas: Most of the quadrature formulas can be found in http://code-aster.org/doc/v11/en/man_r/r3/r3.01.01.pdf 01/2021

Parameters

[in]	Dimension	Space dimension d of the domain of f:IR^d-->IR.
[in]	Degree	Order of polynomial that must be integrated exactly in exact arithmetic with the returned formula.
[out]	QuadPts	Quadrature points
[out]	QuadW	Quadrature weights
[in]	FEType	Finite element type, e.g., "P1", "Q2" etc.

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◆ getQuadratureValuesOnSurface()

vec2D_dbl_Type FEDD::Helper::getQuadratureValuesOnSurface	(	int	dim,
		std::string	FEType,
		vec_dbl_Type &	QuadW,
		vec_LO_Type	surfaceIDs,
		vec2D_dbl_ptr_Type	points )

static

Returns quadrature formula on surface element.

Is distinguishes between needing Element or Surface information. !! Input can be improved with just delivering the coordinates of the surface nodes to determine the quad points

Keep in mind that elementwise quadPoints are defined on reference element whereas surface quadPoints at hand are defined on the input surface, which is typically not the reference Element.

Parameters

[in]	dim	Space dimension of the underlying domain, e.g., 3 for a triangle in IR^3..
[in]	FEType	Finite element type of the underlying element (P1, P2, Q1 etc.), e.g., a "P2" tetrahedron for which a quadrature formula on one of its surface elements (triangles) is required.
[out]	QuadW	Vector to be filled with the quadrature weights
[in]	vec_LO_Type	surfaceIDs for which you need the quadrature points.
[in]	points	The repeated(!) points of current problem to identify the surface node ids.

Returns: Quadrature points

◆ gradPhi()

void FEDD::Helper::gradPhi	(	int	Dimension,
		int	intFE,
		int	i,
		vec_dbl_Type &	QuadPts,
		vec_dbl_ptr_Type &	value )

static

Returning gradient of phi evaluated at the quadrature points.

Parameters

[in]	Dimension	Dimension
[in]	intFE	number corresponding to FE disc.
[in]	i	basisfunction i
[in]	QuadPts	quadpoints
[out]	value	vector including values

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◆ phi()

void FEDD::Helper::phi	(	int	dim,
		int	intFE,
		int	i,
		vec_dbl_Type &	p,
		double *	value )

static

Get phi i.

Parameters

dim
intFE
i
p
value

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

feddlib/core/FE/Helper.hpp
feddlib/core/FE/Helper.cpp

Public Types

Static Public Member Functions

Detailed Description

Member Enumeration Documentation

◆ VarType

Member Function Documentation

◆ applyBTinv()

◆ buildTransformation() [1/2]

◆ buildTransformation() [2/2]

◆ buildTransformationSurface()

◆ computeSurfaceNormal()

◆ determineDegree()

◆ getDPhi()

◆ getDPhiAtCM()

◆ getPhi()

◆ getQuadratureValues()

◆ getQuadratureValuesOnSurface()

◆ gradPhi()

◆ phi()