namespace for finite elements. More...

Classes
class	DiffOp
	Differential Operator. More...
class	DifferentialOperator
	Differential Operator. More...
class	BlockDifferentialOperator
class	T_DifferentialOperator
	Connect compile-time polymorph DiffOp to run-time polymorph DifferentialOperator. More...
class	T_FunctionDiffOp
class	DiffOpGradient
	Gradient operator of dimension D. More...
class	DiffOpGradientBoundary
	Boundary Gradient operator of dimension D. More...
class	DiffOpGradientRotSym
	Gradient operator in r-z coordinates. More...
class	DiffOpId
	Identity. More...
class	DiffOpIdSys
	Identity. More...
class	DiffOpIdBoundary
	Identity on boundary. More...
class	DiffOpIdBoundarySys
	Identity. More...
class	DiagDMat
	diagonal tensor, all values are the same More...
class	OrthoDMat
	orthotropic tensor. More...
class	OrthoDMat< 1 >
class	OrthoDMat< 2 >
class	OrthoDMat< 3 >
class	SymDMat
	full symmetric tensor More...
class	SymDMat< 1 >
class	SymDMat< 2 >
class	SymDMat< 3 >
class	NormalDMat
class	DVec
class	DVecN
class	TVec
class	RotSymLaplaceDMat
	DMat for rot.-sym. Laplace operator. More...
class	DiffOpNormal
	Identity on boundary. More...
class	NormalRobinIntegrator
	integrator for $\int_\Gamma u_n v_n \, ds$ More...
class	LaplaceIntegrator
	Integrator for grad u grad v. More...
class	LaplaceBoundaryIntegrator
class	RotSymLaplaceIntegrator
class	OrthoLaplaceIntegrator
class	MassIntegrator
class	RobinIntegrator
	integrator for $\int_\Gamma u v \, ds$ More...
class	DiffOpDiv
class	DivDivIntegrator
class	DiffOpCurl
class	CurlCurlIntegrator
class	DiffOpCurl3d
class	CurlCurl3dIntegrator
class	SourceIntegrator
	integrator for $\int_\Omega f v$ More...
class	NeumannIntegrator
class	NormalNeumannIntegrator
	integrator for $\int_\Gamma v_n \, ds$ More...
class	GradSourceIntegrator
class	DMatOp
	Coefficient tensor. More...
class	T_BDBIntegrator
	Element assembling. More...
class	T_NonlinearBDBIntegrator
class	T_BIntegrator
	Element vector assembling. More...
class	CoefficientFunction
	coefficient functions More...
class	ConstantCoefficientFunction
	The coefficient is constant everywhere. More...
class	DomainConstantCoefficientFunction
	The coefficient is constant in every sub-domain. More...
class	DomainVariableCoefficientFunction
class	DomainInternalCoefficientFunction
class	IntegrationPointCoefficientFunction
	coefficient function that is defined in every integration point. More...
class	PolynomialCoefficientFunction
	Coefficient function that depends (piecewise polynomially) on a parameter. More...
class	FileCoefficientFunction
class	ElementTopology
	Topology and coordinate information of master element: More...
class	Node
	A Node of an element. More...
class	NodeSet
	A binary representation of selecting V-E-F-C Nodes. More...
class	TopologicElement
class	ET_trait
class	ET_trait< ET_POINT >
class	ET_trait< ET_SEGM >
class	ET_trait< ET_TRIG >
class	ET_trait< ET_QUAD >
class	ET_trait< ET_TET >
class	ET_trait< ET_PRISM >
class	ET_trait< ET_PYRAMID >
class	ET_trait< ET_HEX >
class	ElementTransformation
	Transformation from reference element to physical element. More...
class	FE_ElementTransformation
class	FacetFEFacet
class	FacetVolumeFiniteElement
class	FiniteElement
	Define the degree of freedom. More...
class	CompoundFiniteElement
	A compound of several elements. More...
class	DummyFE
	a placeholder finite element More...
class	ScalarFiniteElement
	Scalar finite element. More...
class	DShapeElement
	Extracts and assigns gradient from autodiff. More...
class	DShapeAssign
	Assign gradients from generic shape functions. More...
class	EvaluateShapeElement
	Evaluate shape. More...
class	EvaluateShape
	Computes function value from generic shape functions. More...
class	EvaluateShapeTransElement
	todo More...
class	EvaluateShapeTrans
class	EvaluateDShapeElement
class	EvaluateDShape
class	EvaluateDShapeTransElement
class	EvaluateDShapeTrans
	todo More...
class	T_ScalarFiniteElement
	Base-element for template polymorphism. More...
class	T_ScalarFiniteElement2
	Base-element for template polymorphism. More...
class	RecPol
	Generic recursive polynomial. More...
class	RecPolMonomial
	Initialize coefficients with x^i. More...
class	RecPolJacobi
	Initialize coefficients with Jacobi polynomials. More...
class	RecPolLegendre
	Initialize coefficients with Legendre polynomials. More...
class	H1HighOrderFiniteElement
	High order finite elements for H^1. More...
class	T_H1HighOrderFiniteElement
	Barton-Nackman base class for H1 - high order finite elements. More...
class	H1HighOrderFE
	High order finite elements for H1. More...
class	H1HighOrderFE_Shape< ET_POINT >
	High order 0D finite element. More...
class	H1HighOrderFE_Shape< ET_SEGM >
	High order segment finite element. More...
class	H1HighOrderFE_Shape< ET_TRIG >
	High order triangular finite element. More...
class	H1HighOrderFE_Shape< ET_QUAD >
	High order quadrilateral finite element. More...
class	H1HighOrderFE_Shape< ET_TET >
	High order tetrahedral finite element. More...
class	H1HighOrderFE_Shape< ET_PRISM >
	High order prismatic finite element. More...
class	H1HighOrderFE_Shape< ET_HEX >
	High order hexahedral finite element. More...
class	H1HighOrderFE_Shape< ET_PYRAMID >
	High order pyramid shape functions. More...
class	DIM_CURL_TRAIT
class	DIM_CURL_TRAIT< 1 >
class	HCurlFiniteElement
	H(Curl) finite element of dimension D. More...
class	Du
class	uDv
class	uDv_minus_vDu
class	wuDv_minus_wvDu
class	HCurlShapeElement
class	HCurlCurlShapeElement
class	HCurlEvaluateCurlElement
class	HCurlShapeAssign
class	HCurlCurlShapeAssign
class	HCurlEvaluateCurl
class	T_HCurlFiniteElement
	Base-element for template polymorphism. More...
class	HCurlHighOrderFiniteElement
	High order H(curl) finite element of dimension D. More...
class	T_HCurlHighOrderFiniteElement
	HCurlHighOrderFE of shape ET. More...
class	HCurlHighOrderFE< ET_SEGM >
	A segment high order H(curl) element. More...
class	HCurlHighOrderFE< ET_TRIG >
	A triangular high order H(curl) element. More...
class	HCurlHighOrderFE< ET_QUAD >
	A quadrilateral high order H(curl) element. More...
class	HCurlHighOrderFE< ET_TET >
	A tetrahedral high order H(curl) element. More...
class	HCurlHighOrderFE< ET_HEX >
	A hexahedral high order H(curl) element. More...
class	HCurlHighOrderFE< ET_PRISM >
	A prismatic high order H(curl) element. More...
class	HCurlHighOrderFE< ET_PYRAMID >
	A pyramidal high order H(curl) element. More...
class	DiffOpIdHDiv
	Identity operator, Piola transformation. More...
class	DiffOpDivHDiv
	divergence Operator More...
class	DiffOpIdHDivBoundary
	Identity for boundary-normal elements. More...
class	DiffOpIdVecHDivBoundary
	Identity for boundary-normal elements, gives q_n n. More...
class	MassHDivIntegrator
	Integrator for term of zero-th order. More...
class	DivDivHDivIntegrator
	Integrator for div u div v. More...
class	DivSourceHDivIntegrator
	source term integrator for div v More...
class	BaseSourceHDivIntegrator
class	SourceHDivIntegrator< 2 >
class	SourceHDivIntegrator< 3 >
class	SourceHDivIntegratorN
class	NeumannHDivIntegrator
class	RobinHDivIntegrator
	integrator for $\int_\Gamma \sigma_n \tau_n \, ds$ More...
class	HDivFiniteElement
	Finite Elements for H(div) Raviart-Thomas, BDM, BDFM. More...
class	HDivNormalFiniteElement
	HDivNormalFiniteElement. More...
class	HDivHighOrderFiniteElement
class	HDivHighOrderNormalFiniteElement
class	HDivHighOrderNormalSegm
class	HDivHighOrderNormalTrig
class	HDivHighOrderNormalQuad
class	T_HDivHighOrderFiniteElement
class	HDivHighOrderFE< ET_TRIG >
class	HDivHighOrderFE< ET_QUAD >
class	HDivHighOrderFE< ET_TET >
class	HDivHighOrderFE< ET_PRISM >
class	HDivHighOrderFE< ET_HEX >
class	Integrator
	Base class for linear-form and bilinear-form integrators. More...
class	BilinearFormIntegrator
	A BilinearFormIntegrator computes the element matrices. More...
class	FacetBilinearFormIntegrator
class	BlockBilinearFormIntegrator
class	ComplexBilinearFormIntegrator
class	CompoundBilinearFormIntegrator
class	LinearFormIntegrator
	Integrator for element vector. More...
class	FacetLinearFormIntegrator
class	BlockLinearFormIntegrator
class	ComplexLinearFormIntegrator
class	CompoundLinearFormIntegrator
class	Integrators
	container for all integrators More...
class	RegisterBilinearFormIntegrator
class	RegisterLinearFormIntegrator
class	IntegrationPoint
	An integration point. More...
class	BaseMappedIntegrationPoint
	Base class for MappedIntegrationPoint. More...
class	DimMappedIntegrationPoint
class	MappedIntegrationPoint
	ip, dimension source, dimension range More...
class	IntegrationRule
	An integration rule. More...
class	IntegrationRuleTP
class	Facet2ElementTrafo
class	Facet2SurfaceElementTrafo
class	BaseMappedIntegrationRule
class	MappedIntegrationRule
class	L2HighOrderFiniteElement
	Base class for L2 - high order finite elements, i.e., a discontinuous approximation. More...
class	T_L2HighOrderFiniteElement
	Template family of L2 - high order finite elements. More...
class	PrecomputedScalShapes
class	L2HighOrderFE
class	L2HighOrderFE_Shape< ET_SEGM >
	L2 high order 1D finite element. More...
class	L2HighOrderFE_Shape< ET_TRIG >
	L2 high order triangular finite element. More...
class	L2HighOrderFE_Shape< ET_QUAD >
	L2 high order quadrilateral finite element. More...
class	L2HighOrderFE_Shape< ET_TET >
	L2 high order tetrahedral finite element. More...
class	L2HighOrderFE_Shape< ET_PRISM >
	L2 high order prismatic finite element. More...
class	L2HighOrderFE_Shape< ET_PYRAMID >
	L2 high order pyramid finite element. More...
class	L2HighOrderFE_Shape< ET_HEX >
	L2 high order hexahedral finite element. More...
class	PML_BDBIntegrator
class	CEvalFO
class	CEvalFO< REC,-1 >
class	CEvalFO< REC, 0 >
class	CEvalFO< REC, 1 >
class	RecursivePolynomial
class	LegendrePolynomial
class	JacobiPolynomialFix
class	DubinerJacobiPolynomialsFO
class	DubinerJacobiPolynomialsFO< n,-1, alpha0, beta >
class	DubinerJacobiPolynomialsPowFO
class	DubinerJacobiPolynomialsPowFO< n,-1, alpha0, beta >
class	DubinerJacobiPolynomialsDiag
class	DubinerJacobiPolynomialsDiag< ALPHA0, BETA, DIAG,-1 >
class	DubinerBasis
class	IntegratedLegendreMonomialExt
	Compute triangle edge-shape functions. More...
class	ConvertJacobi
class	TReduceAlpha
class	TReduceAlpha< 0, AL >
class	TReduceAlphaFactor
class	TReduceAlphaFactor< 0, AL, HIGHEST >
class	TDifferentiateJacobi
class	TDifferentiateJacobi< 0, AL >
class	TDifferentiateLegendre
class	TDifferentiateLegendre< 0 >
class	TTriangleReduceFactorCol
class	TTriangleReduceFactorCol< N, J,-1, AL, BE >
class	TTriangleReduceFactor
class	TTriangleReduceFactor< N,-1, AL, BE >
class	TTriangleReduceLoop2New
class	TTriangleReduceLoop2New< N, I,-1, AL, BE >
class	TTriangleReduceNew
class	TTriangleReduceNew< N,-1, AL, BE >
class	TetShapesInnerLegendre
class	TetShapesInnerJacobi
class	TetShapesFaceLegendre
class	TetShapesFaceJacobi
class	TetShapesFaceOpt1
class	TetShapesFaceOpt2
class	TrigShapesInnerLegendre
	Computes face shape functions for triangles. More...
class	TrigShapesInnerJacobi
	Compute triangular face shape functions. More...
class	TrigExtensionMonomial
	Compute triangle edge-shape functions. More...
class	TrigExtensionOptimal
	Evaluete optimal edge-shape function. More...
class	TrigExtensionMin
	....... More...
class	SpecialElement
class	VectorFacetFacetFiniteElement
class	VectorFacetFacetSegm
	High order 1D finite element. More...
class	VectorFacetFacetTrig
	High order triangular finite element. More...
class	VectorFacetFacetQuad
	High order quadrilateral finite element. More...
class	VectorFacetVolumeFiniteElement
class	VectorFacetVolumeTrig
class	VectorFacetVolumeQuad
class	VectorFacetVolumeTet
class	VectorFacetVolumeHex
class	VectorFacetVolumePrism
class	VectorFacetVolumePyramid
Typedefs
typedef double	POINT3D [3]
	point coordinates
typedef int	EDGE [2]
	initial point, end point
typedef int	FACE [4]
	points, last one is -1 for trig
typedef double	NORMAL [3]
	normal vector
Enumerations
enum	ELEMENT_TYPE { ET_POINT = 0, ET_SEGM = 1, ET_TRIG = 10, ET_QUAD = 11, ET_TET = 20, ET_PYRAMID = 21, ET_PRISM = 22, ET_HEX = 24 }
	Geometry of element. More...
enum	NODE_TYPE { NT_VERTEX = 0, NT_EDGE = 1, NT_FACE = 2, NT_CELL = 3 }
	Type of node. More...
Functions
template<typename DOP , typename F >
DifferentialOperator *	CreateFunctionDiffOp (const DOP &dop, const F &func, int dim=1)
template<int M>
NGS_DLL_HEADER void	FastMat (int n, Complex ba, Complex pb, Complex *pc)
template<int M>
NGS_DLL_HEADER void	FastMat (int n, double __restrict__ ba, double __restrict__ pb, double *__restrict__ pc)
double	Evaluate (const CoefficientFunction &fun, const BaseMappedIntegrationPoint &ip)
void	operator++ (NODE_TYPE &nt, int)
int	CalcNodeId (ELEMENT_TYPE et, const Node &node)
Node	CalcNodeFromId (ELEMENT_TYPE et, int nodeid)
ostream &	operator<< (ostream &ost, const Node &node)
ostream &	operator<< (ostream &ost, const TopologicElement &etop)
int	PolBubbleDimension (ELEMENT_TYPE ET, const INT< 1 > &order)
int	PolBubbleDimension (ELEMENT_TYPE ET, const INT< 2 > &order)
int	PolBubbleDimension (ELEMENT_TYPE ET, const INT< 3 > &order)
template<typename TFA >
void	SetZero (TFA &shape, int first, int next)
void	SetZero (EvaluateShape &shape, int first, int next)
void	SetZero (EvaluateShapeTrans &shape, int first, int next)
ostream &	operator<< (ostream &ost, const RecPol &pol)
	output coefficients
void	GenerateMatrix (const RecPol &pol1, const RecPol &pol2, FlatVector<> pts, FlatVector<> coefs, FlatMatrix<> mat)
void	GenerateMatrix (const RecPol &pol1, FlatMatrix<> pol1_vals, const RecPol &pol2, FlatMatrix<> pol2_vals, FlatVector<> coefs, FlatMatrix<> mat)
AutoDiff< 3 >	Cross (const AutoDiff< 3 > &u, const AutoDiff< 3 > &v)
AutoDiff< 1 >	Cross (const AutoDiff< 2 > &u, const AutoDiff< 2 > &v)
template<int D>
void	ComputeGradientMatrix (const ScalarFiniteElement< D > &h1fe, const HCurlFiniteElement< D > &hcurlfe, FlatMatrix<> gradient)
NGS_DLL_HEADER Integrators &	GetIntegrators ()
template<int DIMS, int DIMR, typename SCAL >
ostream &	operator<< (ostream &ost, const MappedIntegrationPoint< DIMS, DIMR, SCAL > &sip)
ostream &	operator<< (ostream &ost, const IntegrationRule &ir)
NGS_DLL_HEADER void	ComputeGaussRule (int n, Array< double > &xi, Array< double > &wi)
	Computes Gaussean integration.
NGS_DLL_HEADER void	ComputeGaussJacobiRule (int n, Array< double > &xi, Array< double > &wi, double alf, double bet)
	Computes Gauss-Jacobi integration rule.
NGS_DLL_HEADER void	ComputeHermiteRule (int n, Array< double > &x, Array< double > &w)
	Computes Gauss-Hermite integration rule.
NGS_DLL_HEADER const IntegrationRule &	SelectIntegrationRule (ELEMENT_TYPE eltype, int order)
NGS_DLL_HEADER const IntegrationRule &	SelectIntegrationRuleJacobi10 (int order)
NGS_DLL_HEADER const IntegrationRule &	SelectIntegrationRuleJacobi20 (int order)
void	SetPMLParameters ()
template<class S , class T >
void	LegendrePolynomial1 (int n, S x, T &values)
	Legendre polynomials P_i on (-1,1), up to order n --> n+1 values.
template<class S , class Sc , class T >
void	LegendrePolynomialMult (int n, S x, Sc c, T &values)
template<class S , class T >
void	JacobiPolynomial (int n, S x, double alpha, double beta, T &values)
template<class S , class Sc , class T >
void	JacobiPolynomialMult (int n, S x, double alpha, double beta, Sc c, T &values)
template<class S , class St , class T >
void	ScaledJacobiPolynomial (int n, S x, St t, double alpha, double beta, T &values)
template<class S , class St , class Sc , class T >
void	ScaledJacobiPolynomialMult (int n, S x, St t, double alpha, double beta, Sc c, T &values)
template<class S , class T >
void	DubinerJacobiPolynomials1 (int n, S x, int alpha0, int beta, T &values)
template<int ALPHA0, int BETA, class S , class T >
void	DubinerJacobiPolynomials2 (int n, S x, T &values)
template<int ALPHA0, int BETA, class S , class T >
void	DubinerJacobiPolynomials (int n, S x, T &values)
template<class S , class St , class T >
void	DubinerJacobiPolynomialsScaled1 (int n, S x, St t, int alpha0, int beta, T &values)
template<int ALPHA0, int BETA, class S , class St , class T >
void	DubinerJacobiPolynomialsScaled (int n, S x, St t, T &values)
template<class S , class T >
void	GegenbauerPolynomial (int n, S x, double lam, T &values)
template<class S , class T >
void	IntegratedLegendrePolynomial (int n, S x, T &values)
	Integrated Legendre polynomials on (-1,1)
template<class S , class T >
void	HermitePolynomial (int n, S x, T &values)
	Hermite polynomials H_i, orthogonal w.r.t.
template<class Sx , class Sy , class T >
void	TriangleExtensionMonomial (int n, Sx x, Sy y, T &values)
	Compute triangle edge-shape functions.
template<class Sx , class Sy , class T >
void	DiffTriangleExtensionMonomial (int n, Sx x, Sy y, T &values)
template<class Sx , class Sy , class T >
void	TriangleExtensionJacobi (int n, Sx x, Sy y, T &values)
	Extension is the optimal averaging extension:
template<class Sx , class Sy , class T >
void	DiffTriangleExtensionJacobi (int n, Sx x, Sy y, T &values)
template<class Sx , class Sy , class T >
void	TriangleExtensionOpt (int n, Sx x, Sy y, T &values)
	Extension is the optimal averaging extension:
template<class Sx , class Sy , class T >
void	DiffTriangleExtensionOpt (int n, Sx x, Sy y, T &values)
template<class S1 , class S2 , class S3 >
void	StdOp (S1 &v1, const S2 &tt, const S3 &v2, double fac)
template<int D>
void	StdOp (AutoDiff< D > &v1, const AutoDiff< D > &tt, const AutoDiff< D > &v2, double fac)
template<class Sx , class St , class T >
void	ScaledLegendrePolynomial (int n, Sx x, St t, T &values)
template<class Sx , class St , class Sc , class T >
void	ScaledLegendrePolynomialMult (int n, Sx x, St t, Sc c, T &values)
template<class T >
void	DiffScaledLegendrePolynomial (int n, double x, double t, T &values)
template<class Sx , class St , class T >
void	ScaledIntegratedLegendrePolynomial (int n, Sx x, St t, T &values)
template<class T >
void	ScaledLegendrePolynomialandDiff (int n, double x, double t, T &P, T &Px, T &Pt)
template<class T >
void	LegendrePolynomialandDiff (int n, double x, T &P, T &Px)
template<class T >
void	ConvertJacobiReduceAlpha (int n, int alpha, T &inout)
template<class T >
void	ConvertJacobiReduceAlphaFactor (int n, double alpha, T &inout)
template<class T >
void	DifferentiateJacobi (int n, double alpha, T &inout)
template<class T >
void	DifferentiateJacobiTrans (int n, double alpha, T &inout)
template<class T >
void	DifferentiateLegendre (int n, T &inout)
template<class T >
void	DifferentiateLegendreTrans (int n, T &inout)
Variables
class NGS_DLL_HEADER	FacetVolumeFiniteElement
class NGS_DLL_HEADER	ElementTransformation
Complex	alpha
double	pml_r
double	pml_x
double	pml_xmin [3]
double	pml_xmax [3]
int	rect_pml
bool	apply_deriv_alpha

Detailed Description

namespace for finite elements.

Definition of reference FiniteElement, ScalarFiniteElement, and vector-valued elements HDivFiniteElement and HCurlFiniteElement

Definition of the geometry of the element, i.e., ElementTransformation

IntegrationPoint on the reference element, and SpecificIntegrationPoint on the mapped element

Element-matrix and element-vector calculation by BilinearFormIntegrator and LinearFormIntegrator

Enumeration Type Documentation

enum ngfem::ELEMENT_TYPE

Geometry of element.

Possible are ET_POINT, ET_SEGM, ET_TRIG, ET_QUAD, ET_TET, ET_PYRAMID, ET_PRISM, ET_HEX

enum ngfem::NODE_TYPE

Type of node.

vertex nodes are 0 dimensional, edge nodes are 1 dimensional face nodes are 2 dimensional cell nodes are 3 dimensional

2D elements have vertex, edge, and face nodes

3D elements have vertex, edge, face and cell nodes

Function Documentation

NGS_DLL_HEADER void ngfem::ComputeGaussJacobiRule	(	int	n,
		Array< double > &	xi,
		Array< double > &	wi,
		double	alf,
		double	bet
	)

Computes Gauss-Jacobi integration rule.

Integration rule on (0,1), contains n points. Assumes that the polynomial has alpha roots in 1, and beta roots in 0. Exact for polynomials up to order 2n-1 + alpha + beta

NGS_DLL_HEADER void ngfem::ComputeGaussRule	(	int	n,
		Array< double > &	xi,
		Array< double > &	wi
	)

Computes Gaussean integration.

Integration rule on (0,1), contains n points, Exact for polynomials up to order 2n-1

NGS_DLL_HEADER void ngfem::ComputeHermiteRule	(	int	n,
		Array< double > &	x,
		Array< double > &	w
	)

Computes Gauss-Hermite integration rule.

Integration rule on R, contains n points. Exact for exp{-x*x} * p(x), with polynomials p(x) up to order 2n-1

template<class S , class T >

void ngfem::HermitePolynomial	(	int	n,
		S	x,
		T &	values
	)		`[inline]`

Hermite polynomials H_i, orthogonal w.r.t.

exp(-x*x) up to order n --> n+1 values

H_l = 2 x H_{l-1} - 2 (l-1) H_{l-2}

P_0 = 1 P_1 = 2*x P_2 = 4*x*x - 2 P_2 = 8*x*x*x - 12 x

template<class S , class T >

void ngfem::IntegratedLegendrePolynomial	(	int	n,
		S	x,
		T &	values
	)		`[inline]`

Integrated Legendre polynomials on (-1,1)

value[0] = -1 value[1] = x value[i] (x) = {-1}^x P_{i-1} (s) ds for i >= 2

WARNING: is not P_i

template<class S , class T >

void ngfem::LegendrePolynomial1	(	int	n,
		S	x,
		T &	values
	)		`[inline]`

Legendre polynomials P_i on (-1,1), up to order n --> n+1 values.

l P_l = (2 l - 1) x P_{l-1} - (l-1) P_{l-2}

P_0 = 1 P_1 = x P_2 = -1/2 + 3/2 x^2

template<class Sx , class Sy , class T >

void ngfem::TriangleExtensionMonomial	(	int	n,
		Sx	x,
		Sy	y,
		T &	values
	)		`[inline]`

Compute triangle edge-shape functions.

functions vanish on upper two edges

x,y: coordinates in triangle (-1, 0), (1, 0), (0, 1)

f_i (x, 0) = IntegratedLegendrePol_i (x)

f_i ... pol of order i

Monomial extension:

Classes

Typedefs

Enumerations

Functions

Variables

Detailed Description

Enumeration Type Documentation

Function Documentation