Implements the shape functions of a linear (1D) element. Shape. More...

#include <pzshapelinear.h>

Inheritance diagram for pzshape::TPZShapeLinear:

Collaboration diagram for pzshape::TPZShapeLinear:

Static Public Member Functions
static void	Shape (TPZVec< REAL > &pt, TPZVec< int64_t > &id, TPZVec< int > &order, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Functions which computes the shapefunctions of a one-d element. More...

static void	ShapeCorner (TPZVec< REAL > &pt, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)

static void	SideShape (int side, TPZVec< REAL > &pt, TPZVec< int64_t > &id, TPZVec< int > &order, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)

static void	ShapeOrder (TPZVec< int64_t > &id, TPZVec< int > &order, TPZGenMatrix< int > &shapeorders)
	returns the polynomial order in the natural ksi, eta of the side associated with each shapefunction More...

static void	SideShapeOrder (int side, TPZVec< int64_t > &id, int order, TPZGenMatrix< int > &shapeorders)
	returns the polynomial order in the natural ksi, eta of the internal shapefunctions of a side More...

static void	ShapeInternal (TPZVec< REAL > &x, int ord, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi, int transformation_index)
	Computes the values of the orthogonal shapefunctions before multiplying them by the corner shapefunctions. More...

static void	ShapeInternal (TPZVec< REAL > &x, int ord, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Computes the values of the orthogonal shapefunctions before multiplying them by the corner shapefunctions. More...

static void	ShapeGenerating (TPZVec< REAL > &pt, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Computes the generating shape functions for a quadrilateral element. More...

static void	TransformPoint1d (int transid, REAL in, REAL &out)
	Computes the transformation applied to the variational parameter of the one-d element. More...

static void	TransformDerivative1d (int transid, int num, TPZFMatrix< REAL > &in)
	Applies the transformation on the values of the derivatives of the shape functions of the internal shape functions. More...

static int	GetTransformId1d (TPZVec< int64_t > &id)
	Computes the id of the transformation which will be applied on the parameter of the element . More...

static int	NConnectShapeF (int side, int order)
	Number of shapefunctions of the connect associated with the side, considering the order of interpolation of the element. More...

static int	NShapeF (TPZVec< int > &order)
	Total number of shapefunctions, considering the order of interpolation of the element. More...

static void	TransformPoint1d (int transid, double &val)

static TPZTransform< REAL >	ParametricTransform (int transid)

static void	ShapeInternal (int side, TPZVec< REAL > &x, int order, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)

Static Public Member Functions inherited from pztopology::TPZLine
static void	Shape (TPZVec< REAL > &loc, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Compute the shape being used to construct the x mapping from local parametric coordinates. More...

template<class T >
static void	TShape (const TPZVec< T > &loc, TPZFMatrix< T > &phi, TPZFMatrix< T > &dphi)
	Compute the shape being used to construct the x mapping from local parametric coordinates. More...

static void	GetSideHDivPermutation (int transformationid, TPZVec< int > &permgather)
	Identifies the permutation of the nodes needed to make neighbouring elements compatible in terms of order of shape functions. More...

static constexpr REAL	RefElVolume ()
	Volume of the master element (measure of the element) More...

static void	ComputeDirections (int side, TPZFMatrix< REAL > &gradx, TPZFMatrix< REAL > &directions, TPZVec< int > &sidevectors)

static void	GetSideHDivDirections (TPZVec< int > &sides, TPZVec< int > &dir, TPZVec< int > &bilinearounao)

static void	GetSideHDivDirections (TPZVec< int > &sides, TPZVec< int > &dir, TPZVec< int > &bilinearounao, TPZVec< int > &sidevectors)

template<class TVar >
static void	ComputeHDivDirections (TPZFMatrix< TVar > &gradx, TPZFMatrix< TVar > &directions)
	Compute the directions of the HDiv vectors. More...

static int	NBilinearSides ()

template<class T >
static void	BlendFactorForSide (const int &side, const TPZVec< T > &xi, T &blendFactor, TPZVec< T > &corrFactorDxi)

static int	SideDimension (int side)
	Returns the dimension of the side. More...

static void	LowerDimensionSides (int side, TPZStack< int > &smallsides)
	Get all sides with lower dimension on side. More...

static void	LowerDimensionSides (int side, TPZStack< int > &smallsides, int DimTarget)
	Get all sides with lower dimension but equal to DimTarget on side. More...

static void	HigherDimensionSides (int side, TPZStack< int > &high)
	Returns all sides whose closure contains side. More...

static int	NSideNodes (int side)
	Returns the number of nodes (not connectivities) associated with a side. More...

static int	SideNodeLocId (int side, int node)
	Returns the local node number of the node "node" along side "side". More...

static int	NumSides ()
	Returns the number of connects for a set dimension. More...

static int	NumSides (int dimension)
	Returns the number of connects for a set dimension. More...

static int	NContainedSides (int side)
	Returns the number of nodes (not connectivities) associated with a side. More...

static int	ContainedSideLocId (int side, int c)
	Returns the local connect number of the connect "c" along side "side". More...

static void	CenterPoint (int side, TPZVec< REAL > &center)
	Returns the barycentric coordinates in the master element space of the original element. More...

static bool	IsInParametricDomain (const TPZVec< REAL > &pt, REAL tol=pztopology::gTolerance)
	Verifies if the parametric point pt is in the element parametric domain. More...

static void	RandomPoint (TPZVec< REAL > &pt)
	Generates a random point in the master domain. More...

template<class T >
static bool	CheckProjectionForSingularity (const int &side, const TPZVec< T > &xiInterior)

template<class T >
static void	MapToSide (int side, TPZVec< T > &InternalPar, TPZVec< T > &SidePar, TPZFMatrix< T > &JacToSide)

static void	ParametricDomainNodeCoord (int node, TPZVec< REAL > &nodeCoord)

static MElementType	Type ()
	Returns the type of the element as specified in file pzeltype.h. More...

static MElementType	Type (int side)
	Returns the type of the element side as specified in file pzeltype.h. More...

static TPZTransform	SideToSideTransform (int sidefrom, int sideto)
	Returns the transformation which takes a point from the side sidefrom to the side sideto. More...

static TPZTransform	TransformSideToElement (int side)
	Returns the transformation which transform a point from the side to the interior of the element. More...

static TPZTransform	TransformElementToSide (int side)
	Returns the transformation which transform a point from the interior of the element to the side. More...

static int	GetTransformId (TPZVec< int64_t > &id)
	Method which identifies the transformation based on the IDs of the corner nodes. More...

static int	GetTransformId (int side, TPZVec< int64_t > &id)
	Method which identifies the transformation of a side based on the IDs of the corner nodes. More...

static TPZIntPoints *	CreateSideIntegrationRule (int side, int order)
	Create an integration rule over side. More...

Static Public Member Functions inherited from TPZSavable
static std::set< TPZRestoreClassBase * > &	RestoreClassSet ()
	This static function guarantees that the gMap object is available when needed. More...

static std::map< int, TPZRestore_t > &	ClassIdMap ()
	This static function guarantees that the gMap object is available when needed. More...

static std::pair< std::string, uint64_t >	NeoPZVersion ()

static void	Register (TPZRestoreClassBase *restore)

static void	RegisterClassId (int classid, TPZRestore_t fun)

static TPZSavable *	CreateInstance (const int &classId)

Orthogonal polynomials family
static void(*	fOrthogonal )(REAL x, int num, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Pointer to function which returns num orthogonal functions at the point x. More...

static REAL	JacobiA
	Jacobi parameters orthogonal polynomials. More...

static REAL	JacobiB

static void	Chebyshev (REAL x, int num, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Chebyshev orthogonal polynomial, computes num orthogonal functions at the point x. More...

static void	Expo (REAL x, int num, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Exponential polynomial, computes num orthogonal functions at the point x. More...

static void	Legendre (REAL x, int num, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Legendre orthogonal polynomial, computes num orthogonal functions at the point x. More...

static void	Jacobi (REAL x, int num, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Jacobi orthogonal polynomials. More...

static void	Hermite (REAL x, int num, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Hermite orthogonal polynomials. More...

static void	Legendre (REAL x, int num, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi, int nderiv)
	Legendre function computing several derivatives. More...

Additional Inherited Members
Public Types inherited from pztopology::TPZLine
enum	{ NCornerNodes, NSides, Dimension, NFaces, NPermutations }
	Enumerate for topological characteristics. More...

typedef TPZInt1d	IntruleType
	Typedef to numerical integration rule. More...

typedef TPZGraphEl1dd	GraphElType
	Typedef to graphical element type. More...

Public Member Functions inherited from pztopology::TPZLine
int	ClassId () const override
	Define the class id associated with the class. More...

void	Read (TPZStream &buf, void *context) override
	read objects from the stream More...

void	Write (TPZStream &buf, int withclassid) const override
	Writes this object to the TPZStream buffer. Include the classid if withclassid = true. More...

	TPZLine ()
	Default constructor. More...

virtual	~TPZLine ()
	Default destructor. More...

Public Member Functions inherited from TPZSavable
	TPZSavable ()

virtual	~TPZSavable ()

virtual std::list< std::map< std::string, uint64_t > >	VersionHistory () const

virtual std::pair< std::string, uint64_t >	Version () const

virtual bool	Compare (TPZSavable *copy, bool override=false)
	Compares the object for identity with the object pointed to, eventually copy the object. More...

virtual bool	Compare (TPZSavable *copy, bool override=false) const
	Compares the object for identity with the object pointed to, eventually copy the object. More...

Public Member Functions inherited from TPZRegisterClassId
template<typename T >
	TPZRegisterClassId (int(T::*)() const)

	TPZRegisterClassId ()=default

Static Protected Attributes inherited from pztopology::TPZLine
static int	fPermutations [2][3]
	Valid permutations between nodes. More...

Detailed Description

Implements the shape functions of a linear (1D) element. Shape.

The linear shape functions form the basis of all other shape function computations
The range of the master element is -1,1
The orthogonal function which generates the linear shape functions can be modified by changing the function pointer fOrthogonal
all static tables and functions concerning one-d elements will be grouped in this class

Definition at line 33 of file pzshapelinear.h.

Member Function Documentation

◆ Chebyshev()

void pzshape::TPZShapeLinear::Chebyshev	(	REAL	x,
		int	num,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Chebyshev orthogonal polynomial, computes num orthogonal functions at the point x.

Parameters

x	coordinate of the point
num	number of shape functions to be computed
phi	shapefunction values
dphi	values of the derivatives of the shape functions

Definition at line 15 of file pzshapelinear.cpp.

References TPZMatrix< TVar >::Put(), and TPZFMatrix< TVar >::Zero().

◆ Expo()

void pzshape::TPZShapeLinear::Expo	(	REAL	x,
		int	num,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Exponential polynomial, computes num orthogonal functions at the point x.

Parameters

x	coordinate of the point
num	number of shape functions to be computed
phi	shapefunction values
dphi	values of the derivatives of the shape functions

Definition at line 35 of file pzshapelinear.cpp.

References TPZMatrix< TVar >::Put().

◆ GetTransformId1d()

int pzshape::TPZShapeLinear::GetTransformId1d ( TPZVec< int64_t > & id )

static

Computes the id of the transformation which will be applied on the parameter of the element
.

Parameters

id	contains two distinct integer numbers which determine the orientation of the element

Returns: index of the tranformation The return value is used in several methods of this class

Definition at line 357 of file pzshapelinear.cpp.

Referenced by pzshape::TPZShapeTriang::Shape().

◆ Hermite()

void pzshape::TPZShapeLinear::Hermite	(	REAL	x,
		int	num,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Hermite orthogonal polynomials.

Definition at line 179 of file pzshapelinear.cpp.

References TPZMatrix< TVar >::Put().

◆ Jacobi()

void pzshape::TPZShapeLinear::Jacobi	(	REAL	x,
		int	num,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Jacobi orthogonal polynomials.

Definition at line 158 of file pzshapelinear.cpp.

References TPZMatrix< TVar >::Put().

◆ Legendre() [1/2]

void pzshape::TPZShapeLinear::Legendre	(	REAL	x,
		int	num,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Legendre orthogonal polynomial, computes num orthogonal functions at the point x.

Parameters

x	coordinate of the point
num	number of shape functions to be computed
phi	shapefunction values
dphi	values of the derivatives of the shape functions

Definition at line 50 of file pzshapelinear.cpp.

References TPZMatrix< TVar >::Put().

◆ Legendre() [2/2]

void pzshape::TPZShapeLinear::Legendre	(	REAL	x,
		int	num,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi,
		int	nderiv
	)

static

Legendre function computing several derivatives.

See also: Legendre(Real, int, TPZFMatrix, TPZFMatrix)

Definition at line 94 of file pzshapelinear.cpp.

References TPZMatrix< TVar >::Put().

◆ NConnectShapeF()

int pzshape::TPZShapeLinear::NConnectShapeF	(	int	side,
		int	order
	)

static

Number of shapefunctions of the connect associated with the side, considering the order of interpolation of the element.

Parameters

side	associated side
order	vector of integers indicating the interpolation order of the element

Returns: number of shape functions

Definition at line 362 of file pzshapelinear.cpp.

References PZError.

◆ NShapeF()

int pzshape::TPZShapeLinear::NShapeF ( TPZVec< int > & order )

static

Total number of shapefunctions, considering the order of interpolation of the element.

Parameters

order vector of integers indicating the interpolation order of the element

Returns: number of shape functions

Definition at line 369 of file pzshapelinear.cpp.

References test::res.

◆ ParametricTransform()

TPZTransform< REAL > pzshape::TPZShapeLinear::ParametricTransform ( int transid )

static

Definition at line 335 of file pzshapelinear.cpp.

References TPZTransform< T >::Mult().

Referenced by GetSideTransform().

◆ Shape()

void pzshape::TPZShapeLinear::Shape	(	TPZVec< REAL > &	pt,
		TPZVec< int64_t > &	id,
		TPZVec< int > &	order,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Functions which computes the shapefunctions of a one-d element.

Parameters

pt	coordinate of the point
order	order of the shape functions to be computed 0<= order
phi	shapefunction values
dphi	values of the derivatives of the shape functions
id	determines the orientation of the shape functions The orientation of the shapefunctions depend on the order of the id parameters if the shapefunctions are unchanged if the odd ordered shapefunctions are inverted

Definition at line 214 of file pzshapelinear.cpp.

References TPZMatrix< TVar >::Cols(), PZError, TPZFMatrix< TVar >::Resize(), and TPZMatrix< TVar >::Rows().

◆ ShapeCorner()

void pzshape::TPZShapeLinear::ShapeCorner	(	TPZVec< REAL > &	pt,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Definition at line 269 of file pzshapelinear.cpp.

◆ ShapeGenerating()

void pzshape::TPZShapeLinear::ShapeGenerating	(	TPZVec< REAL > &	pt,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Computes the generating shape functions for a quadrilateral element.

Parameters

pt	(input) point where the shape function is computed
phi	(input/output) value of the shape functions
dphi	(input/output) value of the derivatives of the shape functions holding the derivatives in a column

Computes the generating shape functions for a linear element

Parameters

pt	(input) point where the shape function is computed
phi	(input/output) value of the shape functions
dphi	(input/output) value of the derivatives of the shape functions holding the derivatives in a column

Definition at line 203 of file pzshapelinear.cpp.

◆ ShapeInternal() [1/3]

void pzshape::TPZShapeLinear::ShapeInternal	(	TPZVec< REAL > &	x,
		int	ord,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi,
		int	transformation_index
	)

static

Computes the values of the orthogonal shapefunctions before multiplying them by the corner shapefunctions.

Parameters

x	coordinate of the point
ord	order of the shape functions to be computed 0<= order
phi	shapefunction values
dphi	values of the derivatives of the shape functions
transformation_index	determines the transformation applied to the internal shape functions. This parameter is computed by the GetTransformId1d method

See also: GetTransformId1d The shape1dInternal function is extensively used by the shapefunction computation of the other elements

Definition at line 312 of file pzshapelinear.cpp.

Referenced by pzshape::TPZShapeTriang::Shape(), pzshape::TPZShapePiram::ShapeInternal(), pzshape::TPZShapeTriang::ShapeInternal(), pzshape::TPZShapePrism::ShapeInternal(), pzshape::TPZShapeTetra::ShapeInternal(), pzshape::TPZShapeQuad::ShapeInternal(), and pzshape::TPZShapeCube::ShapeInternal().

◆ ShapeInternal() [2/3]

void pzshape::TPZShapeLinear::ShapeInternal	(	TPZVec< REAL > &	x,
		int	ord,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Computes the values of the orthogonal shapefunctions before multiplying them by the corner shapefunctions.

Parameters

x	coordinate of the point
ord	order of the shape functions to be computed 0<= order
phi	shapefunction values
dphi	values of the derivatives of the shape functions
transformation_index	= 0; functions. This parameter is computed by the GetTransformId1d method

See also: GetTransformId1d The shape1dInternal function is extensively used by the shapefunction computation of the other elements

Definition at line 303 of file pzshapelinear.cpp.

◆ ShapeInternal() [3/3]

void pzshape::TPZShapeLinear::ShapeInternal	(	int	side,
		TPZVec< REAL > &	x,
		int	order,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Definition at line 324 of file pzshapelinear.cpp.

◆ ShapeOrder()

void pzshape::TPZShapeLinear::ShapeOrder	(	TPZVec< int64_t > &	id,
		TPZVec< int > &	order,
		TPZGenMatrix< int > &	shapeorders
	)

static

returns the polynomial order in the natural ksi, eta of the side associated with each shapefunction

Definition at line 284 of file pzshapelinear.cpp.

References DebugStop, and TPZGenMatrix< TObj >::Rows().

◆ SideShape()

void pzshape::TPZShapeLinear::SideShape	(	int	side,
		TPZVec< REAL > &	pt,
		TPZVec< int64_t > &	id,
		TPZVec< int > &	order,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Definition at line 272 of file pzshapelinear.cpp.

References Shape().

◆ SideShapeOrder()

void pzshape::TPZShapeLinear::SideShapeOrder	(	int	side,
		TPZVec< int64_t > &	id,
		int	order,
		TPZGenMatrix< int > &	shapeorders
	)

static

returns the polynomial order in the natural ksi, eta of the internal shapefunctions of a side

Parameters

sides is a vector with copy of side as much as needed, it depends on the order

Definition at line 298 of file pzshapelinear.cpp.

References DebugStop.

◆ TransformDerivative1d()

void pzshape::TPZShapeLinear::TransformDerivative1d	(	int	transid,
		int	num,
		TPZFMatrix< REAL > &	in
	)

static

Applies the transformation on the values of the derivatives of the shape functions of the internal shape functions.

Parameters

transid	identifier of the transformation of the one-d element as obtained by the GetTransformId1d method
num	number of shapefunctions needed to transform
in	matrix containing the values of the derivatives of the shapefunctions as a row vector the values of the derivatives contained in this matrix are modified upon return

Definition at line 350 of file pzshapelinear.cpp.

◆ TransformPoint1d() [1/2]

void pzshape::TPZShapeLinear::TransformPoint1d	(	int	transid,
		REAL	in,
		REAL &	out
	)

static

Computes the transformation applied to the variational parameter of the one-d element.

Parameters

transid	identifier of the transformation of the one-d element as obtained by the GetTransformId1d method
in	coordinate of the variational parameter
out	transformed parameter The transformation applied to compensate for odd/even brokerage between elements can also be viewed by the transformation of a variational parameter.

Definition at line 331 of file pzshapelinear.cpp.

◆ TransformPoint1d() [2/2]

void pzshape::TPZShapeLinear::TransformPoint1d	(	int	transid,
		double &	val
	)

static

Definition at line 343 of file pzshapelinear.cpp.

Member Data Documentation

◆ fOrthogonal

void(* pzshape::TPZShapeLinear::fOrthogonal)(REAL, int, TPZFMatrix< REAL > &, TPZFMatrix< REAL > &)

static

Pointer to function which returns num orthogonal functions at the point x.

Parameters

x	coordinate of the point
num	number of shape functions to be computed
phi	shapefunction values
dphi	values of the derivatives of the shape functions

Definition at line 48 of file pzshapelinear.h.

Referenced by TPZCompEl::SetOrthogonalFunction().

◆ JacobiA

REAL pzshape::TPZShapeLinear::JacobiA

static

Jacobi parameters orthogonal polynomials.

Definition at line 85 of file pzshapelinear.h.

◆ JacobiB

REAL pzshape::TPZShapeLinear::JacobiB

static

Definition at line 86 of file pzshapelinear.h.

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

Shape/pzshapelinear.h
Shape/pzshapelinear.cpp

Static Public Member Functions

Orthogonal polynomials family

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ Chebyshev()

◆ Expo()

◆ GetTransformId1d()

◆ Hermite()

◆ Jacobi()

◆ Legendre() [1/2]

◆ Legendre() [2/2]

◆ NConnectShapeF()

◆ NShapeF()

◆ ParametricTransform()

◆ Shape()

◆ ShapeCorner()

◆ ShapeGenerating()

◆ ShapeInternal() [1/3]

◆ ShapeInternal() [2/3]

◆ ShapeInternal() [3/3]

◆ ShapeOrder()

◆ SideShape()

◆ SideShapeOrder()

◆ TransformDerivative1d()

◆ TransformPoint1d() [1/2]

◆ TransformPoint1d() [2/2]

Member Data Documentation

◆ fOrthogonal

◆ JacobiA

◆ JacobiB