Implements the shape functions of a tetrahedral (3D) element. Shape. More...

#include <pzshapetetra.h>

Inheritance diagram for pzshape::TPZShapeTetra:

Collaboration diagram for pzshape::TPZShapeTetra:

Static Public Member Functions
static void	Shape (TPZVec< REAL > &pt, TPZVec< int64_t > &id, TPZVec< int > &order, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Computes the values of the shape functions and their derivatives for a tetrahedral element. More...

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	CornerShape (TPZVec< REAL > &pt, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Computes the corner shape functions for a tetrahedral element. 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	ShapeInternal (TPZVec< REAL > &x, int order, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Compute the internal functions of the tetrahedral shape function at a point. More...

static void	ProjectPoint3dTetraToRib (int rib, TPZVec< REAL > &in, REAL &outval)
	Projects a point from the interior of the element to a rib. More...

static void	ProjectPoint3dTetrSide (int side, TPZVec< REAL > &in, REAL &out)
	Projects a point from the interior of the element to a rib. More...

static void	ProjectPoint3dTetraToFace (int face, TPZVec< REAL > &in, TPZVec< REAL > &outval)
	Projects a point from the interior of the element to a face. More...

static void	ProjectPoint3dTetrFace (int face, TPZVec< REAL > &in, TPZVec< REAL > &out)
	Projects a point from the interior of the element to a face. More...

static void	TransformDerivativeFromRibToTetra (int rib, int num, TPZFMatrix< REAL > &dphi)
	Transforms the derivative of a shapefunction computed on the rib into the three dimensional derivative of the function with respect to the element. The parameter dphi should be dimensioned (3,num), at least. More...

static void	TransformDerivativeFromFaceToTetra (int face, int num, TPZFMatrix< REAL > &dphi)
	Transforms the derivative of a shapefunction computed on the face into the three dimensional derivative of the function with respect to the element. The parameter dphi should be dimensioned (3,num), at least. 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	ShapeInternal (int side, TPZVec< REAL > &x, int order, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)

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

Static Public Member Functions inherited from pztopology::TPZTetrahedron
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) 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...

template<class TVar >
static void	ComputeHCurlDirections (TPZFMatrix< TVar > &gradx, TPZFMatrix< TVar > &directions, const TPZVec< int > &transformationIds)

static int	NBilinearSides ()

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 ()
	Number of connects of the element (27) 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	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...

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

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 projects 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)

Static Public Attributes
static REAL	gVet1dTetr [6]
	Data structure which defines the tetrahedral transformations and topology. More...

static REAL	gFaceTrans3dTetr2d [4][2][3]
	Data structure which defines the tetrahedral transformations and topology. More...

static REAL	gVet2dTetr [4][2]
	Data structure which defines the tetrahedral transformations and topology. More...

static REAL	gRibTrans3dTetr1d [6][3]
	Data structure which defines the tetrahedral transformations and topology. More...

static REAL	gFaceSum3dTetra2d [4][2]
	Data structure which defines the tetrahedral transformations and topology. More...

static REAL	gFaceTrans3dTetra2d [4][2][3]
	Data structure which defines the tetrahedral transformations and topology. More...

static REAL	gRibSum3dTetra1d [6]
	Data structure which defines the tetrahedral transformations and topology. More...

static REAL	gRibTrans3dTetra1d [6][3]
	Data structure which defines the tetrahedral transformations and topology. More...

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

typedef TPZIntTetra3D	IntruleType
	Typedef to numerical integration rule. More...

typedef TPZGraphElT3d	GraphElType
	Typedef to graphical element type. More...

Public Member Functions inherited from pztopology::TPZTetrahedron
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...

	TPZTetrahedron ()
	Default constructor. More...

virtual	~TPZTetrahedron ()
	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::TPZTetrahedron
static int	FaceNodes [4][3]
	Nodes over quadrilateral sides (2d - faces). More...

static int	SideNodes [6][2]
	Nodes over lines sides (1d) More...

static int	ShapeFaceId [4][3]
	Ids of the shape face. More...

static int	fPermutations [24][15]
	Valid permutations between nodes. More...

Detailed Description

Implements the shape functions of a tetrahedral (3D) element. Shape.

The range of the master element is 0,1

Definition at line 25 of file pzshapetetra.h.

Member Function Documentation

◆ CornerShape()

void pzshape::TPZShapeTetra::CornerShape	(	TPZVec< REAL > &	pt,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi
	)

static

Computes the corner shape functions for a tetrahedral element.

Parameters

pt	(input) point where the shape function is computed
phi	(output) value of the (4) shape functions
dphi	(output) value of the derivatives of the (4) shape functions holding the derivatives in a column

Definition at line 75 of file pzshapetetra.cpp.

◆ NConnectShapeF()

int pzshape::TPZShapeTetra::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 393 of file pzshapetetra.cpp.

References PZError.

◆ NShapeF()

int pzshape::TPZShapeTetra::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 414 of file pzshapetetra.cpp.

References test::res.

◆ ProjectPoint3dTetraToFace()

void pzshape::TPZShapeTetra::ProjectPoint3dTetraToFace	(	int	face,
		TPZVec< REAL > &	in,
		TPZVec< REAL > &	outval
	)

static

Projects a point from the interior of the element to a face.

Parameters

face	face index to which the point should be projected
in	coordinate of the point at the interior of the element
outval	coordinates of the point on the face

Definition at line 381 of file pzshapetetra.cpp.

◆ ProjectPoint3dTetraToRib()

void pzshape::TPZShapeTetra::ProjectPoint3dTetraToRib	(	int	rib,
		TPZVec< REAL > &	in,
		REAL &	outval
	)

static

Projects a point from the interior of the element to a rib.

Parameters

rib	rib index to which the point should be projected
in	coordinate of the point at the interior of the element
outval	coordinate of the point on the rib

Definition at line 377 of file pzshapetetra.cpp.

◆ ProjectPoint3dTetrFace()

void pzshape::TPZShapeTetra::ProjectPoint3dTetrFace	(	int	face,
		TPZVec< REAL > &	in,
		TPZVec< REAL > &	out
	)

static

Projects a point from the interior of the element to a face.

Parameters

face	face index to which the point should be projected
in	coordinate of the point at the interior of the element
out	coordinates of the point on the face

Definition at line 281 of file pzshapetetra.cpp.

◆ ProjectPoint3dTetrSide()

void pzshape::TPZShapeTetra::ProjectPoint3dTetrSide	(	int	side,
		TPZVec< REAL > &	in,
		REAL &	out
	)

static

Projects a point from the interior of the element to a rib.

Parameters

side	side to which the point should be projected
in	coordinate of the point at the interior of the element
out	coordinate of the point on the rib

Definition at line 276 of file pzshapetetra.cpp.

◆ Shape()

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

static

Computes the values of the shape functions and their derivatives for a tetrahedral element.

Parameters

pt	(input) point where the shape functions are computed
id	(input) indexes of the corner points which determine the orientation of the shape functions
order	(input) order of the side connects different from the corner connects (11 connects in this case)
phi	(output) values of the shape functions
dphi	(output) values of the derivatives of the shapefunctions These values depend on the point, the order of interpolation and ids of the corner points The shapefunction computation uses the shape functions of the linear and triangular element for its implementation

Definition at line 162 of file pzshapetetra.cpp.

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

◆ ShapeCorner()

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

static

Definition at line 53 of file pzshapetetra.cpp.

◆ ShapeGenerating()

void pzshape::TPZShapeTetra::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 (4) shape functions
dphi	(input/output) value of the derivatives of the (4) shape functions holding the derivatives in a column

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 (4) shape functions
dphi	(input/output) value of the derivatives of the (4) shape functions holding the derivatives in a column

Definition at line 101 of file pzshapetetra.cpp.

References DebugStop.

◆ ShapeInternal() [1/2]

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

static

Compute the internal functions of the tetrahedral shape function at a point.

Parameters

x	coordinate of the point
order	maximum order of shape functions to be computed
phi	shapefunction values
dphi	values of the derivatives of the shape functions The internal shape functions are the shapefunctions before being multiplied by the corner shape functions Shape3dTetraInternal is basically a call to the orthogonal shapefunction with the transformation determined by the transformation index (also on the faces)

Definition at line 287 of file pzshapetetra.cpp.

◆ ShapeInternal() [2/2]

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

static

Definition at line 315 of file pzshapetetra.cpp.

References DebugStop, pzshape::TPZShapeTriang::ShapeInternal(), and pzshape::TPZShapeLinear::ShapeInternal().

◆ ShapeOrder()

void pzshape::TPZShapeTetra::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 434 of file pzshapetetra.cpp.

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

◆ SideShape()

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

static

Definition at line 420 of file pzshapetetra.cpp.

References PZError, and Shape().

◆ SideShapeOrder()

void pzshape::TPZShapeTetra::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 469 of file pzshapetetra.cpp.

References DebugStop, TPZStack< T, NumExtAlloc >::Push(), TPZGenMatrix< TObj >::Rows(), and TPZVec< T >::size().

◆ TransformDerivativeFromFaceToTetra()

void pzshape::TPZShapeTetra::TransformDerivativeFromFaceToTetra	(	int	face,
		int	num,
		TPZFMatrix< REAL > &	dphi
	)

static

Transforms the derivative of a shapefunction computed on the face into the three dimensional derivative of the function with respect to the element. The parameter dphi should be dimensioned (3,num), at least.

Parameters

face	face index to which the point should be projected
num	number of shapefunction derivatives which need to be transformed
dphi	values of the derivatives of the shapefunctions (modified in place)

Definition at line 367 of file pzshapetetra.cpp.

◆ TransformDerivativeFromRibToTetra()

void pzshape::TPZShapeTetra::TransformDerivativeFromRibToTetra	(	int	rib,
		int	num,
		TPZFMatrix< REAL > &	dphi
	)

static

Transforms the derivative of a shapefunction computed on the rib into the three dimensional derivative of the function with respect to the element. The parameter dphi should be dimensioned (3,num), at least.

Parameters

rib	rib index along which the shapefunction is defined
num	number of shapefunction derivatives which need to be transformed
dphi	values of the derivatives of the shapefunctions (modified in place)

Definition at line 359 of file pzshapetetra.cpp.