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

#include <pzshapecube.h>

Inheritance diagram for pzshape::TPZShapeCube:

Collaboration diagram for pzshape::TPZShapeCube:

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 hexahedral 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	ShapeCorner (TPZVec< REAL > &pt, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Computes the corner shape functions for a hexahedral 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 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 Public Member Functions inherited from pztopology::TPZCube
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. More...

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

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

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	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 ()
	Returns 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 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 Private Member Functions
static void	ShapeInternal (TPZVec< REAL > &x, int order, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Compute the internal functions of the hexahedral shape function at a point. More...

static void	ProjectPoint3dCubeToRib (int face, TPZVec< REAL > &in, REAL &outval)
	Projects a point from the interior of the element to a rib. More...

static void	ProjectPoint3dCubeSide (int face, TPZVec< REAL > &in, REAL &out)
	Projects a point from the interior of the element to a rib. More...

static void	ProjectPoint3dCubeFace (int face, TPZVec< REAL > &in, TPZVec< REAL > &out)
	Projects a point from the interior of the element to a face. More...

static void	ProjectPoint3dCubeToFace (int face, TPZVec< REAL > &in, TPZVec< REAL > &outval)
	Projects a point from the interior of the element to a face. More...

static void	TransformDerivativeFromRibToCube (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	TransformDerivativeFromFaceToCube (int rib, 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 Private Attributes
static REAL	gFaceTrans3dCube2d [6][2][3]
	Data structure which defines the hexahedral transformations. More...

static REAL	gRibTrans3dCube1d [12][3]
	Data structure which defines the hexahedral transformations. More...

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

typedef TPZIntCube3D	IntruleType
	Typedef to numerical integration rule. More...

typedef TPZGraphElQ3dd	GraphElType
	Typedef to graphical element type. More...

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

	TPZCube ()
	Default constructor. More...

virtual	~TPZCube ()
	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 Public Attributes inherited from pztopology::TPZCube
static int	FaceNodes [6][4]
	Nodes over quadrilateral sides (2d - faces). More...

static int	SideNodes [12][2]
	Nodes over lines sides (1d) More...

Static Protected Attributes inherited from pztopology::TPZCube
static int	ShapeFaceId [6][2]
	Ids of the shape face. More...

static int	fPermutations [48][27]
	Valid permutations between nodes. More...

Detailed Description

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

The range of the master element is [-1 ,1]

Definition at line 29 of file pzshapecube.h.

Member Function Documentation

◆ NConnectShapeF()

int pzshape::TPZShapeCube::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 501 of file pzshapecube.cpp.

References PZError.

◆ NShapeF()

int pzshape::TPZShapeCube::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 514 of file pzshapecube.cpp.

References test::res, and TPZVec< T >::Resize().

◆ ProjectPoint3dCubeFace()

void pzshape::TPZShapeCube::ProjectPoint3dCubeFace	(	int	face,
		TPZVec< REAL > &	in,
		TPZVec< REAL > &	out
	)

staticprivate

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 495 of file pzshapecube.cpp.

◆ ProjectPoint3dCubeSide()

void pzshape::TPZShapeCube::ProjectPoint3dCubeSide	(	int	face,
		TPZVec< REAL > &	in,
		REAL &	out
	)

staticprivate

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

Parameters

face	rib index 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 490 of file pzshapecube.cpp.

◆ ProjectPoint3dCubeToFace()

void pzshape::TPZShapeCube::ProjectPoint3dCubeToFace	(	int	face,
		TPZVec< REAL > &	in,
		TPZVec< REAL > &	outval
	)

staticprivate

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 475 of file pzshapecube.cpp.

◆ ProjectPoint3dCubeToRib()

void pzshape::TPZShapeCube::ProjectPoint3dCubeToRib	(	int	face,
		TPZVec< REAL > &	in,
		REAL &	outval
	)

staticprivate

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

Parameters

face	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 471 of file pzshapecube.cpp.

◆ Shape()

void pzshape::TPZShapeCube::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 hexahedral 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 (19 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 quadrilateral element for its implementation

Definition at line 152 of file pzshapecube.cpp.

References TPZFMatrix< TVar >::Zero().

◆ ShapeCorner()

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

static

Computes the corner shape functions for a hexahedral element.

Parameters

pt	(input) point where the shape function is computed
phi	(output) value of the (8) shape functions
dphi	(output) value of the derivatives of the (8) shape functions holding the derivatives in a column

Definition at line 34 of file pzshapecube.cpp.

References dx().

Referenced by TPZGraphElPrismMapped::QsiEta(), and TPZGraphElPyramidMapped::QsiEta().

◆ ShapeGenerating()

void pzshape::TPZShapeCube::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) value of the (4) shape functions
dphi	(input) value of the derivatives of the (4) shape functions holding the derivatives in a column
pt	(input) point where the shape function is computed
phi	(input) value of the (8) shape functions
dphi	(input) value of the derivatives of the (8) shape functions holding the derivatives in a column

Definition at line 90 of file pzshapecube.cpp.

References h, pztopology::highsides, and TPZVec< T >::NElements().

◆ ShapeInternal() [1/2]

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

staticprivate

Compute the internal functions of the hexahedral 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 Shape3dCubeInternal is basically a call to the orthogonal shapefunction with the transformation determined by the transformation index

Definition at line 388 of file pzshapecube.cpp.

References TPZFMatrix< TVar >::Resize().

◆ ShapeInternal() [2/2]

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

static

Definition at line 415 of file pzshapecube.cpp.

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

◆ ShapeOrder()

void pzshape::TPZShapeCube::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 266 of file pzshapecube.cpp.

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

◆ SideShape()

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

static

Definition at line 250 of file pzshapecube.cpp.

References PZError, and Shape().

◆ SideShapeOrder()

void pzshape::TPZShapeCube::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 300 of file pzshapecube.cpp.

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

◆ TransformDerivativeFromFaceToCube()

void pzshape::TPZShapeCube::TransformDerivativeFromFaceToCube	(	int	rib,
		int	num,
		TPZFMatrix< REAL > &	dphi
	)

staticprivate

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

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

Definition at line 480 of file pzshapecube.cpp.

◆ TransformDerivativeFromRibToCube()

void pzshape::TPZShapeCube::TransformDerivativeFromRibToCube	(	int	rib,
		int	num,
		TPZFMatrix< REAL > &	dphi
	)

staticprivate

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 463 of file pzshapecube.cpp.

Member Data Documentation

◆ gFaceTrans3dCube2d

REAL pzshape::TPZShapeCube::gFaceTrans3dCube2d

staticprivate

Data structure which defines the hexahedral transformations.

Definition at line 200 of file pzshapecube.h.

◆ gRibTrans3dCube1d

REAL pzshape::TPZShapeCube::gRibTrans3dCube1d

staticprivate

Data structure which defines the hexahedral transformations.

Definition at line 202 of file pzshapecube.h.

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

Shape/pzshapecube.h
Shape/pzshapecube.cpp

Static Public Member Functions

Static Private Member Functions

Static Private Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ NConnectShapeF()

◆ NShapeF()

◆ ProjectPoint3dCubeFace()

◆ ProjectPoint3dCubeSide()

◆ ProjectPoint3dCubeToFace()

◆ ProjectPoint3dCubeToRib()

◆ Shape()

◆ ShapeCorner()

◆ ShapeGenerating()

◆ ShapeInternal() [1/2]

◆ ShapeInternal() [2/2]

◆ ShapeOrder()

◆ SideShape()

◆ SideShapeOrder()

◆ TransformDerivativeFromFaceToCube()

◆ TransformDerivativeFromRibToCube()

Member Data Documentation

◆ gFaceTrans3dCube2d

◆ gRibTrans3dCube1d