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

#include <pzshapeextend.h>

Inheritance diagram for pzshape::SPr< TFather >:

Collaboration diagram for pzshape::SPr< TFather >:

Classes
class	TMem
	Temporary storage to accelerate the computation of shape functions. More...

Public Types
typedef TFather::TMem	FatMem

typedef TFather::Top	FatTop

typedef pztopology::Pr< FatTop >	Top

typedef TFather::TMem	FatMem

typedef TFather::Top	FatTop

typedef pztopology::Pr< FatTop >	Top

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

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

static void	ShapeCorner (TPZVec< REAL > &pt, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Computes the corner shape functions for a hexahedral element. More...

static int	NSideShapeF (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	NSideShapeF (int side, const TMem &mem)
	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 (TPZVec< REAL > &x, int order, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Compute the internal functions of the hexahedral shape function at a point The internal shape functions are the shapefunctions before being multiplied by the corner shape functions. More...

static void	Shape (TPZVec< REAL > &pt, TPZVec< int64_t > &id, TPZVec< int > &order, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi, TMem &memory)
	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	ShapeCorner (TPZVec< REAL > &pt, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Computes the corner shape functions for a hexahedral element. More...

static int	NSideShapeF (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	NSideShapeF (int side, const TMem &mem)
	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 (TPZVec< REAL > &x, int order, TPZFMatrix< REAL > &phi, TPZFMatrix< REAL > &dphi)
	Compute the internal functions of the hexahedral shape function at a point . More...

Detailed Description

template<class TFather>
class pzshape::SPr< TFather >

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

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

Definition at line 26 of file pzshapeextend.h.

Member Typedef Documentation

◆ FatMem [1/2]

template<class TFather >

typedef TFather::TMem pzshape::SPr< TFather >::FatMem

Definition at line 27 of file pzshapeextend.h.

◆ FatMem [2/2]

template<class TFather >

typedef TFather::TMem pzshape::SPr< TFather >::FatMem

Definition at line 30 of file pzshapeextend.h.

◆ FatTop [1/2]

template<class TFather >

typedef TFather::Top pzshape::SPr< TFather >::FatTop

Definition at line 28 of file pzshapeextend.h.

◆ FatTop [2/2]

template<class TFather >

typedef TFather::Top pzshape::SPr< TFather >::FatTop

Definition at line 31 of file pzshapeextend.h.

◆ Top [1/2]

template<class TFather >

typedef pztopology::Pr<FatTop> pzshape::SPr< TFather >::Top

Definition at line 30 of file pzshapeextend.h.

◆ Top [2/2]

template<class TFather >

typedef pztopology::Pr<FatTop> pzshape::SPr< TFather >::Top

Definition at line 33 of file pzshapeextend.h.

Member Function Documentation

◆ NShapeF() [1/2]

template<class TFather >

static int pzshape::SPr< TFather >::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

◆ NShapeF() [2/2]

template<class TFather >

static int pzshape::SPr< TFather >::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

◆ NSideShapeF() [1/4]

template<class TFather >

static int pzshape::SPr< TFather >::NSideShapeF	(	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	order associated with the side

Returns: number of shape functions

◆ NSideShapeF() [2/4]

template<class TFather >

static int pzshape::SPr< TFather >::NSideShapeF	(	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	order associated with the side

Returns: number of shape functions

◆ NSideShapeF() [3/4]

template<class TFather >

static int pzshape::SPr< TFather >::NSideShapeF	(	int	side,
		const TMem &	mem
	)

static

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

Parameters

side	associated side
mem	auxiliar structure to accellerate computing

Returns: number of shape functions

◆ NSideShapeF() [4/4]

template<class TFather >

static int pzshape::SPr< TFather >::NSideShapeF	(	int	side,
		const TMem &	mem
	)

static

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

Total number of shapefunctions, considering the order of interpolation of the element @ param order vector of integers indicating the interpolation order of the element @ return number of shape functions

Parameters

side	associated side
mem	auxiliar structure to accellerate computing

Returns: number of shape functions

◆ Shape() [1/2]

template<class TFather >

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

inlinestatic

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 (5 connects in this case)
phi	(output) values of the shape functions
dphi	(output) values of the derivatives of the shapefunctions
memory	auxiliar structure to accellerate computing 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 129 of file pzshapeextend.h.

◆ Shape() [2/2]

template<class TFather >

void pzshape::SPr< TFather >::Shape	(	TPZVec< REAL > &	pt,
		TPZVec< int > &	id,
		TPZVec< int > &	order,
		TPZFMatrix< REAL > &	phi,
		TPZFMatrix< REAL > &	dphi,
		TMem &	memory
	)

inlinestatic

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 (5 connects in this case)
phi	(output) values of the shape functions
dphi	(output) values of the derivatives of the shapefunctions
memory	auxiliar structure to accellerate computing 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 141 of file pzshapeextend.h.

References pztopology::Pr< TFather >::Dimension, pzshape::SPr< TFather >::TMem::fExtension, pzshape::SPr< TFather >::TMem::fExtShapes, pzshape::SPr< TFather >::TMem::fLower, pzshape::SPr< TFather >::TMem::fMaxOrder, pzshape::SPr< TFather >::TMem::fNShape, pzshape::SPr< TFather >::TMem::fNShapeBefore, pzshape::SPr< TFather >::TMem::fUpper, TPZVec< T >::NElements(), TPZMatrix< TVar >::Rows(), and Shape().

◆ ShapeCorner() [1/2]

template<class TFather >

static void pzshape::SPr< TFather >::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

◆ ShapeCorner() [2/2]

template<class TFather >

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

inlinestatic

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 230 of file pzshapeextend.h.

References pztopology::Pr< TFather >::Dimension, pztopology::Pr< TFather >::NCornerNodes, and TPZFMatrix< TVar >::Resize().

Referenced by pzshape::SPr< TFather >::Shape().

◆ ShapeInternal() [1/2]

template<class TFather >

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

static

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

◆ ShapeInternal() [2/2]

template<class TFather >

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

static

Compute the internal functions of the hexahedral shape function at a point
The internal shape functions are the shapefunctions before being multiplied by the corner shape functions.

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 Shape3dCubeInternal is basically a call to the orthogonal shapefunction with the transformation determined by the transformation index

◆ SideShape() [1/2]

template<class TFather >

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

static

◆ SideShape() [2/2]

template<class TFather >

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

static

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

Geom/pzshapeextend.h

Classes

Public Types

Static Public Member Functions

Detailed Description

template<class TFather> class pzshape::SPr< TFather >

Member Typedef Documentation

◆ FatMem [1/2]

◆ FatMem [2/2]

◆ FatTop [1/2]

◆ FatTop [2/2]

◆ Top [1/2]

◆ Top [2/2]

Member Function Documentation

◆ NShapeF() [1/2]

◆ NShapeF() [2/2]

◆ NSideShapeF() [1/4]

◆ NSideShapeF() [2/4]

◆ NSideShapeF() [3/4]

◆ NSideShapeF() [4/4]

◆ Shape() [1/2]

◆ Shape() [2/2]

◆ ShapeCorner() [1/2]

◆ ShapeCorner() [2/2]

◆ ShapeInternal() [1/2]

◆ ShapeInternal() [2/2]

◆ SideShape() [1/2]

◆ SideShape() [2/2]

template<class TFather>
class pzshape::SPr< TFather >