A 3D FEM element: a hexahedron. More...

#include <hexahedron.hh>

Inheritance diagram for hp3D::Hexahedron:

Public Types
enum	intFormType { ZERO, ONE, TWO, THREE }
	Integration form, which determines terms coming from integration over reference element. More...

typedef Real	type

Public Member Functions
void	appendT (concepts::TColumn< Real > *T)
	Appends the T columns to the T matrix. More...

virtual const concepts::Hexahedron3d &	cell () const

virtual const concepts::Cell3 &	cell () const=0
	Returns the cell on which the element is built. More...

concepts::Real3d	chi (const Real x, const Real y, const Real z) const
	Computes the element map. More...

const concepts::AdaptiveControlP< 1 > &	edgeP (const uint i) const
	Get polynomial degree of edge `i`. More...

void	edgeP (const uint i, const concepts::AdaptiveControlP< 1 > &p)
	Set polynomial degree of edge `i` to `p`. More...

Real3d	elemMap (const Real coord_local) const

Real3d	elemMap (const Real2d &coord_local) const

Real3d	elemMap (const Real3d &coord_local) const

const concepts::AdaptiveControlP< 2 > &	faceP (const uint i) const
	Get polynomial degree of face `i`. More...

void	faceP (const uint i, const concepts::AdaptiveControlP< 2 > &p)
	Set polynomial degree of face `i` to `p`. More...

const concepts::Hex3dSubdivision *	getStrategy () const
	Returns the subdivision strategy of the underlying cell of this element. More...

virtual const concepts::ElementGraphics< Real > *	graphics () const

bool	hasSameMatrix (const Hexahedron &elm) const
	Returns true if element matrix is the same. More...

concepts::MapReal3d	hessian (const uint i, const Real x, const Real y, const Real z) const
	Computes the Hessian. More...

	Hexahedron (concepts::Hexahedron3d &cell, const ushort p, concepts::TColumn< Real > T0, concepts::TColumn< Real > *T1)
	Constructor. More...

const concepts::QuadratureRule1d *	integrationX () const
	Returns the integration rule in x direction. More...

const concepts::QuadratureRule1d *	integrationY () const
	Returns the integration rule in y direction. More...

const concepts::QuadratureRule1d *	integrationZ () const
	Returns the integration rule in z direction. More...

concepts::MapReal3d	jacobian (const Real x, const Real y, const Real z) const
	Computes the Jacobian. More...

Real	jacobianDeterminant (const Real x, const Real y, const Real z) const
	Computes the determinant of the Jacobian. More...

concepts::MapReal3d	jacobianInverse (const Real x, const Real y, const Real z) const
	Computes the inverse of the Jacobian. More...

virtual bool	operator< (const Element< Real > &elm) const
	Comparison operator for elements. More...

const ushort *	p () const
	Returns the polynomial degree. More...

virtual bool	quadraturePoint (uint i, intPoint &p, intFormType form, bool localCoord) const
	Delivers a quadrature point. More...

void	recomputeShapefunctions ()

void	recomputeShapefunctions (const uint nq[2])

void	setStrategy (const concepts::Hex3dSubdivision *strategy=0) throw (concepts::StrategyChange)
	Sets the subdivision strategy of the underlying cell of this element. More...

const concepts::Karniadakis< 1, 1 > *	shpfctDX () const
	Returns the derivatives of the shape functions in x direction. More...

const concepts::Karniadakis< 1, 1 > *	shpfctDY () const
	Returns the shape functions in y direction. More...

const concepts::Karniadakis< 1, 1 > *	shpfctDZ () const
	Returns the shape functions in z direction. More...

const concepts::Karniadakis< 1, 0 > *	shpfctX () const
	Returns the shape functions in x direction. More...

const concepts::Karniadakis< 1, 0 > *	shpfctY () const
	Returns the shape functions in y direction. More...

const concepts::Karniadakis< 1, 0 > *	shpfctZ () const
	Returns the shape functions in z direction. More...

virtual const concepts::Hexahedron &	support () const

virtual const concepts::Connector3 &	support () const=0
	Returns the topolgical support of the element. More...

virtual const concepts::TMatrix< Real > &	T () const
	Returns the T matrix of the element. More...

virtual concepts::Real3d	vertex (uint i) const
	Returns the coordinates of the ith vertex of this element. More...

virtual	~Hexahedron ()

Static Public Member Functions
static concepts::QuadRuleFactory &	rule ()
	Access to the quadrature rule, which is valid for all elements of this type (hp3D::Hexaedron). More...

Protected Member Functions
void	computeShapefunctions_ (const concepts::QuadratureRule1d intX, const concepts::QuadratureRule1d intY, const concepts::QuadratureRule1d *intZ)
	gets the shapefunctions, used in both constructors More...

virtual std::ostream &	info (std::ostream &os) const

Protected Attributes
concepts::TMatrix< Real >	T_
	T matrix of the element. More...

Private Attributes
concepts::Hexahedron3d &	cell_
	The cell. More...

const concepts::AdaptiveControlP< 1 > *	edges_ [12]
	Polynomial degree of edges. More...

const concepts::AdaptiveControlP< 2 > *	faces_ [6]
	Polynomial degree of faces. More...

std::unique_ptr< concepts::QuadratureRule1d >	intX_
	The integration rules. More...

std::unique_ptr< concepts::QuadratureRule1d >	intY_

std::unique_ptr< concepts::QuadratureRule1d >	intZ_

ushort	p_ [3]
	Polynomial degree. More...

std::unique_ptr< concepts::Karniadakis< 1, 1 > >	shpfctDX_
	The derivatives of the shape functions. More...

std::unique_ptr< concepts::Karniadakis< 1, 1 > >	shpfctDY_

std::unique_ptr< concepts::Karniadakis< 1, 1 > >	shpfctDZ_

std::unique_ptr< concepts::Karniadakis< 1, 0 > >	shpfctX_
	The shape functions. More...

std::unique_ptr< concepts::Karniadakis< 1, 0 > >	shpfctY_

std::unique_ptr< concepts::Karniadakis< 1, 0 > >	shpfctZ_

Static Private Attributes
static std::unique_ptr< HexahedronGraphics >	graphics_

static concepts::QuadRuleFactory	rule_

Detailed Description

A 3D FEM element: a hexahedron.

Todo:: remove this statement

Author: Philipp Frauenfelder, 2000

Definition at line 37 of file hexahedron.hh.

Member Typedef Documentation

◆ type

typedef Real concepts::ElementWithCell< Real >::type

inherited

Definition at line 81 of file element.hh.

Member Enumeration Documentation

◆ intFormType

enum concepts::IntegrationCell::intFormType

inherited

Integration form, which determines terms coming from integration over reference element.

Enumerator
ZERO
ONE
TWO
THREE

Definition at line 29 of file integral.hh.

Constructor & Destructor Documentation

◆ Hexahedron()

hp3D::Hexahedron::Hexahedron	(	concepts::Hexahedron3d &	cell,
		const ushort *	p,
		concepts::TColumn< Real > *	T0,
		concepts::TColumn< Real > *	T1
	)

Constructor.

Parameters

cell	Cell on which the element is defined
p	Polynomial degree (can be anisotropic), this array must have at least 3 entries.
T0	Part of the T matrix
T1	Part of the T matrix

◆ ~Hexahedron()

virtual hp3D::Hexahedron::~Hexahedron ( )

virtual

Member Function Documentation

◆ appendT()

void hp3D::Element< Real >::appendT ( concepts::TColumn< Real > * T )

inlineinherited

Appends the T columns to the T matrix.

Definition at line 62 of file element.hh.

◆ cell() [1/2]

virtual const concepts::Hexahedron3d& hp3D::Hexahedron::cell ( ) const

inlinevirtual

Definition at line 56 of file hexahedron.hh.

◆ cell() [2/2]

virtual const concepts::Cell3& hp3D::Element< Real >::cell

pure virtualinherited

Returns the cell on which the element is built.

Possible are tetrahedrons, hexahedron, prims and pyramids.

Implements concepts::ElementWithCell< Real >.

◆ chi()

concepts::Real3d hp3D::Hexahedron::chi	(	const Real	x,
		const Real	y,
		const Real	z
	)		const

inline

Computes the element map.

The reference element is the unit cube.

Definition at line 101 of file hexahedron.hh.

◆ computeShapefunctions_()

void hp3D::Hexahedron::computeShapefunctions_	(	const concepts::QuadratureRule1d *	intX,
		const concepts::QuadratureRule1d *	intY,
		const concepts::QuadratureRule1d *	intZ
	)

protected

gets the shapefunctions, used in both constructors

◆ edgeP() [1/2]

const concepts::AdaptiveControlP<1>& hp3D::Hexahedron::edgeP ( const uint i ) const

inline

Get polynomial degree of edge i.

Definition at line 169 of file hexahedron.hh.

◆ edgeP() [2/2]

void hp3D::Hexahedron::edgeP	(	const uint	i,
		const concepts::AdaptiveControlP< 1 > &	p
	)

inline

Set polynomial degree of edge i to p.

Definition at line 164 of file hexahedron.hh.

◆ elemMap() [1/3]

Real3d concepts::ElementWithCell< Real >::elemMap ( const Real coord_local ) const

inlineinherited

Definition at line 86 of file element.hh.

◆ elemMap() [2/3]

Real3d concepts::ElementWithCell< Real >::elemMap ( const Real2d & coord_local ) const

inlineinherited

Definition at line 90 of file element.hh.

◆ elemMap() [3/3]

Real3d concepts::ElementWithCell< Real >::elemMap ( const Real3d & coord_local ) const

inlineinherited

Definition at line 94 of file element.hh.

◆ faceP() [1/2]

const concepts::AdaptiveControlP<2>& hp3D::Hexahedron::faceP ( const uint i ) const

inline

Get polynomial degree of face i.

Definition at line 180 of file hexahedron.hh.

◆ faceP() [2/2]

void hp3D::Hexahedron::faceP	(	const uint	i,
		const concepts::AdaptiveControlP< 2 > &	p
	)

inline

Set polynomial degree of face i to p.

Definition at line 175 of file hexahedron.hh.

◆ getStrategy()

const concepts::Hex3dSubdivision* hp3D::Hexahedron::getStrategy ( ) const

inline

Returns the subdivision strategy of the underlying cell of this element.

Definition at line 148 of file hexahedron.hh.

◆ graphics()

virtual const concepts::ElementGraphics<Real>* hp3D::Hexahedron::graphics ( ) const

virtual

◆ hasSameMatrix()

bool hp3D::Hexahedron::hasSameMatrix ( const Hexahedron & elm ) const

Returns true if element matrix is the same.

This method returns true if the element matrix of this element and elm are the same. To find this out, the length of the edges and their angles and the polynomial degrees are compared.

◆ hessian()

concepts::MapReal3d hp3D::Hexahedron::hessian	(	const uint	i,
		const Real	x,
		const Real	y,
		const Real	z
	)		const

inline

Computes the Hessian.

Definition at line 126 of file hexahedron.hh.

◆ info()

virtual std::ostream& hp3D::Hexahedron::info ( std::ostream & os ) const

protectedvirtual

Reimplemented from hp3D::Element< Real >.

◆ integrationX()

const concepts::QuadratureRule1d* hp3D::Hexahedron::integrationX ( ) const

inline

Returns the integration rule in x direction.

Definition at line 87 of file hexahedron.hh.

◆ integrationY()

const concepts::QuadratureRule1d* hp3D::Hexahedron::integrationY ( ) const

inline

Returns the integration rule in y direction.

Definition at line 91 of file hexahedron.hh.

◆ integrationZ()

const concepts::QuadratureRule1d* hp3D::Hexahedron::integrationZ ( ) const

inline

Returns the integration rule in z direction.

Definition at line 95 of file hexahedron.hh.

◆ jacobian()

concepts::MapReal3d hp3D::Hexahedron::jacobian	(	const Real	x,
		const Real	y,
		const Real	z
	)		const

inline

Computes the Jacobian.

Definition at line 107 of file hexahedron.hh.

◆ jacobianDeterminant()

Real hp3D::Hexahedron::jacobianDeterminant	(	const Real	x,
		const Real	y,
		const Real	z
	)		const

inline

Computes the determinant of the Jacobian.

Definition at line 121 of file hexahedron.hh.

◆ jacobianInverse()

concepts::MapReal3d hp3D::Hexahedron::jacobianInverse	(	const Real	x,
		const Real	y,
		const Real	z
	)		const

inline

Computes the inverse of the Jacobian.

Definition at line 115 of file hexahedron.hh.

◆ operator<()

virtual bool hp3D::Hexahedron::operator< ( const Element< Real > & elm ) const

virtual

Comparison operator for elements.

Implements hp3D::Element< Real >.

◆ p()

const ushort* hp3D::Element< Real >::p

inlineinherited

Returns the polynomial degree.

The returned array has 3 elements.

Definition at line 51 of file element.hh.

◆ quadraturePoint()

virtual bool hp3D::Hexahedron::quadraturePoint	(	uint	i,
		intPoint &	p,
		intFormType	form,
		bool	localCoord
	)		const

virtual

Delivers a quadrature point.

Quadrature point consists of coordinates (for evaluation of formulas) and intermediate data, consisting of the weight and term coming from mapping.

Returns false, if the number of quadrature points is overstepped.

Parameters

i	number of quadrature point
intPoint	data given back
form	Integration form
localCoord	If true, local coordinates are returned. Else physical coordinates.

Implements concepts::IntegrationCell.

◆ recomputeShapefunctions() [1/2]

void hp3D::Hexahedron::recomputeShapefunctions ( )

◆ recomputeShapefunctions() [2/2]

void hp3D::Hexahedron::recomputeShapefunctions ( const uint nq[2] )

◆ rule()

static concepts::QuadRuleFactory& hp3D::Hexahedron::rule ( )

inlinestatic

Access to the quadrature rule, which is valid for all elements of this type (hp3D::Hexaedron).

Change of the quadrature rule is put into practice for newly created elements and for already created elements by precomputing the integration points and shape functions on them.

Definition at line 193 of file hexahedron.hh.

◆ setStrategy()

void hp3D::Hexahedron::setStrategy	(	const concepts::Hex3dSubdivision *	strategy = `0`	)
throw	(	concepts::StrategyChange
	)

inline

Sets the subdivision strategy of the underlying cell of this element.

It calls Quad2d::setStrategy.

Parameters

strategy Pointer to an instance of a subdivision strategy.

Exceptions

StrategyChange if the change is not allowed (the change is not allowed if there are children present)

Definition at line 140 of file hexahedron.hh.

◆ shpfctDX()

const concepts::Karniadakis<1, 1>* hp3D::Hexahedron::shpfctDX ( ) const

inline

Returns the derivatives of the shape functions in x direction.

Definition at line 74 of file hexahedron.hh.

◆ shpfctDY()

const concepts::Karniadakis<1, 1>* hp3D::Hexahedron::shpfctDY ( ) const

inline

Returns the shape functions in y direction.

Definition at line 78 of file hexahedron.hh.

◆ shpfctDZ()

const concepts::Karniadakis<1, 1>* hp3D::Hexahedron::shpfctDZ ( ) const

inline

Returns the shape functions in z direction.

Definition at line 82 of file hexahedron.hh.

◆ shpfctX()

const concepts::Karniadakis<1, 0>* hp3D::Hexahedron::shpfctX ( ) const

inline

Returns the shape functions in x direction.

Definition at line 61 of file hexahedron.hh.

◆ shpfctY()

const concepts::Karniadakis<1, 0>* hp3D::Hexahedron::shpfctY ( ) const

inline

Returns the shape functions in y direction.

Definition at line 65 of file hexahedron.hh.

◆ shpfctZ()

const concepts::Karniadakis<1, 0>* hp3D::Hexahedron::shpfctZ ( ) const

inline

Returns the shape functions in z direction.

Definition at line 69 of file hexahedron.hh.

◆ support() [1/2]

virtual const concepts::Hexahedron& hp3D::Hexahedron::support ( ) const

inlinevirtual

Definition at line 50 of file hexahedron.hh.

◆ support() [2/2]

virtual const concepts::Connector3& hp3D::Element< Real >::support

pure virtualinherited

Returns the topolgical support of the element.

Possible supports for an element are hexahedrons, tetrahedrons, prisms and pyramids.

◆ T()

virtual const concepts::TMatrix<Real>& hp3D::Element< Real >::T

inlinevirtualinherited

Returns the T matrix of the element.

Implements concepts::ElementWithCell< Real >.

Definition at line 59 of file element.hh.

◆ vertex()

virtual concepts::Real3d hp3D::Hexahedron::vertex ( uint i ) const

inlinevirtual

Returns the coordinates of the ith vertex of this element.

Parameters

i	Index of the vertex

Implements hp3D::Element< Real >.

Definition at line 53 of file hexahedron.hh.

Member Data Documentation

◆ cell_

concepts::Hexahedron3d& hp3D::Hexahedron::cell_

private

The cell.

Definition at line 210 of file hexahedron.hh.

◆ edges_

const concepts::AdaptiveControlP<1>* hp3D::Hexahedron::edges_[12]

private

Polynomial degree of edges.

Definition at line 219 of file hexahedron.hh.

◆ faces_

const concepts::AdaptiveControlP<2>* hp3D::Hexahedron::faces_[6]

private

Polynomial degree of faces.

Definition at line 221 of file hexahedron.hh.

◆ graphics_

std::unique_ptr<HexahedronGraphics> hp3D::Hexahedron::graphics_

staticprivate

Definition at line 223 of file hexahedron.hh.

◆ intX_

std::unique_ptr<concepts::QuadratureRule1d> hp3D::Hexahedron::intX_

private

The integration rules.

Definition at line 216 of file hexahedron.hh.

◆ intY_

std::unique_ptr<concepts::QuadratureRule1d> hp3D::Hexahedron::intY_

private

Definition at line 216 of file hexahedron.hh.

◆ intZ_

std::unique_ptr<concepts::QuadratureRule1d> hp3D::Hexahedron::intZ_

private

Definition at line 216 of file hexahedron.hh.

◆ p_

ushort hp3D::Hexahedron::p_[3]

private

Polynomial degree.

Definition at line 229 of file hexahedron.hh.

◆ rule_

concepts::QuadRuleFactory hp3D::Hexahedron::rule_

staticprivate

Definition at line 226 of file hexahedron.hh.

◆ shpfctDX_

std::unique_ptr<concepts::Karniadakis<1, 1> > hp3D::Hexahedron::shpfctDX_

private

The derivatives of the shape functions.

Definition at line 214 of file hexahedron.hh.

◆ shpfctDY_

std::unique_ptr<concepts::Karniadakis<1, 1> > hp3D::Hexahedron::shpfctDY_

private

Definition at line 214 of file hexahedron.hh.

◆ shpfctDZ_

std::unique_ptr<concepts::Karniadakis<1, 1> > hp3D::Hexahedron::shpfctDZ_

private

Definition at line 214 of file hexahedron.hh.

◆ shpfctX_

std::unique_ptr<concepts::Karniadakis<1, 0> > hp3D::Hexahedron::shpfctX_

private

The shape functions.

Definition at line 212 of file hexahedron.hh.

◆ shpfctY_

std::unique_ptr<concepts::Karniadakis<1, 0> > hp3D::Hexahedron::shpfctY_

private

Definition at line 212 of file hexahedron.hh.

◆ shpfctZ_

std::unique_ptr<concepts::Karniadakis<1, 0> > hp3D::Hexahedron::shpfctZ_

private

Definition at line 212 of file hexahedron.hh.

◆ T_

concepts::TMatrix<Real> hp3D::Element< Real >::T_

protectedinherited

T matrix of the element.

Definition at line 81 of file element.hh.

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

hp3D/hexahedron.hh

hp3D::Hexahedron Class Referenceabstract

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ type

Member Enumeration Documentation

◆ intFormType

Constructor & Destructor Documentation

◆ Hexahedron()

◆ ~Hexahedron()

Member Function Documentation

◆ appendT()

◆ cell() [1/2]

◆ cell() [2/2]

◆ chi()

◆ computeShapefunctions_()

◆ edgeP() [1/2]

◆ edgeP() [2/2]

◆ elemMap() [1/3]

◆ elemMap() [2/3]

◆ elemMap() [3/3]

◆ faceP() [1/2]

◆ faceP() [2/2]

◆ getStrategy()

◆ graphics()

◆ hasSameMatrix()

◆ hessian()

◆ info()

◆ integrationX()

◆ integrationY()

◆ integrationZ()

◆ jacobian()

◆ jacobianDeterminant()

◆ jacobianInverse()

◆ operator<()

◆ p()

◆ quadraturePoint()

◆ recomputeShapefunctions() [1/2]

◆ recomputeShapefunctions() [2/2]

◆ rule()

◆ setStrategy()

◆ shpfctDX()

◆ shpfctDY()

◆ shpfctDZ()

◆ shpfctX()

◆ shpfctY()

◆ shpfctZ()

◆ support() [1/2]

◆ support() [2/2]

◆ T()

◆ vertex()

Member Data Documentation

◆ cell_

◆ edges_

◆ faces_

◆ graphics_

◆ intX_

◆ intY_

◆ intZ_

◆ p_

◆ rule_

◆ shpfctDX_

◆ shpfctDY_

◆ shpfctDZ_

◆ shpfctX_

◆ shpfctY_

◆ shpfctZ_

◆ T_