2D FE element based inside a thin sheet on quadrilateral cell. More...

#include <thinSheetElm.hh>

Inheritance diagram for hp2D::ThinSheetQuad:

Collaboration diagram for hp2D::ThinSheetQuad:

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.
virtual const concepts::Quad2d &	cell () const
	Returns the cell on which the element is built.
concepts::Real2d	chi (const Real x, const Real y) const
	Computes the element map, the map from the reference element to the real geometry of the quad.
Real3d	elemMap (const Real coord_local) const
Real3d	elemMap (const Real2d &coord_local) const
Real3d	elemMap (const Real3d &coord_local) const
const concepts::Quad2dSubdivision *	getStrategy () const
	Returns the subdivision strategy of the underlying cell of this element.
virtual const concepts::ElementGraphics < Real > *	graphics () const
	Returns element graphics class.
const concepts::QuadratureRule *	integrationX () const
	Returns the integration rule in x direction.
const concepts::QuadratureRule *	integrationY () const
	Returns the integration rule in y direction.
concepts::MapReal2d	jacobian (const Real x, const Real y) const
	Computes the Jacobian.
Real	jacobianDeterminant (const Real x, const Real y) const
	Computes the determinant of the Jacobian.
concepts::MapReal2d	jacobianInverse (const Real x, const Real y) const
	Computes the inverse of the Jacobian.
const ushort	p () const
	Returns the polynomial degree.
virtual bool	quadraturePoint (uint i, intPoint &p, intFormType form=ZERO, bool localCoord=false) const
	Delivers a quadrature point.
void	recomputeShapefunctions ()
	Recompute shape functions, e.g.
void	recomputeShapefunctions (const uint nq[2])
void	setStrategy (const concepts::Quad2dSubdivision *strategy=0) throw (concepts::StrategyChange)
	Sets the subdivision strategy of the underlying cell of this element.
const concepts::Karniadakis< 1, 0 > *	shpfct () const
	Returns the shape functions.
const concepts::Karniadakis< 1, 1 > *	shpfctD () const
	Returns the derivatives of the shape functions.
virtual const concepts::Quad &	support () const
	Returns the topological support of the element.
virtual const concepts::TMatrix< Real > &	T () const
	Returns the T matrix of the element.
uint &	tag ()
	Returns the tag.
	ThinSheetQuad (concepts::Quad2d &cell, const ushort p, concepts::TColumn< Real > T0, concepts::TColumn< Real > T1)
	Constructor.
virtual concepts::Real3d	vertex (uint i) const
	Returns the coordinates of the ith vertex of this element.
	~ThinSheetQuad ()
Static Public Member Functions
static concepts::QuadRuleFactory &	rule ()
	Access to the quadrature rule, which is valid for all elements of this type (hp2D::IntegrableQuad).
Protected Member Functions
void	computeShapefunctions_ (const concepts::QuadratureRule *intX)
	gets the shapefunctions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Protected Attributes
concepts::Quad2d &	cell_
	The cell.
std::auto_ptr < concepts::QuadratureRule >	intX_
	The integration rules.
std::auto_ptr < concepts::QuadratureRule >	intY_
concepts::TMatrix< Real >	T_
	T matrix of the element.
Static Protected Attributes
static concepts::QuadRuleFactory	rule_
Static Private Attributes
static std::auto_ptr < concepts::ElementGraphics < Real > >	graphics_
	Appropiate element graphics object.

Detailed Description

2D FE element based inside a thin sheet on quadrilateral cell.

The functions are piecewise polynomial on the boundary.

Author:: Kersten Schmidt, 2006

Definition at line 139 of file thinSheetElm.hh.

Member Typedef Documentation

typedef Real concepts::Element< Real >::type [inherited]

Definition at line 53 of file element.hh.

Member Enumeration Documentation

enum concepts::IntegrationCell::intFormType [inherited]

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

Enumerator:

ZERO
ONE
TWO
THREE

Definition at line 27 of file integral.hh.

Constructor & Destructor Documentation

hp2D::ThinSheetQuad::ThinSheetQuad	(	concepts::Quad2d &	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
T0	Part of the T matrix
T1	Part of the T matrix

The thickness direction is along the 2nd and the 4th edge.

hp2D::ThinSheetQuad::~ThinSheetQuad ( )

Member Function Documentation

void hp2D::Element< Real >::appendT ( concepts::TColumn< Real > * T ) [inline, inherited]

Appends the T columns to the T matrix.

Definition at line 41 of file element.hh.

virtual const concepts::Quad2d& hp2D::BaseQuad< Real >::cell ( ) const [inline, virtual, inherited]

Returns the cell on which the element is built.

Possible are tetrahedrons, hexahedron, prims and pyramids.

Implements hp2D::Element< Real >.

Definition at line 135 of file quad.hh.

concepts::Real2d hp2D::IntegrableQuad::chi	(	const Real	x,
		const Real	y
	)		const `[inline, inherited]`

Computes the element map, the map from the reference element to the real geometry of the quad.

The reference element is the unit quad.

Definition at line 55 of file quad.hh.

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void hp1D::LineShapeFunctions::computeShapefunctions_ ( const concepts::QuadratureRule * intX ) [protected, inherited]

gets the shapefunctions

Real3d concepts::ElementWithCell< Real >::elemMap ( const Real coord_local ) const [inline, inherited]

Definition at line 83 of file element.hh.

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Real3d concepts::ElementWithCell< Real >::elemMap ( const Real2d & coord_local ) const [inline, inherited]

Definition at line 87 of file element.hh.

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Real3d concepts::ElementWithCell< Real >::elemMap ( const Real3d & coord_local ) const [inline, inherited]

Definition at line 91 of file element.hh.

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const concepts::Quad2dSubdivision* hp2D::IntegrableQuad::getStrategy ( ) const [inline, inherited]

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

Definition at line 96 of file quad.hh.

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virtual const concepts::ElementGraphics<Real>* hp2D::ThinSheetQuad::graphics ( ) const [virtual]

Returns element graphics class.

Implements hp2D::BaseQuad< Real >.

virtual std::ostream& hp2D::ThinSheetQuad::info ( std::ostream & os ) const [protected, virtual]

Returns information in an output stream.

Reimplemented from hp2D::BaseQuad< Real >.

const concepts::QuadratureRule* hp2D::IntegrableQuad::integrationX ( ) const [inline, inherited]

Returns the integration rule in x direction.

Definition at line 34 of file quad.hh.

const concepts::QuadratureRule* hp2D::IntegrableQuad::integrationY ( ) const [inline, inherited]

Returns the integration rule in y direction.

Definition at line 38 of file quad.hh.

concepts::MapReal2d hp2D::IntegrableQuad::jacobian	(	const Real	x,
		const Real	y
	)		const `[inline, inherited]`

Computes the Jacobian.

Definition at line 60 of file quad.hh.

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Real hp2D::IntegrableQuad::jacobianDeterminant	(	const Real	x,
		const Real	y
	)		const `[inline, inherited]`

Computes the determinant of the Jacobian.

Definition at line 75 of file quad.hh.

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concepts::MapReal2d hp2D::IntegrableQuad::jacobianInverse	(	const Real	x,
		const Real	y
	)		const `[inline, inherited]`

Computes the inverse of the Jacobian.

Definition at line 68 of file quad.hh.

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const ushort hp1D::LineShapeFunctions::p ( ) const [inline, inherited]

Returns the polynomial degree.

The returned array has 2 elements.

Definition at line 36 of file thinSheetElm.hh.

virtual bool hp2D::IntegrableQuad::quadraturePoint	(	uint	i,
		intPoint &	p,
		intFormType	form = `ZERO`,
		bool	localCoord = `false`
	)		const `[virtual, inherited]`

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.

void hp2D::ThinSheetQuad::recomputeShapefunctions ( const uint nq[2] )

void hp2D::ThinSheetQuad::recomputeShapefunctions ( )

Recompute shape functions, e.g.

for other abscissas redefined through hp2D::IntegrableQuad::rule().set(...)

static concepts::QuadRuleFactory& hp2D::IntegrableQuad::rule ( ) [inline, static, inherited]

Access to the quadrature rule, which is valid for all elements of this type (hp2D::IntegrableQuad).

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.

Examples:: BGT_0.cc, exactDtN.cc, inhomDirichletBCs.cc, inhomDirichletBCsLagrange.cc, inhomNeumannBCs.cc, and RobinBCs.cc.

Definition at line 48 of file quad.hh.

void hp2D::IntegrableQuad::setStrategy ( const concepts::Quad2dSubdivision * strategy = 0 ) throw (concepts::StrategyChange) [inline, inherited]