A 2D FEM element: a quad. More...

#include <quad.hh>

Inheritance diagram for hp2D::Quad< F >:

Collaboration diagram for hp2D::Quad< F >:

Public Types
enum	intFormType { ZERO, ONE, TWO, THREE }
	Integration form, which determines terms coming from integration over reference element. More...
typedef F	type
Public Member Functions
void	appendT (concepts::TColumn< F > *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.
void	edgeP (const uint i, const uint &p)
	Set polynomial degree of edge `i` to `p`.
const uint	edgeP (const uint i) const
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< F > *	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.
	Quad (concepts::Quad2d &cell, const ushort p, concepts::TColumn< F > T0, concepts::TColumn< F > *T1)
	Constructor.
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, 1 > *	shpfctDX () const
	Returns the derivatives of the shape functions in x direction.
const concepts::Karniadakis< 1, 1 > *	shpfctDY () const
	Returns the shape functions in y direction.
const concepts::Karniadakis< 1, 0 > *	shpfctX () const
	Returns the shape functions in x direction.
const concepts::Karniadakis< 1, 0 > *	shpfctY () const
	Returns the shape functions in y direction.
virtual const concepts::Quad &	support () const
	Returns the topological support of the element.
virtual const concepts::TMatrix< F > &	T () const
	Returns the T matrix of the element.
uint &	tag ()
	Returns the tag.
virtual concepts::Real3d	vertex (uint i) const
	Returns the coordinates of the ith vertex of this element.
virtual	~Quad ()
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, const concepts::QuadratureRule intY)
	gets the shapefunctions, used in both constructors
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< F >	T_
	T matrix of the element.
Static Protected Attributes
static concepts::QuadRuleFactory	rule_
Private Attributes
const uint *	edges_ [4]
	Polynomial degree of edges.
Static Private Attributes
static std::auto_ptr < concepts::ElementGraphics< F > >	graphics_
	Appropiate element graphics object.

Detailed Description

template<class F = Real>
class hp2D::Quad< F >

A 2D FEM element: a quad.

The reference shape functions are products of the polynomials of Karniadakis and Sherwin. The index of the shape functions rises first over the polynomials in local x-direction.

Definition at line 210 of file quad.hh.

Member Typedef Documentation

template<class F>

typedef F concepts::Element< F >::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

template<class F = Real>

hp2D::Quad< F >::Quad	(	concepts::Quad2d &	cell,
		const ushort *	p,
		concepts::TColumn< F > *	T0,
		concepts::TColumn< F > *	T1
	)

Constructor.

Parameters:

cell	Cell on which the element is defined
p	Polynomial degree (might be anisotropic)
T0	Part of the T matrix
T1	Part of the T matrix

template<class F = Real>

virtual hp2D::Quad< F >::~Quad ( ) [virtual]

Member Function Documentation

template<class F>

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

Appends the T columns to the T matrix.

Definition at line 41 of file element.hh.

template<class F = Real>

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

Returns the cell on which the element is built.

Possible are tetrahedrons, hexahedron, prims and pyramids.

Implements hp2D::Element< F >.

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 hp2D::QuadShapeFunctions::computeShapefunctions_	(	const concepts::QuadratureRule *	intX,
		const concepts::QuadratureRule *	intY
	)		`[protected, inherited]`

gets the shapefunctions, used in both constructors

template<class F = Real>

const uint hp2D::Quad< F >::edgeP ( const uint i ) const [inline]

Definition at line 234 of file quad.hh.

template<class F = Real>

void hp2D::Quad< F >::edgeP	(	const uint	i,
		const uint &	p
	)		`[inline]`

Set polynomial degree of edge i to p.

Definition at line 231 of file quad.hh.

template<typename F>

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

Definition at line 87 of file element.hh.

template<typename F>

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

Definition at line 83 of file element.hh.

template<typename F>

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

Definition at line 91 of file element.hh.

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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template<class F = Real>

virtual const concepts::ElementGraphics<F>* hp2D::Quad< F >::graphics ( ) const [virtual]

Returns element graphics class.

Implements hp2D::BaseQuad< F >.

template<class F = Real>

virtual std::ostream& hp2D::Quad< F >::info ( std::ostream & os ) const [protected, virtual]

Returns information in an output stream.

Reimplemented from hp2D::BaseQuad< F >.

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* hp2D::QuadShapeFunctions::p ( ) const [inline, inherited]

Returns the polynomial degree.

The returned array has 2 elements.

Definition at line 172 of file quad.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.

template<class F = Real>

void hp2D::Quad< F >::recomputeShapefunctions ( )

Recompute shape functions, e.g.

for other abscissas redefined through setIntegrationRule

template<class F = Real>

void hp2D::Quad< F >::recomputeShapefunctions ( const uint nq[2] )

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]

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 87 of file quad.hh.

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const concepts::Karniadakis<1,1>* hp2D::QuadShapeFunctions::shpfctDX ( ) const [inline, inherited]

Returns the derivatives of the shape functions in x direction.

Definition at line 183 of file quad.hh.

const concepts::Karniadakis<1,1>* hp2D::QuadShapeFunctions::shpfctDY ( ) const [inline, inherited]

Returns the shape functions in y direction.

Definition at line 186 of file quad.hh.

const concepts::Karniadakis<1,0>* hp2D::QuadShapeFunctions::shpfctX ( ) const [inline, inherited]

Returns the shape functions in x direction.

Definition at line 175 of file quad.hh.

const concepts::Karniadakis<1,0>* hp2D::QuadShapeFunctions::shpfctY ( ) const [inline, inherited]

Returns the shape functions in y direction.

Definition at line 179 of file quad.hh.

template<class F = Real>

virtual const concepts::Quad& hp2D::BaseQuad< F >::support ( ) const [inline, virtual, inherited]

Returns the topological support of the element.

Possible supports for an element are quadrilaterals and triangles.

Implements hp2D::Element< F >.

Definition at line 133 of file quad.hh.

template<class F>

virtual const concepts::TMatrix<F>& hp2D::Element< F >::T ( ) const [inline, virtual, inherited]

Returns the T matrix of the element.

Implements concepts::Element< F >.

Definition at line 38 of file element.hh.

template<class F>

uint& concepts::Element< F >::tag ( ) [inline, inherited]

Returns the tag.

Definition at line 65 of file element.hh.

template<class F = Real>

virtual concepts::Real3d hp2D::BaseQuad< F >::vertex ( uint i ) const [inline, virtual, inherited]

Returns the coordinates of the ith vertex of this element.

Parameters:

i	Index of the vertex

Implements hp2D::Element< F >.

Definition at line 134 of file quad.hh.

Member Data Documentation

concepts::Quad2d& hp2D::IntegrableQuad::cell_ [protected, inherited]

The cell.

Definition at line 110 of file quad.hh.

template<class F = Real>

const uint* hp2D::Quad< F >::edges_[4] [private]

Polynomial degree of edges.

Definition at line 245 of file quad.hh.

template<class F = Real>

std::auto_ptr<concepts::ElementGraphics<F> > hp2D::Quad< F >::graphics_ [static, private]

Appropiate element graphics object.

Definition at line 243 of file quad.hh.

std::auto_ptr<concepts::QuadratureRule> hp2D::IntegrableQuad::intX_ [protected, inherited]

The integration rules.

Definition at line 106 of file quad.hh.

std::auto_ptr<concepts::QuadratureRule> hp2D::IntegrableQuad::intY_ [protected, inherited]

Definition at line 107 of file quad.hh.

concepts::QuadRuleFactory hp2D::IntegrableQuad::rule_ [static, protected, inherited]

Definition at line 113 of file quad.hh.

template<class F>

concepts::TMatrix<F> hp2D::Element< F >::T_ [protected, inherited]

T matrix of the element.

Definition at line 57 of file element.hh.

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

hp2D/quad.hh

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Private Attributes

Static Private Attributes

Detailed Description

template<class F = Real> class hp2D::Quad< F >

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class F = Real>
class hp2D::Quad< F >