A 2D FEM element: an infinite quad with basis based on Laguerre functions. More...

#include <quad.hh>

Inheritance diagram for hp2D::InfiniteLaguerreQuad:

Collaboration diagram for hp2D::InfiniteLaguerreQuad:

Public Types
typedef Real	type
Public Member Functions
void	appendT (concepts::TColumn< Real > *T)
	Appends the T columns to the T matrix.
const concepts::InfiniteQuad2d &	cell () const
	Returns the cell on which the element is built.
Real3d	elemMap (const Real coord_local) const
Real3d	elemMap (const Real2d &coord_local) const
Real3d	elemMap (const Real3d &coord_local) const
virtual const concepts::ElementGraphics < Real > *	graphics () const
	InfiniteLaguerreQuad (concepts::InfiniteQuad2d &cell, const ushort p, concepts::TColumn< Real > T0, concepts::TColumn< Real > *T1)
	Constructor.
const concepts::QuadratureRule *	integrationX () const
	Returns the integration rule in x direction.
const concepts::QuadratureRule *	integrationY () const
	Returns the integration rule in y direction.
const ushort *	p () const
	Returns the polynomial degree.
void	recomputeShapefunctions ()
const concepts::Karniadakis< 1, 1 > *	shpfctDX () const
	Returns the derivatives of the shape functions in x direction.
const concepts::LaguerreBasis< 1 > *	shpfctDY () const
	Returns the derivatives of the shape functions in x direction.
const concepts::Karniadakis< 1, 0 > *	shpfctX () const
	Returns the shape functions in x direction.
const concepts::LaguerreBasis< 0 > *	shpfctY () const
	Returns the shape functions in x direction.
const concepts::Connector2 &	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.
concepts::Real3d	vertex (uint i) const
	Returns the coordinates of the ith vertex of this element.
virtual	~InfiniteLaguerreQuad ()
Static Public Member Functions
static Real &	borderY ()
	Largest value in local y coordinates. Default is 1.0.
static std::string	integrationRule ()
	Returns information on the settings of the quadrature rule.
static void	resetIntegrationRule ()
	Set the standard type of integration.
static void	setIntegrationRuleX (enum concepts::intRule rule, bool constant, uint points)
	Sets the type of integration rule in x direction to use.
static void	setIntegrationRuleY (bool constant, uint points, const Real border)
	Sets the type of integration rule in y direction to use.
Protected Member Functions
void	computeIntegrationRule_ (const uint nq[2])
void	computeIntegrationRuleFromP_ (const ushort *p)
void	computeShapefunctionsX_ ()
	gets the shapefunctions in x direction
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Protected Attributes
std::auto_ptr < concepts::QuadratureRule >	intX_
	The integration rules.
std::auto_ptr < concepts::QuadratureRule >	intY_
ushort	p_ [2]
	Polynomial degree.
concepts::TMatrix< Real >	T_
	T matrix of the element.
Private Member Functions
void	computeShapefunctionsY_ ()
	gets the shapefunctions in x direction
Private Attributes
std::auto_ptr < concepts::LaguerreBasis< 1 > >	shpfctDY_
	The derivatives of the shape functions in local y-direction.
std::auto_ptr < concepts::LaguerreBasis< 0 > >	shpfctY_
	The shape functions in local y-direction.
Static Private Attributes
static std::auto_ptr < concepts::ElementGraphics < Real > >	graphics_
	Appropiate element graphics object.

Detailed Description

A 2D FEM element: an infinite quad with basis based on Laguerre functions.

The reference shape functions are products of the polynomials of Karniadakis and Sherwin in local x-direction and a basis based on Laguerre functions in local y-direction. The index of the shape functions rises first over the polynomials in local x-direction.

Author:: Kersten Schmidt, 2009.

Definition at line 390 of file quad.hh.

Member Typedef Documentation

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

Definition at line 53 of file element.hh.

Constructor & Destructor Documentation

hp2D::InfiniteLaguerreQuad::InfiniteLaguerreQuad	(	concepts::InfiniteQuad2d &	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 (might be anisotropic)
T0	Part of the T matrix
T1	Part of the T matrix

virtual hp2D::InfiniteLaguerreQuad::~InfiniteLaguerreQuad ( ) [virtual]

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.

static Real& hp2D::InfiniteQuad::borderY ( ) [inline, static, inherited]

Largest value in local y coordinates. Default is 1.0.

Definition at line 326 of file quad.hh.

const concepts::InfiniteQuad2d& hp2D::InfiniteQuad::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 270 of file quad.hh.

void hp2D::InfiniteQuad::computeIntegrationRule_ ( const uint nq[2] ) [protected, inherited]

void hp2D::InfiniteQuad::computeIntegrationRuleFromP_ ( const ushort * p ) [protected, inherited]

void hp2D::InfiniteQuad::computeShapefunctionsX_ ( ) [protected, inherited]

gets the shapefunctions in x direction

void hp2D::InfiniteLaguerreQuad::computeShapefunctionsY_ ( ) [private]

gets the shapefunctions in x direction

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

Implements hp2D::InfiniteQuad.

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

Returns information in an output stream.

Reimplemented from hp2D::InfiniteQuad.

static std::string hp2D::InfiniteQuad::integrationRule ( ) [static, inherited]

Returns information on the settings of the quadrature rule.

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

Returns the integration rule in x direction.

Definition at line 277 of file quad.hh.

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

Returns the integration rule in y direction.

Definition at line 281 of file quad.hh.

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

Returns the polynomial degree.

The returned array has 2 elements.

Definition at line 274 of file quad.hh.

void hp2D::InfiniteLaguerreQuad::recomputeShapefunctions ( )

static void hp2D::InfiniteQuad::resetIntegrationRule ( ) [static, inherited]

Set the standard type of integration.

static void hp2D::InfiniteQuad::setIntegrationRuleX	(	enum concepts::intRule	rule,
		bool	constant,
		uint	points
	)		`[static, inherited]`

Sets the type of integration rule in x direction to use.

Parameters:

rule	Determines the integration rule
constant	Use constant number of points
points	Number of points to use (for `constant = true`) or points to add to approximation order (for `constant = false`)

static void hp2D::InfiniteQuad::setIntegrationRuleY	(	bool	constant,
		uint	points,
		const Real	border
	)		`[static, inherited]`

Sets the type of integration rule in y direction to use.

Parameters:

constant	Use constant number of points
points	Number of points to use (for `constant = true`) or points to add to approximation order (for `constant = false`)
border	Largest value in local y coordinates.

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

Returns the derivatives of the shape functions in x direction.

Definition at line 314 of file quad.hh.

const concepts::LaguerreBasis<1>* hp2D::InfiniteLaguerreQuad::shpfctDY ( ) const [inline, virtual]

Returns the derivatives of the shape functions in x direction.

Implements hp2D::InfiniteQuad.

Definition at line 408 of file quad.hh.

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

Returns the shape functions in x direction.

Definition at line 309 of file quad.hh.

const concepts::LaguerreBasis<0>* hp2D::InfiniteLaguerreQuad::shpfctY ( ) const [inline, virtual]

Returns the shape functions in x direction.

Implements hp2D::InfiniteQuad.

Definition at line 404 of file quad.hh.

const concepts::Connector2& hp2D::InfiniteQuad::support ( ) const [inline, virtual, inherited]

Returns the topological support of the element.

Possible supports for an element are quadrilaterals and triangles.

Implements hp2D::Element< Real >.

Definition at line 268 of file quad.hh.

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

Returns the T matrix of the element.

Implements concepts::Element< Real >.

Definition at line 38 of file element.hh.

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

Returns the tag.

Definition at line 65 of file element.hh.

concepts::Real3d hp2D::InfiniteQuad::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< Real >.

Definition at line 269 of file quad.hh.

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Member Data Documentation

std::auto_ptr<concepts::ElementGraphics<Real> > hp2D::InfiniteLaguerreQuad::graphics_ [static, private]

Appropiate element graphics object.

Definition at line 418 of file quad.hh.

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

The integration rules.

Definition at line 341 of file quad.hh.

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

Definition at line 342 of file quad.hh.

ushort hp2D::InfiniteQuad::p_[2] [protected, inherited]

Polynomial degree.

Definition at line 338 of file quad.hh.

std::auto_ptr<concepts::LaguerreBasis<1> > hp2D::InfiniteLaguerreQuad::shpfctDY_ [private]

The derivatives of the shape functions in local y-direction.

Definition at line 423 of file quad.hh.

std::auto_ptr<concepts::LaguerreBasis<0> > hp2D::InfiniteLaguerreQuad::shpfctY_ [private]

The shape functions in local y-direction.

Definition at line 421 of file quad.hh.

concepts::TMatrix<Real > hp2D::Element< Real >::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

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation