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

#include <quad.hh>

Inheritance 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. More...

const concepts::InfiniteQuad2d &	cell () const

virtual const concepts::Cell2 &	cell () const=0
	Returns the cell on which the element is built. More...

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

void	recomputeShapefunctions ()

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

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

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

const concepts::LaguerreBasis< 0 > *	shpfctY () const
	Returns the shape functions in x direction. More...

const concepts::Connector2 &	support () const

virtual const concepts::Connector2 &	support () const=0
	Returns the topological support of the element. More...

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

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

virtual	~InfiniteLaguerreQuad ()

Static Public Member Functions
static Real &	borderY ()
	Largest value in local y coordinates. Default is 1.0. More...

static std::string	integrationRule ()
	Returns information on the settings of the quadrature rule. More...

static void	resetIntegrationRule ()
	Set the standard type of integration. More...

static void	setIntegrationRuleX (enum concepts::intRule rule, bool constant, uint points)
	Sets the type of integration rule in x direction to use. More...

static void	setIntegrationRuleY (bool constant, uint points, const Real border)
	Sets the type of integration rule in y direction to use. More...

Protected Member Functions
void	computeIntegrationRule_ (const uint nq[2])

void	computeIntegrationRuleFromP_ (const ushort *p)

void	computeShapefunctionsX_ ()
	gets the shapefunctions in x direction More...

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

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

std::unique_ptr< concepts::QuadratureRule1d >	intY_

ushort	p_ [2]
	Polynomial degree. More...

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

Private Member Functions
void	computeShapefunctionsY_ ()
	gets the shapefunctions in x direction More...

Private Attributes
concepts::InfiniteQuad2d &	cell_
	The cell. More...

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

std::unique_ptr< concepts::LaguerreBasis< 1 > >	shpfctDY_
	The derivatives of the shape functions in local y-direction. More...

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

std::unique_ptr< concepts::LaguerreBasis< 0 > >	shpfctY_
	The shape functions in local y-direction. More...

Static Private Attributes
static uint	addNumberOfPointsX_
	Number of integration points to add to approximation order when varying number of integration points is requested. More...

static uint	addNumberOfPointsY_

static Real	borderY_
	Largest value in local y coordinates. Default is 1.0. More...

static uint	constNumerOfPointsX_
	Number of integration points to use when constant number is requested. More...

static uint	constNumerOfPointsY_

static std::unique_ptr< concepts::ElementGraphics< Real > >	graphics_
	Appropiate element graphics object. More...

static enum concepts::intRule	integrationTypeX_
	Default behaviour: integration rule Gauss Jacobi (highest order). More...

static enum concepts::intRule	integrationTypeY_
	Default behaviour: uniform points in [0, border] (Trapezoidal rule). More...

static bool	useConstantNumberOfPointsX_
	Use constant number of integration points (true) or not (false). More...

static bool	useConstantNumberOfPointsY_

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 452 of file quad.hh.

Member Typedef Documentation

◆ type

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

inherited

Definition at line 81 of file element.hh.

Constructor & Destructor Documentation

◆ InfiniteLaguerreQuad()

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

◆ ~InfiniteLaguerreQuad()

virtual hp2D::InfiniteLaguerreQuad::~InfiniteLaguerreQuad ( )

virtual

Member Function Documentation

◆ appendT()

void hp2D::Element< Real >::appendT ( concepts::TColumn< Real > * T )

inlineinherited

Appends the T columns to the T matrix.

Definition at line 43 of file element.hh.

◆ borderY()

static Real& hp2D::InfiniteQuad::borderY ( )

inlinestaticinherited

Largest value in local y coordinates. Default is 1.0.

Definition at line 388 of file quad.hh.

◆ cell() [1/2]

const concepts::InfiniteQuad2d& hp2D::InfiniteQuad::cell ( ) const

inlineinherited

Definition at line 332 of file quad.hh.

◆ cell() [2/2]

virtual const concepts::Cell2& hp2D::Element< Real >::cell

pure virtualinherited

Returns the cell on which the element is built.

Implements concepts::ElementWithCell< Real >.

◆ computeIntegrationRule_()

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

protectedinherited

◆ computeIntegrationRuleFromP_()

void hp2D::InfiniteQuad::computeIntegrationRuleFromP_ ( const ushort * p )

protectedinherited

◆ computeShapefunctionsX_()

void hp2D::InfiniteQuad::computeShapefunctionsX_ ( )

protectedinherited

gets the shapefunctions in x direction

◆ computeShapefunctionsY_()

void hp2D::InfiniteLaguerreQuad::computeShapefunctionsY_ ( )

private

gets the shapefunctions in x direction

◆ 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.

◆ graphics()

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

virtual

Implements hp2D::InfiniteQuad.

◆ info()

virtual std::ostream& hp2D::InfiniteLaguerreQuad::info ( std::ostream & os ) const

protectedvirtual

Reimplemented from hp2D::InfiniteQuad.

◆ integrationRule()

static std::string hp2D::InfiniteQuad::integrationRule ( )

staticinherited

Returns information on the settings of the quadrature rule.

◆ integrationX()

const concepts::QuadratureRule1d* hp2D::InfiniteQuad::integrationX ( ) const

inlineinherited

Returns the integration rule in x direction.

Definition at line 339 of file quad.hh.

◆ integrationY()

const concepts::QuadratureRule1d* hp2D::InfiniteQuad::integrationY ( ) const

inlineinherited

Returns the integration rule in y direction.

Definition at line 343 of file quad.hh.

◆ p()

const ushort* hp2D::InfiniteQuad::p ( ) const

inlineinherited

Returns the polynomial degree.

The returned array has 2 elements.

Definition at line 336 of file quad.hh.

◆ recomputeShapefunctions()

void hp2D::InfiniteLaguerreQuad::recomputeShapefunctions ( )

◆ resetIntegrationRule()

static void hp2D::InfiniteQuad::resetIntegrationRule ( )

staticinherited

Set the standard type of integration.

◆ setIntegrationRuleX()

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

staticinherited

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`)

◆ setIntegrationRuleY()

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

staticinherited

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.

◆ shpfctDX()

const concepts::Karniadakis<1,1>* hp2D::InfiniteQuad::shpfctDX ( ) const

inlineinherited

Returns the derivatives of the shape functions in x direction.

Definition at line 376 of file quad.hh.

◆ shpfctDY()

const concepts::LaguerreBasis<1>* hp2D::InfiniteLaguerreQuad::shpfctDY ( ) const

inlinevirtual

Returns the derivatives of the shape functions in x direction.

Implements hp2D::InfiniteQuad.

Definition at line 470 of file quad.hh.

◆ shpfctX()

const concepts::Karniadakis<1,0>* hp2D::InfiniteQuad::shpfctX ( ) const

inlineinherited

Returns the shape functions in x direction.

Definition at line 371 of file quad.hh.

◆ shpfctY()

const concepts::LaguerreBasis<0>* hp2D::InfiniteLaguerreQuad::shpfctY ( ) const

inlinevirtual

Returns the shape functions in x direction.

Implements hp2D::InfiniteQuad.

Definition at line 466 of file quad.hh.

◆ support() [1/2]

const concepts::Connector2& hp2D::InfiniteQuad::support ( ) const

inlineinherited

Definition at line 330 of file quad.hh.

◆ support() [2/2]

virtual const concepts::Connector2& hp2D::Element< Real >::support

pure virtualinherited

Returns the topological support of the element.

Possible supports for an element are quadrilaterals and triangles.

◆ T()

virtual const concepts::TMatrix<Real >& hp2D::Element< Real >::T

inlinevirtualinherited

Returns the T matrix of the element.

Implements concepts::ElementWithCell< Real >.

Definition at line 40 of file element.hh.

◆ vertex()

concepts::Real3d hp2D::InfiniteQuad::vertex ( uint i ) const

inlinevirtualinherited

Returns the coordinates of the ith vertex of this element.

Parameters

i	Index of the vertex

Implements hp2D::Element< Real >.

Definition at line 331 of file quad.hh.

Member Data Documentation

◆ addNumberOfPointsX_

uint hp2D::InfiniteQuad::addNumberOfPointsX_

staticprivateinherited

Number of integration points to add to approximation order when varying number of integration points is requested.

Default is 2.

Definition at line 425 of file quad.hh.

◆ addNumberOfPointsY_

uint hp2D::InfiniteQuad::addNumberOfPointsY_

staticprivateinherited

Definition at line 425 of file quad.hh.

◆ borderY_

Real hp2D::InfiniteQuad::borderY_

staticprivateinherited

Largest value in local y coordinates. Default is 1.0.

Definition at line 431 of file quad.hh.

◆ cell_

concepts::InfiniteQuad2d& hp2D::InfiniteQuad::cell_

privateinherited

The cell.

Definition at line 407 of file quad.hh.

◆ constNumerOfPointsX_

uint hp2D::InfiniteQuad::constNumerOfPointsX_

staticprivateinherited

Number of integration points to use when constant number is requested.

Default values are 10 and 5.

Definition at line 421 of file quad.hh.

◆ constNumerOfPointsY_

uint hp2D::InfiniteQuad::constNumerOfPointsY_

staticprivateinherited

Definition at line 421 of file quad.hh.

◆ graphics_

std::unique_ptr<concepts::ElementGraphics<Real> > hp2D::InfiniteLaguerreQuad::graphics_

staticprivate

Appropiate element graphics object.

Definition at line 480 of file quad.hh.

◆ integrationTypeX_

enum concepts::intRule hp2D::InfiniteQuad::integrationTypeX_

staticprivateinherited

Default behaviour: integration rule Gauss Jacobi (highest order).

The default value is 4 (Gauss Jacobi). Other possible values are 0 (Gauss Lobatto) for better graphics (connected elements). Use setIntegrationRule() to change it.

Definition at line 407 of file quad.hh.

◆ integrationTypeY_

enum concepts::intRule hp2D::InfiniteQuad::integrationTypeY_

staticprivateinherited

Default behaviour: uniform points in [0, border] (Trapezoidal rule).

Definition at line 407 of file quad.hh.

◆ intX_

std::unique_ptr<concepts::QuadratureRule1d> hp2D::InfiniteQuad::intX_

protectedinherited

The integration rules.

Definition at line 403 of file quad.hh.

◆ intY_

std::unique_ptr<concepts::QuadratureRule1d> hp2D::InfiniteQuad::intY_

protectedinherited

Definition at line 404 of file quad.hh.

◆ p_

ushort hp2D::InfiniteQuad::p_[2]

protectedinherited

Polynomial degree.

Definition at line 400 of file quad.hh.

◆ shpfctDX_

std::unique_ptr<concepts::Karniadakis<1,1> > hp2D::InfiniteQuad::shpfctDX_

privateinherited

The derivatives of the shape functions.

Definition at line 436 of file quad.hh.

◆ shpfctDY_

std::unique_ptr<concepts::LaguerreBasis<1> > hp2D::InfiniteLaguerreQuad::shpfctDY_

private

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

Definition at line 485 of file quad.hh.

◆ shpfctX_

std::unique_ptr<concepts::Karniadakis<1,0> > hp2D::InfiniteQuad::shpfctX_

privateinherited

The shape functions.

Definition at line 434 of file quad.hh.

◆ shpfctY_

std::unique_ptr<concepts::LaguerreBasis<0> > hp2D::InfiniteLaguerreQuad::shpfctY_

private

The shape functions in local y-direction.

Definition at line 483 of file quad.hh.

◆ T_

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

protectedinherited

T matrix of the element.

Definition at line 57 of file element.hh.

◆ useConstantNumberOfPointsX_

bool hp2D::InfiniteQuad::useConstantNumberOfPointsX_

staticprivateinherited

Use constant number of integration points (true) or not (false).

Default is false (ie. varying number of points).

Definition at line 429 of file quad.hh.

◆ useConstantNumberOfPointsY_

bool hp2D::InfiniteQuad::useConstantNumberOfPointsY_

staticprivateinherited

Definition at line 429 of file quad.hh.

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

hp2D/quad.hh

hp2D::InfiniteLaguerreQuad Class Referenceabstract

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

◆ type

Constructor & Destructor Documentation

◆ InfiniteLaguerreQuad()

◆ ~InfiniteLaguerreQuad()

Member Function Documentation

◆ appendT()

◆ borderY()

◆ cell() [1/2]

◆ cell() [2/2]

◆ computeIntegrationRule_()

◆ computeIntegrationRuleFromP_()

◆ computeShapefunctionsX_()

◆ computeShapefunctionsY_()

◆ elemMap() [1/3]

◆ elemMap() [2/3]

◆ elemMap() [3/3]

◆ graphics()

◆ info()

◆ integrationRule()

◆ integrationX()

◆ integrationY()

◆ p()

◆ recomputeShapefunctions()

◆ resetIntegrationRule()

◆ setIntegrationRuleX()

◆ setIntegrationRuleY()

◆ shpfctDX()

◆ shpfctDY()

◆ shpfctX()

◆ shpfctY()

◆ support() [1/2]

◆ support() [2/2]

◆ T()

◆ vertex()

Member Data Documentation

◆ addNumberOfPointsX_

◆ addNumberOfPointsY_

◆ borderY_

◆ cell_

◆ constNumerOfPointsX_

◆ constNumerOfPointsY_

◆ graphics_

◆ integrationTypeX_

◆ integrationTypeY_

◆ intX_

◆ intY_

◆ p_

◆ shpfctDX_

◆ shpfctDY_

◆ shpfctX_

◆ shpfctY_

◆ T_

◆ useConstantNumberOfPointsX_

◆ useConstantNumberOfPointsY_