#include <quad.hh>

Inheritance diagram for hp2D::Quad< F >:

Public Types
typedef F	type

enum	intFormType { ZERO , ONE , TWO , THREE }

Public Member Functions
	Quad (concepts::QuadNd &cell, const ushort p, concepts::TColumn< F > T0, concepts::TColumn< F > *T1)

virtual const concepts::ElementGraphics< F > *	graphics () const
	Returns element graphics class.

void	recomputeShapefunctions ()

void	recomputeShapefunctions (const uint nq[2])

void	edgeP (const uint i, const uint &p)
	Set polynomial degree of edge `i` to `p`.

const uint	edgeP (const uint i) const

virtual const concepts::Quad &	support () const

virtual concepts::Real3d	vertex (uint i) const

virtual const concepts::QuadNd &	cell () const
	Returns the cell on which the element is built.

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

void	appendT (concepts::TColumn< F > *T)
	Appends the T columns to the T matrix.

Real3d	elemMap (const Real coord_local) const

Real3d	elemMap (const Real2d &coord_local) const

Real3d	elemMap (const Real3d &coord_local) const

uint &	tag ()
	Returns the tag.

concepts::Real2d	chi (const Real x, const Real y) const

concepts::MapReal2d	jacobian (const Real x, const Real y) const
	Computes the Jacobian.

concepts::MapReal2d	jacobianInverse (const Real x, const Real y) const
	Computes the inverse of the Jacobian.

concepts::MapReal2d	inverseLaplace (const Real x, const Real y) const

Real	gramDeterminantRoot (const Real x, const Real y) const

void	setStrategy (const concepts::Quad2dSubdivision *strategy=0)

const concepts::Quad2dSubdivision *	getStrategy () const

virtual bool	quadraturePoint (uint i, intPoint &p, intFormType form=ZERO, bool localCoord=false) const

const concepts::QuadratureRule2d *const	intRule () const

const ushort *	p () const

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.

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.

Static Public Member Functions
static std::unique_ptr< concepts::QuadRuleFactoryTensor2d > &	factory ()

static concepts::QuadRuleFactoryTensor2d *	factory_rp ()

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.

void	computeShapefunctions_ (const concepts::QuadratureRule2d *intRule)
	gets the shapefunctions, used in both constructors

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

std::unique_ptr< concepts::QuadratureRule2d >	intRule_
	The integration rules.

concepts::QuadNd &	cell_
	The cell.

Static Protected Attributes
static std::unique_ptr< concepts::QuadRuleFactoryTensor2d >	factory_

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 271 of file quad.hh.

Member Typedef Documentation

◆ type

template<typename F >

typedef F concepts::ElementWithCell< F >::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

Definition at line 29 of file integral.hh.

Constructor & Destructor Documentation

◆ Quad()

template<class F = Real>

hp2D::Quad< F >::Quad	(	concepts::QuadNd &	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

Member Function Documentation

◆ appendT()

template<class F >

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

inlineinherited

Appends the T columns to the T matrix.

Definition at line 43 of file element.hh.

◆ cell()

template<class F = Real>

virtual const concepts::QuadNd & hp2D::BaseQuad< F >::cell ( ) const

inlinevirtualinherited

Returns the cell on which the element is built.

Implements hp2D::Element< F >.

Definition at line 196 of file quad.hh.

◆ chi()

concepts::Real2d hp2D::IntegrableQuad::chi	(	const Real	x,
		const Real	y
	)		const

inlineinherited

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 40 of file quad.hh.

◆ computeShapefunctions_()

void hp2D::QuadShapeFunctions::computeShapefunctions_ ( const concepts::QuadratureRule2d * intRule )

protectedinherited

gets the shapefunctions, used in both constructors

◆ edgeP() [1/2]

template<class F = Real>

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

inline

Definition at line 295 of file quad.hh.

◆ edgeP() [2/2]

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 292 of file quad.hh.

◆ elemMap() [1/3]

template<typename F >

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

inlineinherited

Definition at line 86 of file element.hh.

◆ elemMap() [2/3]

template<typename F >

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

inlineinherited

Definition at line 90 of file element.hh.

◆ elemMap() [3/3]

template<typename F >

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

inlineinherited

Definition at line 94 of file element.hh.

◆ factory()

static std::unique_ptr< concepts::QuadRuleFactoryTensor2d > & hp2D::IntegrableQuad::factory ( )

inlinestaticinherited

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, RobinBCs.cc, elasticity2D_tutorial.cc, exactDtN.cc, howToGetStarted.cc, inhomDirichletBCs.cc, inhomDirichletBCsLagrange.cc, inhomNeumannBCs.cc, and parallelizationTutorial.cc.

Definition at line 144 of file quad.hh.

◆ factory_rp()

static concepts::QuadRuleFactoryTensor2d * hp2D::IntegrableQuad::factory_rp ( )

inlinestaticinherited

Access to the quadrature rule ( as factory() ) through a raw pointer.

Definition at line 148 of file quad.hh.

◆ getStrategy()

const concepts::Quad2dSubdivision * hp2D::IntegrableQuad::getStrategy ( ) const

inlineinherited

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

Definition at line 121 of file quad.hh.

◆ gramDeterminantRoot()

Real hp2D::IntegrableQuad::gramDeterminantRoot	(	const Real	x,
		const Real	y
	)		const

inlineinherited

Computes the sqaure root of the Gram determinant multiplied by 0.25 to incorporate the transformation factor for the integration weights.

Definition at line 91 of file quad.hh.

◆ graphics()

template<class F = Real>

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

virtual

Returns element graphics class.

Implements hp2D::BaseQuad< F >.

◆ info()

template<class F = Real>

virtual std::ostream & hp2D::Quad< F >::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from hp2D::BaseQuad< F >.

Reimplemented in hp3D::NeumannTraceElement3d< F >.

◆ intRule()

const concepts::QuadratureRule2d *const hp2D::IntegrableQuad::intRule ( ) const

inlineinherited

Definition at line 135 of file quad.hh.

◆ inverseLaplace()

concepts::MapReal2d hp2D::IntegrableQuad::inverseLaplace	(	const Real	x,
		const Real	y
	)		const

inlineinherited

Definition at line 66 of file quad.hh.

◆ jacobian()

concepts::MapReal2d hp2D::IntegrableQuad::jacobian	(	const Real	x,
		const Real	y
	)		const

inlineinherited

Computes the Jacobian.

Definition at line 45 of file quad.hh.

◆ jacobianInverse()

concepts::MapReal2d hp2D::IntegrableQuad::jacobianInverse	(	const Real	x,
		const Real	y
	)		const

inlineinherited

Computes the inverse of the Jacobian.

Definition at line 59 of file quad.hh.

◆ p()

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

inlineinherited

Returns the polynomial degree. The returned array has 2 elements.

Definition at line 229 of file quad.hh.

◆ quadraturePoint()

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

virtualinherited

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()

template<class F = Real>

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

Recompute shape functions, e.g. for other abscissas redefined through setIntegrationRule

◆ setStrategy()

void hp2D::IntegrableQuad::setStrategy ( const concepts::Quad2dSubdivision * strategy = 0 )

inlineinherited

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 109 of file quad.hh.

◆ shpfctDX()

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

inlineinherited

Returns the derivatives of the shape functions in x direction.

Definition at line 240 of file quad.hh.

◆ shpfctDY()

const concepts::Karniadakis< 1, 1 > * hp2D::QuadShapeFunctions::shpfctDY ( ) const

inlineinherited

Returns the shape functions in y direction.

Definition at line 243 of file quad.hh.

◆ shpfctX()

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

inlineinherited

Returns the shape functions in x direction.

Definition at line 232 of file quad.hh.

◆ shpfctY()

const concepts::Karniadakis< 1, 0 > * hp2D::QuadShapeFunctions::shpfctY ( ) const

inlineinherited

Returns the shape functions in y direction.

Definition at line 236 of file quad.hh.

◆ support()

template<class F = Real>

virtual const concepts::Quad & hp2D::BaseQuad< F >::support ( ) const

inlinevirtualinherited

Returns the topological support of the element. Possible supports for an element are quadrilaterals and triangles.

Implements hp2D::Element< F >.

Definition at line 194 of file quad.hh.

◆ T()

template<class F >

virtual const concepts::TMatrix< F > & hp2D::Element< F >::T ( ) const

inlinevirtualinherited

Returns the T matrix of the element.

Implements concepts::ElementWithCell< F >.

Reimplemented in hp3D::NeumannTraceElement3d< F >.

Definition at line 40 of file element.hh.

◆ tag()

template<class F >

uint & concepts::Element< F >::tag ( )

inlineinherited

Returns the tag.

Definition at line 66 of file element.hh.

◆ vertex()

template<class F = Real>

virtual concepts::Real3d hp2D::BaseQuad< F >::vertex ( uint i ) const

inlinevirtualinherited

Returns the coordinates of the ith vertex of this element.

Parameters

i	Index of the vertex

Implements hp2D::Element< F >.

Definition at line 195 of file quad.hh.

Member Data Documentation

◆ cell_

concepts::QuadNd& hp2D::IntegrableQuad::cell_

protectedinherited

The cell.

Definition at line 161 of file quad.hh.

◆ factory_

std::unique_ptr<concepts::QuadRuleFactoryTensor2d> hp2D::IntegrableQuad::factory_

staticprotectedinherited

Definition at line 165 of file quad.hh.

◆ intRule_

std::unique_ptr<concepts::QuadratureRule2d> hp2D::IntegrableQuad::intRule_

protectedinherited

The integration rules.

Definition at line 158 of file quad.hh.

◆ T_

template<class F >

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

protectedinherited

T matrix of the element.

Definition at line 57 of file element.hh.

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

hp2D/bf_advection.hh
hp2D/quad.hh

Class documentation of Concepts

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Detailed Description

Member Typedef Documentation

◆ type

Member Enumeration Documentation

◆ intFormType

Constructor & Destructor Documentation

◆ Quad()

Member Function Documentation

◆ appendT()

◆ cell()

◆ chi()

◆ computeShapefunctions_()

◆ edgeP() [1/2]

◆ edgeP() [2/2]

◆ elemMap() [1/3]

◆ elemMap() [2/3]

◆ elemMap() [3/3]

◆ factory()

◆ factory_rp()

◆ getStrategy()

◆ gramDeterminantRoot()

◆ graphics()

◆ info()

◆ intRule()

◆ inverseLaplace()

◆ jacobian()

◆ jacobianInverse()

◆ p()

◆ quadraturePoint()

◆ recomputeShapefunctions()

◆ setStrategy()

◆ shpfctDX()

◆ shpfctDY()

◆ shpfctX()

◆ shpfctY()

◆ support()

◆ T()

◆ tag()

◆ vertex()

Member Data Documentation

◆ cell_

◆ factory_

◆ intRule_

◆ T_