The following two types are shape function mixins. More...

#include <element.hh>

Inheritance diagram for hp1D::KarniadakisMixin< F >:

Public Types
typedef F	FieldT

enum	intFormType { ZERO, ONE, TWO, THREE }
	Integration form, which determines terms coming from integration over reference element. More...

typedef F	type

Public Member Functions
virtual const concepts::EdgeNd &	cell () const
	Returns the cell on which the element is built. More...

const concepts::Real3d	chi (const Real x) const
	Computes the element map. 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
	Returns element graphics class. More...

const concepts::QuadratureRule1d *	integration () const
	Returns the integration rule. More...

Real	jacobianDeterminant (const Real x) const
	Computes the determinant of the Jacobian. More...

	KarniadakisMixin (const concepts::EdgeNd &cell, ushort p)

ushort	p () const

virtual bool	quadraturePoint (uint i, intPoint &p, intFormType form=ZERO, bool localCoord=false) const
	Delivers a quadrature point. More...

void	recomputeShapefunctions () override
	Recompute shape functions, e.g. More...

const concepts::Karniadakis< 1, 0 > *	shpfct () const override
	Returns the shape functions. More...

const concepts::Karniadakis< 1, 1 > *	shpfctD () const
	Returns the derivatives of the shape functions. More...

const concepts::Karniadakis< 1, 2 > *	shpfctDD () const
	Returns the second derivatives of the shape functions. More...

virtual const concepts::Edge &	support () const

virtual const TMatrixBase< F > &	T () const =0
	Returns the T matrix of the element. More...

virtual concepts::Real3d	vertex (uint i) const

Static Public Member Functions
static concepts::QuadRuleFactory &	rule ()
	Access to the quadrature rule, which is valid for all elements of this type (hp1D::IntegrableElm). More...

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const

Protected Attributes
const concepts::EdgeNd &	cell_
	The cell. More...

std::unique_ptr< concepts::QuadratureRule1d >	int_
	The integration rule. More...

ushort	p_
	T matrix of the element. More...

Static Protected Attributes
static std::unique_ptr< LineGraphics >	graphics_

static concepts::QuadRuleFactory	rule_

Private Member Functions
void	recomputeSecondDerivativeOfShapefunctions_ ()
	Recompute second derivative of the shape functions, e.g. More...

Private Attributes
bool	secondDerivativeUsed_

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

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

std::unique_ptr< concepts::Karniadakis< 1, 2 > >	shpfctDD_
	The second derivatives of the shape functions. More...

Detailed Description

template<class F>
class hp1D::KarniadakisMixin< F >

The following two types are shape function mixins.

Karniadakis shape functions mixin

Author: Lukas Drescher 2015

Definition at line 137 of file element.hh.

Member Typedef Documentation

◆ FieldT

template<class F >

typedef F hp1D::BaseElement< F >::FieldT

inherited

Definition at line 82 of file element.hh.

◆ 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.

Enumerator
ZERO
ONE
TWO
THREE

Definition at line 29 of file integral.hh.

Constructor & Destructor Documentation

◆ KarniadakisMixin()

template<class F >

hp1D::KarniadakisMixin< F >::KarniadakisMixin	(	const concepts::EdgeNd &	cell,
		ushort	p
	)

inline

Definition at line 139 of file element.hh.

Member Function Documentation

◆ cell()

template<class F >

virtual const concepts::EdgeNd& hp1D::BaseElement< F >::cell ( ) const

inlinevirtualinherited

Returns the cell on which the element is built.

Implements concepts::ElementWithCell< F >.

Definition at line 99 of file element.hh.

◆ chi()

const concepts::Real3d hp1D::IntegrableElm::chi ( const Real x ) const

inlineinherited

Computes the element map.

The reference element is [0,1].

Definition at line 40 of file element.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.

◆ graphics()

template<class F >

virtual const concepts::ElementGraphics<Real>* hp1D::BaseElement< F >::graphics ( ) const

virtualinherited

Returns element graphics class.

◆ info()

template<class F >

virtual std::ostream& hp1D::BaseElement< F >::info ( std::ostream & os ) const

protectedvirtualinherited

Reimplemented in hp2D::NeumannTraceElement< F >.

◆ integration()

const concepts::QuadratureRule1d* hp1D::IntegrableElm::integration ( ) const

inlineinherited

Returns the integration rule.

Definition at line 51 of file element.hh.

◆ jacobianDeterminant()

Real hp1D::IntegrableElm::jacobianDeterminant ( const Real x ) const

inlineinherited

Computes the determinant of the Jacobian.

Definition at line 45 of file element.hh.

◆ p()

template<class F >

ushort hp1D::BaseElement< F >::p ( ) const

inlineinherited

Definition at line 103 of file element.hh.

◆ quadraturePoint()

virtual bool hp1D::IntegrableElm::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.

◆ recomputeSecondDerivativeOfShapefunctions_()

template<class F >

void hp1D::KarniadakisMixin< F >::recomputeSecondDerivativeOfShapefunctions_ ( )

private

Recompute second derivative of the shape functions, e.g.

for other abscissas redefined through IntegrableElm::rule().set(...) If shpfctDD() was ever used, this method also recalculate the second derivatives of the shape functions.

◆ recomputeShapefunctions()

template<class F >

void hp1D::KarniadakisMixin< F >::recomputeShapefunctions ( )

overridevirtual

Recompute shape functions, e.g.

for other abscissas redefined through IntegrableElm::rule().set(...)

Implements hp1D::BaseElement< F >.

◆ rule()

static concepts::QuadRuleFactory& hp1D::IntegrableElm::rule ( )

inlinestaticinherited

Access to the quadrature rule, which is valid for all elements of this type (hp1D::IntegrableElm).

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.

Definition at line 62 of file element.hh.

◆ shpfct()

template<class F >

const concepts::Karniadakis<1, 0>* hp1D::KarniadakisMixin< F >::shpfct ( ) const

inlineoverridevirtual

Returns the shape functions.

Implements hp1D::BaseElement< F >.

Definition at line 151 of file element.hh.

◆ shpfctD()

template<class F >

const concepts::Karniadakis<1, 1>* hp1D::KarniadakisMixin< F >::shpfctD ( ) const

inline

Returns the derivatives of the shape functions.

Definition at line 155 of file element.hh.

◆ shpfctDD()

template<class F >

const concepts::Karniadakis<1, 2>* hp1D::KarniadakisMixin< F >::shpfctDD ( ) const

inline

Returns the second derivatives of the shape functions.

Definition at line 160 of file element.hh.

◆ support()

template<class F >

virtual const concepts::Edge& hp1D::BaseElement< F >::support ( ) const

inlinevirtualinherited

Definition at line 91 of file element.hh.

◆ T()

template<typename F >

virtual const TMatrixBase<F>& concepts::ElementWithCell< F >::T ( ) const

pure virtualinherited

Returns the T matrix of the element.

Implemented in hp3D::Element< F >, hp3D::Element< Real >, hp2D::Element< F >, hp2D::Element< Real >, and bem::Constant3d002< concepts::Real >.

◆ vertex()

template<class F >

virtual concepts::Real3d hp1D::BaseElement< F >::vertex ( uint i ) const

inlinevirtualinherited

Definition at line 95 of file element.hh.

Member Data Documentation

◆ cell_

const concepts::EdgeNd& hp1D::IntegrableElm::cell_

protectedinherited

The cell.

Definition at line 70 of file element.hh.

◆ graphics_

template<class F >

std::unique_ptr<LineGraphics> hp1D::BaseElement< F >::graphics_

staticprotectedinherited

Definition at line 126 of file element.hh.

◆ int_

std::unique_ptr<concepts::QuadratureRule1d> hp1D::IntegrableElm::int_

protectedinherited

The integration rule.

Definition at line 72 of file element.hh.

◆ p_

template<class F >

ushort hp1D::BaseElement< F >::p_

protectedinherited

T matrix of the element.

Definition at line 124 of file element.hh.

◆ rule_

concepts::QuadRuleFactory hp1D::IntegrableElm::rule_

staticprotectedinherited

Definition at line 74 of file element.hh.

◆ secondDerivativeUsed_

template<class F >

bool hp1D::KarniadakisMixin< F >::secondDerivativeUsed_

mutableprivate

Definition at line 185 of file element.hh.

◆ shpfct_

template<class F >

std::unique_ptr<concepts::Karniadakis<1, 0> > hp1D::KarniadakisMixin< F >::shpfct_

private

The shape functions.

Definition at line 178 of file element.hh.

◆ shpfctD_

template<class F >

std::unique_ptr<concepts::Karniadakis<1, 1> > hp1D::KarniadakisMixin< F >::shpfctD_

private

The derivatives of the shape functions.

Definition at line 180 of file element.hh.

◆ shpfctDD_

template<class F >

std::unique_ptr<concepts::Karniadakis<1, 2> > hp1D::KarniadakisMixin< F >::shpfctDD_

mutableprivate

The second derivatives of the shape functions.

Definition at line 183 of file element.hh.

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

hp1D/element.hh

hp1D::KarniadakisMixin< F > Class Template Referenceabstract

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

template<class F> class hp1D::KarniadakisMixin< F >

Member Typedef Documentation

◆ FieldT

◆ type

Member Enumeration Documentation

◆ intFormType

Constructor & Destructor Documentation

◆ KarniadakisMixin()

Member Function Documentation

◆ cell()

◆ chi()

◆ elemMap() [1/3]

◆ elemMap() [2/3]

◆ elemMap() [3/3]

◆ graphics()

◆ info()

◆ integration()

◆ jacobianDeterminant()

◆ p()

◆ quadraturePoint()

◆ recomputeSecondDerivativeOfShapefunctions_()

◆ recomputeShapefunctions()

◆ rule()

◆ shpfct()

◆ shpfctD()

◆ shpfctDD()

◆ support()

◆ T()

◆ vertex()

Member Data Documentation

◆ cell_

◆ graphics_

◆ int_

◆ p_

◆ rule_

◆ secondDerivativeUsed_

◆ shpfct_

◆ shpfctD_

◆ shpfctDD_

template<class F>
class hp1D::KarniadakisMixin< F >