2D hp-FEM for H¹-conforming elements. More...

Namespaces
	l2
	2D hp-FEM for L²-conforming elements.

Classes
class	AdaptiveModel

class	Advection
	A function class to calculate element matrices for the bilinear form. More...

class	ApproxMoments

class	APrioriGeometricRefinement
	Class for holding a rule for geometric refinement towards edges and vertices. More...

class	APrioriRefinement
	Carries out a-priori given refinements. More...

class	APrioriRefinementNew

class	APrioriRefinementRule

class	APrioriRefinementRuleFactory
	Factory class for a refinement rule. More...

class	APrioriRegularRefinement
	Class for holding a rule for a particular h- and p-refinement until an maximum level and maximum polynomial degree is reached. More...

class	ArrayElementFormula
	Array of formula values on quadrature points. More...

class	ArrayQuadWeights
	Class to represent the quadrature weights on all quadrature points. More...

class	BaseEdge

class	BaseQuad
	A base of a 2D quad FEM element for different basis functions. More...

class	BaseQuadGraphics
	Base class for handling graphics for 2D hp quadrilateral FEM elements. More...

class	BilinearFormHelper_0_0
	Helper class for bilinearforms a(u,v), where u and v are 0-forms. More...

class	BilinearFormHelper_0_1_Part
	Helper class for bilinear forms a(u,v) where u is a 0-form and v is a 1-form. More...

class	BilinearFormHelper_1_1
	Helper class for bilinearforms a(u,v), where u and v are 1-forms, which computes intermediate data for element matrix computation. More...

class	BilinearFormHelper_2_1
	Helper class for bilinearforms $a(u,\underline{v})$ , where is a 2-form and $\underline{v}$ a 1-form. More...

class	BilinearFormHelper_2_2
	Helper class for bilinearforms a(u,v), where u and v are 2-forms. More...

class	BilinearFormOnePartDeriv
	A function class to calculate element matrices for the bilinear form related to a partial derivative of the test functions (scalar). More...

class	BilinearFormTwoPartDeriv
	A function class to calculate element matrices for the bilinear form related to a partial derivative of the trial and (!) test functions (scalar). More...

class	BuildDofsBase
	Responsible to build the degrees of freedom in a space. More...

class	BuildEdgeDofs
	Responsible to build the edge degrees of freedom in a space. More...

class	BuildH1EdgeTColumns
	Responsible to build the T columns belonging to edge degrees of freedom in a H1 conforming space with shape functions in tensor product structure. More...

class	BuildH1InnerTColumns
	Responsible to build the T columns belonging to inner degrees of freedom in a H1 conforming space with shape functions in tensor product structure. More...

class	BuildH1InnerTColumnsHypTrunk
	Responsible to build the T columns belonging to inner degrees of freedom in a H1 conforming (trunk) space with shape functions in tensor product structure. More...

class	BuildH1InnerTColumnsLinTrunk
	Responsible to build the T columns belonging to inner degrees of freedom in a H1 conforming (trunk) space with shape functions in tensor product structure. More...

class	BuildH1VtxTColumns
	Responsible to build the T columns belonging to vertex degrees of freedom in a H1 conforming space with shape functions in tensor product structure. More...

class	BuildHCurlEdgeTColumns
	Responsible to build the T columns belonging to edge degrees of freedom in a H(Curl) conforming space with shape functions in tensor product structure. More...

class	BuildHCurlInnerTColumns
	Responsible to build the T columns belonging to inner degrees of freedom in a HCurl conforming space with shape functions in tensor product structure. More...

class	BuildInnerDofs
	Responsible to build the inner degrees of freedom in a space. More...

class	BuildInnerDofsHypTrunk
	Responsible to build the inner degrees of freedom in a (trunk) space. More...

class	BuildInnerDofsLinTrunk
	Responsible to build the inner degrees of freedom in a (trunk) space. More...

class	BuildL2InnerTColumns
	Responsible to build the T columns belonging to inner degrees of freedom in a L2 conforming space with shape functions in tensor product structure. More...

class	BuildL2InnerTColumnsHypTrunk
	Responsible to build the T columns belonging to inner degrees of freedom in a L2 conforming (trunk) space with shape functions in tensor product structure. More...

class	BuildL2InnerTColumnsLinTrunk
	Responsible to build the T columns belonging to inner degrees of freedom in a L2 conforming (trunk) space with shape functions in tensor product structure. More...

class	BuildTColumnsBase
	Base class for classes for building T columns for elements in a space with help of a 2D space pre builder. More...

class	BuildVertexDofs
	Responsible to build the vertex degrees of freedom in a space. More...

struct	DegreeDim
	Dimension of the degrees of freedom in a cell. More...

struct	DegreeDim< concepts::InfiniteQuad >

struct	DegreeDim< concepts::Quad >

struct	DegreeDim< concepts::Triangle >

class	DistancePost
	A function class for weighted regularization. More...

class	DivDiv
	A function class to calculate element matrices for the Div u*Div v Bilinearform. More...

class	Eddy2D_dissipation
	Local contribution to dissipation power loss. More...

class	Eddy2D_E
	Class for calculating Eddy current problem with Maxwell modell in h formulation. More...

class	Eddy2D_eField
	Electrical field. More...

class	Eddy2D_H
	Class for calculating Eddy current problem with Maxwell modell in h formulation. More...

class	Eddy2D_H_Interior
	Class holding size and magnetic field of embedded (interior) area. More...

class	EdgeGraphics
	Handles graphics for 1D hp FEM elements. More...

class	Element
	Abstract class for a 2D FEM element. More...

class	ElementFormulaEdgeJump
	Element formula for a jump value on edges of elements of an other element formula. More...

class	ElementFormulaEdgeMean
	Element formula for a mean value on edges of elements of an other element formula. More...

class	ElementFormulaInterpGrad
	Element formula for the gradient of an scalar element formula. More...

class	ElementFormulaInterpGrad< F, 2 >

class	ElementFormulaInterpGradN
	Element formula for the gradient of an scalar element formula. More...

class	ElementFormulaInterpGradN< F, 2 >

class	ElementFormulaSignNormalVector
	Element formula on 1D elements based on Edge2d returning the 1.0 if the normal vector is the right one and -1.0 otherwise. More...

class	ElementFunction
	Base class for element functions for hp elements in 2D. More...

class	ElementFunction< 1, F, Q >

class	EquilibratedMomentsAO

class	ExplicitResidual2D
	Given a elliptic equation: More...

class	Extrema
	An interface class that computes the maximum/minimum of a function represented as an ElementFormula on an space on `hp2D::Quad<Real>` only. More...

class	Fluxes
	Application of this class is to solve local Problems on one Quad. More...

class	FormulaFromWeight
	Makes it possible to plot a given `Weight`. More...

class	Grad
	The gradient of the approximated function in a FE space. More...

class	GradLinearForm
	Linear form in 2D. More...

class	GridInfo
	Class that represents grid information of a given 2d Fem space. More...

class	H1Extension
	Continuous extension of a formula on edges, e.g. More...

class	hpAdaptiveSpace
	hp-adaptive space with 2D elements. More...

class	hpAdaptiveSpaceDG
	hp-adaptive FEM space in 2D composed of separate spaces hpAdapativeSpace and may be discontinuous. More...

class	hpAdaptiveSpaceH1

class	hpAdaptiveSpaceHCurl

class	hpAdaptiveSpaceHCurl_H1
	Container class for a 2D hp edge element space with an 2D hp nodal element space. More...

class	hpAdaptiveSpaceL2

class	hpFull
	Helper class for building 2D hp-FEM spaces (space pre builder). More...

class	Identity
	A function class to calculate element matrices for the mass matrix. More...

class	ImplicitEquilibratedA0

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

class	InfiniteQuad
	A 2D FEM element: an infinite quad. More...

class	InfiniteQuadFunctions
	Auxiliary functions for infinite quadrilaterals. More...

class	InfiniteQuadGraphics
	Handles graphics for 2D hp quadrilateral infinite FEM elements. More...

class	InputEddy2D_E
	Helps for reading input parameters for single solving of Eddy2D_E. More...

class	InputEddy2D_H
	Helps for reading input parameters for single solving of Eddy2D_H. More...

class	InputMaxwell2D_E
	Helps for reading input parameters for single solving of Maxwell2D_E. More...

class	InputMaxwell2D_H
	Helps for reading input parameters for single solving of Maxwell2D_H_Base. More...

class	IntegrableQuad
	Class holding the quadrature rule and the cell of a quadrilateral element. More...

class	KarniadakisDeriv2
	Part of the multidimensional expansion bases for the shape functions of Karniadakis and Sherwin. More...

class	Laplace
	A function class to calculate element matrices for the Laplacian. More...

class	LaplaceBase
	Base class to calculate element matrices for the Laplacian, for both scalar and matrix formulas. More...

class	LaplaceMatrix
	A function class to calculate element matrices for the Laplacian for matrix formulas. More...

class	Laplacian
	The Laplacian of the approximated function in a FE space. More...

class	LinearFormHelper_0
	Helper class for linearforms l(v), where v is a 0-form. More...

class	LinearFormHelper_1
	Helper class for linearforms l(v), where v is a one form. More...

class	LinearFormHelper_2
	Helper class for linearforms l(v), where v is a two form. More...

class	LocalFluxes

class	Maxwell2D_dissipation
	Local contribution to dissipation power loss. More...

class	Maxwell2D_E
	Class for calculating Eddy current problem with Maxwell modell in e-formulation. More...

class	Maxwell2D_eField
	Electrical field. More...

class	Maxwell2D_H
	Class for calculating Eddy current problem with Maxwell modell in h formulation. More...

class	Maxwell2D_H_Base
	Base class for calculating Eddy current problem with Maxwell modell in h formulation. More...

class	Maxwell2D_H_DD
	Class for calculating Eddy current problem with Maxwell modell in h formulation, with Domain Decomposition. More...

class	Maxwell2D_hField

class	MaxwellSharedData
	Shared data for RotRot and DivDiv. More...

class	NeumannTrace
	The Neumann trace of the approximated function in a FE space. More...

class	NeumannTraceElement
	Element on an edge representing the normal derivatives of neighbouring elements, especially their mean or jump. More...

class	NeumannTraceSpace
	A the NeumannTrace space of a given 2D - Finite Element space. More...

class	NotConnectedIndex
	Exception class to express that a connected index wasn't found. More...

class	NTElement_BA
	Element on an edge representing the normal derivative of neighbouring elements, especially their mean or jump. More...

class	Partial_xx
	Double partial derivative in x direction of the approximated function in a FE space. More...

class	Partial_yy
	Double partial derivative in y direction of the approximated function in a FE space. More...

class	PlCurl
	The vectorial 2D curl of the approximated function in a FE space. More...

class	PlCurlLinearForm
	Linear form in 2D. More...

class	PolyEdgeMax
	Edge gets maximal polynomial degree of adjacent cells. More...

class	PolyEdgeMin
	Edge gets minimum of the polynomial degrees of the adjacent cells. More...

class	PolyEdgeMinNeighMaxChild
	First the maximum polynomial degree of both sides of the edge is choosen. More...

class	PolyEdgeRule
	Base class for rules for polynomial degrees of edges. More...

class	Postprocess4
	Computes `x` to the power of 0.4. More...

class	Postprocess7
	Computes `x` to the power of 0.7. More...

class	Postprocess8
	Computes `x` to the power of 0.8. More...

class	Postprocess9
	Computes `x` to the power of 0.9. More...

class	PostprocessSqrt
	Computes to square root of `x`. More...

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

class	QuadEdgeBase
	Static class to construct an element hp1D::Element out of an hp2D::Quad. More...

class	QuadEdgeFirst

class	QuadEdgeJump

class	QuadEdgeMean

class	QuadFunctions
	Auxiliary functions for quadrilaterals. More...

class	QuadGraphics
	Handles graphics for 2D hp quadrilateral FEM elements. More...

class	QuadShapeFunctions
	A class for holding the shape functions of nodal elements on quadrilaterials for a particular polynomials degree (ie. More...

class	RecomputeShapefct

class	Riesz
	Linear form in 2D. More...

class	RotRot
	A function class to calculate element matrices for the Rot u*Rot v Bilinearform. More...

class	ShapeFunction2D
	Collecting the data of a 2D shape function in one class. More...

class	ShortestDist
	A function class for weighted regularization, which returns the square of the shortest distance of a point to the singular vertices. More...

class	SingularSet
	Class for handling a set of singular vertices. More...

class	SingularVertex
	Class for storing a singular vertex with the coordinates. More...

class	Space
	A 2D hp FEM space with continuous, piecewise polynomial basis functions. More...

class	SpacePreBuilder
	Exception class to express that an inquired dof is not valid. More...

class	SumFactorization
	Sum factorization for an element matrix. More...

class	Trace
	The Dirichlet trace of the approximated function in a FE space. More...

class	TraceDeriv
	The tangential derivative of the Dirichlet trace of the approximated function in a FE space. More...

class	TraceSpace
	Builds the trace space of an FE space. More...

class	TransmissionWeight
	Weight for the 2D transmission problem. More...

class	TransmissionWeightProd
	Weight for the 2D transmission problem. More...

class	TrivialWeight
	A function class for trivial (constant equal 1.0) weight function. More...

class	Value
	The approximated function in a FE space. More...

Typedefs
typedef concepts::Adaptivity< concepts::Connector, concepts::AdaptiveAdjustP< 2 > >	Adaptivity

typedef hpAdaptiveSpaceDG< hpAdaptiveSpaceH1 >	hpAdaptiveSpaceH1_DG

Enumerations
enum	partDerivType { NO_DERIV = 0, X_DERIV = 1, Y_DERIV = 2 }
	Direction of partial derivative. More...

Functions
hpAdaptiveSpaceH1_DG *	hpAdaptiveSpaceH1_DGFromInput (concepts::Mesh2 &msh, const concepts::InOutParameters input, bool verbose=false)
	Builds and refines a piecewise hp-adaptive H^1-conforming space with use of input parameters. More...

hpAdaptiveSpaceH1 *	hpAdaptiveSpaceH1FromInput (concepts::Mesh2 &msh, const concepts::InOutParameters input, bool verbose=false)
	Builds and refines a hp-adaptive H^1-conforming space with use of input parameters. More...

hpAdaptiveSpaceHCurl *	hpAdaptiveSpaceHCurlFromInput (concepts::Mesh2 &msh, const concepts::InOutParameters input, bool verbose=false)
	Builds and refines a hp-adaptive H(curl)-conforming space with use of input parameters. More...

hpAdaptiveSpaceL2 *	hpAdaptiveSpaceL2FromInput (concepts::Mesh2 &msh, const concepts::InOutParameters input, bool verbose=false)
	Builds and refines a hp-adaptive -conforming space with use of input parameters. More...

template<class F >
ShapeFunction2D< F >	makeShapeFunction2D (const Quad< F > &quad)

template<typename DistClass , typename Function >
std::ostream &	operator<< (std::ostream &os, const DistancePost< DistClass, Function > &p)

std::ostream &	operator<< (std::ostream &os, const Postprocess4 &p)

std::ostream &	operator<< (std::ostream &os, const Postprocess7 &p)

std::ostream &	operator<< (std::ostream &os, const Postprocess8 &p)

std::ostream &	operator<< (std::ostream &os, const Postprocess9 &p)

std::ostream &	operator<< (std::ostream &os, const PostprocessSqrt &p)

std::ostream &	operator<< (std::ostream &os, const ShortestDist &p)

std::ostream &	operator<< (std::ostream &os, const TransmissionWeight &p)

std::ostream &	operator<< (std::ostream &os, const TransmissionWeightProd &p)

std::ostream &	operator<< (std::ostream &os, const TrivialWeight &p)

void	refinehpFull (hp2D::hpFull &prebuild, std::string refinement)
	Refines the space prebuilder `prebuild` where the refinement rules are given in the string `refinement`. More...

void	setQuadrature (enum concepts::intRule rule, uint noP)
	Tensor integration setter routine in hp2D for hp2D::IntegrableQuads. More...

template<class F >
void	setupAdvection (vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &bf, const concepts::ElementFormulaContainer< concepts::Point< F, 2 > > frm, bool transpose=true)
	Function to setup a bilinear form related to the vector Advection, namely. More...

template<class F >
void	setupDivDiv (vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &bf, const concepts::ElementFormulaContainer< F, typename concepts::Realtype< F >::type > frm=concepts::ElementFormulaContainer< F, typename concepts::Realtype< F >::type >())
	Function to setup a bilinear form. More...

template<class F >
void	setupGradLinearForm (vectorial::LinearForm< F, typename concepts::Realtype< F >::type > &lf, const concepts::ElementFormulaContainer< concepts::Point< F, 2 > > frm1, const concepts::ElementFormulaContainer< concepts::Point< F, 2 > > frm2)
	Function to setup a linear form related to the vectorial linear form. More...

template<class F >
void	setupIdDiv (vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &bf, const concepts::ElementFormulaContainer< F > frm=concepts::ElementFormulaContainer< F >())
	Function to setup a bilinear form related to the vector Identity, namely. More...

template<class F >
void	setupIdentity (vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &bf, const concepts::ElementFormulaContainer< concepts::Mapping< F, 2 > > frm, bool transpose=false)
	Function to setup a bilinear form related to the vector Identity, namely. More...

template<class F >
void	setupIdentity (vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &bf, const concepts::ElementFormulaContainer< F > frm=concepts::ElementFormulaContainer< F >())
	Function to setup a bilinear form related to the vector Identity, namely. More...

template<class F >
void	setupLaplace (vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &bf, const concepts::ElementFormulaContainer< F, typename concepts::Realtype< F >::type > frm=concepts::ElementFormulaContainer< F, typename concepts::Realtype< F >::type >())
	Function to setup a bilinear form related to the vector Laplace, namely. More...

template<class F >
void	setupLinStrainStrain (vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &bf, const concepts::ElementFormulaContainer< F, typename concepts::Realtype< F >::type > frm=concepts::ElementFormulaContainer< F, typename concepts::Realtype< F >::type >())

template<class F >
void	setupRiesz (vectorial::LinearForm< F, typename concepts::Realtype< F >::type > &lf, const concepts::ElementFormulaContainer< concepts::Point< F, 2 > > frm)
	Function to setup a linear form related to the vector Riesz, namely. More...

Detailed Description

2D hp-FEM for H¹-conforming elements.

The Space can be built using full tensor product polynomial spaces in the elements or trunk spaces (and much more) by changing the way the degrees of freedom are built in the BuildDofsBase class (and its specializations).

Author: Philipp Frauenfelder, 2001

Typedef Documentation

◆ Adaptivity

typedef concepts::Adaptivity<concepts::Connector, concepts::AdaptiveAdjustP<2> > hp2D::Adaptivity

Definition at line 91 of file spacePreBuilder.hh.

◆ hpAdaptiveSpaceH1_DG

typedef hpAdaptiveSpaceDG<hpAdaptiveSpaceH1> hp2D::hpAdaptiveSpaceH1_DG

Definition at line 256 of file hpAdaptiveSpaceDG.hh.

Enumeration Type Documentation

◆ partDerivType

enum hp2D::partDerivType

Direction of partial derivative.

NO_DERIV no derivative X_DERIV partial derivative in x Y_DERIV partial derivative in y

Enumerator
NO_DERIV
X_DERIV
Y_DERIV

Definition at line 59 of file bf_partialderiv.hh.

Function Documentation

◆ hpAdaptiveSpaceH1_DGFromInput()

hpAdaptiveSpaceH1_DG* hp2D::hpAdaptiveSpaceH1_DGFromInput	(	concepts::Mesh2 &	msh,
		const concepts::InOutParameters	input,
		bool	verbose = `false`
	)

Builds and refines a piecewise hp-adaptive H^1-conforming space with use of input parameters.

As input parameter is needed:

"p"             - an integer value for the polynomial degrees,
"domain_Attrib" - cell attributes of the domains, 
                  e.g. taking "1 2 3;4" there are two sub-domains with continuous basis 
                  functions in each, where the first sub-domain consists of cells with
                  attributes 1, 2 or 3, and the second of cells with attributes 4.

There may be used the input parameters:

"refinement"       - string with refinement rules, e.g. "h1|0 in 1 -> v2".
"dirichl_bdAttrib" - string with attributes of edges with homogeneous Dirichlet boundary condition, e.g. "100; 102"

"hpAdaptiveSpace_isTrunk" - boolean indicating the use of linear trunk space or not, by default,
                            the trunk space is built.

See also: refinehpFull

Author: Kersten Schmidt, 2010

◆ hpAdaptiveSpaceH1FromInput()

hpAdaptiveSpaceH1* hp2D::hpAdaptiveSpaceH1FromInput	(	concepts::Mesh2 &	msh,
		const concepts::InOutParameters	input,
		bool	verbose = `false`
	)

Builds and refines a hp-adaptive H^1-conforming space with use of input parameters.

As input parameter is needed:

"p" - an integer value for the polynomial degrees.

There may be used the input parameters:

"refinement"       - string with refinement rules, e.g. "h1|0 in 1 -> v2".
"dirichl_bdAttrib" - string with attributes of edges with homogeneous Dirichlet boundary condition, e.g. "100; 102"

"hpAdaptiveSpace_isTrunk" - boolean indicating the use of linear trunk space or not, by default, non trunk space is built.

See also: refinehpFull

Author: Kersten Schmidt, 2009

◆ hpAdaptiveSpaceHCurlFromInput()

hpAdaptiveSpaceHCurl* hp2D::hpAdaptiveSpaceHCurlFromInput	(	concepts::Mesh2 &	msh,
		const concepts::InOutParameters	input,
		bool	verbose = `false`
	)

Builds and refines a hp-adaptive H(curl)-conforming space with use of input parameters.

As input parameter is needed:

"p" - an integer value for the polynomial degrees.

There may be used the input parameters:

"refinement"       - string with refinement rules, e.g. "h1|0 in 1 -> v2".
"dirichl_bdAttrib" - string with attributes of edges with homogeneous Dirichlet boundary condition, e.g. "100; 102".

See also: refinehpFull

Author: Kersten Schmidt, 2009

◆ hpAdaptiveSpaceL2FromInput()

hpAdaptiveSpaceL2* hp2D::hpAdaptiveSpaceL2FromInput	(	concepts::Mesh2 &	msh,
		const concepts::InOutParameters	input,
		bool	verbose = `false`
	)

Builds and refines a hp-adaptive -conforming space with use of input parameters.

As input parameter is needed:

"p" - an integer value for the polynomial degrees.

There may be used the input parameters:

"refinement"       - string with refinement rules, e.g. "h1|0 in 1 -> v2".
"dirichl_bdAttrib" - string with attributes of edges with homogeneous Dirichlet boundary condition, e.g. "100; 102"

"hpAdaptiveSpace_isTrunk" - boolean indicating the use of linear trunk space or not, by default, non trunk space is built.

See also: refinehpFull

Author: Kersten Schmidt, 2016

◆ makeShapeFunction2D()

template<class F >

ShapeFunction2D<F> hp2D::makeShapeFunction2D ( const Quad< F > & quad )

◆ operator<<() [1/10]

template<typename DistClass , typename Function >

std::ostream& hp2D::operator<<	(	std::ostream &	os,
		const DistancePost< DistClass, Function > &	p
	)

inline

Definition at line 84 of file shortestDist.hh.

◆ operator<<() [2/10]

std::ostream& hp2D::operator<<	(	std::ostream &	os,
		const Postprocess4 &	p
	)

◆ operator<<() [3/10]

std::ostream& hp2D::operator<<	(	std::ostream &	os,
		const Postprocess7 &	p
	)

◆ operator<<() [4/10]

std::ostream& hp2D::operator<<	(	std::ostream &	os,
		const Postprocess8 &	p
	)

◆ operator<<() [5/10]

std::ostream& hp2D::operator<<	(	std::ostream &	os,
		const Postprocess9 &	p
	)

◆ operator<<() [6/10]

std::ostream& hp2D::operator<<	(	std::ostream &	os,
		const PostprocessSqrt &	p
	)

◆ operator<<() [7/10]

std::ostream& hp2D::operator<<	(	std::ostream &	os,
		const ShortestDist &	p
	)

◆ operator<<() [8/10]

std::ostream& hp2D::operator<<	(	std::ostream &	os,
		const TransmissionWeight &	p
	)

◆ operator<<() [9/10]

std::ostream& hp2D::operator<<	(	std::ostream &	os,
		const TransmissionWeightProd &	p
	)

◆ operator<<() [10/10]

std::ostream& hp2D::operator<<	(	std::ostream &	os,
		const TrivialWeight &	p
	)

◆ refinehpFull()

void hp2D::refinehpFull	(	hp2D::hpFull &	prebuild,
		std::string	refinement
	)

Refines the space prebuilder prebuild where the refinement rules are given in the string refinement.

The string can consist of several refinement rules of the following form separated by commas, e.g. "p5, h3", which are applied one after the other.

There are the following refinement strategies.

"p"    - uniform polynomal degree enhancement (p-refinement)
"h"    - uniform refinement of the cells (h-refinement) or 
         h-refinement towards edges or vertices
"hp"   - geometrical hp-refinement towards edges or vertices

Each refinement strategy can be complemented with numbers.

"p5"   - polynomial degrees are enhanced by 5
"p2|1" - polynomial degree is first local direction of the quadrilateral
         is enhanced by 2, in the other direction by 1
"h2"   - twice uniform refinement of the cells
"h2|1" - twice uniform refinement of the cells in first local direction
         and a single refinement in the other direction
"hp2"  - twice geometrical hp-refinement towards edges or vertices

If a number is missing it means a single refinement or polynomial degree enhancement by 1.

Note, that the local directions of the quadrilateral are given by the order of the vertices. The first direction is from the 1st vertex to the 2nd or from the 4th to the 3th.

Each refinement rule can be restricted to a number of cells with a common attribute, e.g. "h in 1" means a uniform refinement in all cells with attribute 1.

For the h- and the hp-refinement rules vertices or edges can be given to which should be refined.

"h  -> v1"  - h-refinement  toward vertices with attribute 1
"h  -> e22" - h-refinement  toward edges with attribute 22
"hp -> v1"  - hp-refinement toward vertices with attribute 1
"hp -> e22" - hp-refinement toward edges with attribute 22

The cells touching these specified vertices and edges are refinement, and for hp-refinement the polynomial degrees in the other cells are increased by 1.

A combination of restriction towards cells and of refinement towards vertices or edges is possible, e.g. "h1|0 in 1 -> v2".

Author: Kersten Schmidt, 2009

◆ setQuadrature()

void hp2D::setQuadrature	(	enum concepts::intRule	rule,
		uint	noP
	)

Tensor integration setter routine in hp2D for hp2D::IntegrableQuads.

Parameters

rule	Quadrature rule type, e.g. concepts::TRAPEZE, concepts::GAUSS_JACOBI
noP	constant number of quadrature points of given type

◆ setupAdvection()

template<class F >

void hp2D::setupAdvection	(	vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &	bf,
		const concepts::ElementFormulaContainer< concepts::Point< F, 2 > >	frm,
		bool	transpose = `true`
	)

Function to setup a bilinear form related to the vector Advection, namely.

$\sum_{i,j=1}^2 \int_K w_j u_i\frac{\partial v_i}{\partial x_j}\mathrm{d}x = \sum_{i=1}^2 \int_K \underline{w}\cdot\nabla v_i u_i \mathrm{d}x = \int_K \underline{w}^\top(\nabla\underline{v})^\top\underline{u}\mathrm{d}x$

if transpose is set to true or

$\sum_{i,j=1}^2 \int_K w_i u_j\frac{\partial v_i}{\partial x_j}\mathrm{d}x = \sum_{i=1}^2 \int_K w_i\underline{u}\cdot\nabla v_i \mathrm{d}x = \int_K \underline{w}^\top(\nabla\underline{v})\underline{u}\mathrm{d}x$

if transpose is set to false, both on vectorial spaces, where $\underline{u}$ and $\underline{v}$ are trial and test functions respectively, $\underline{w}$ is a given vectorial formula, and

$\nabla \underline{v} = \left(\begin{array}{cc} \frac{\partial u_1}{\partial x_1} & \frac{\partial u_1}{\partial x_2} \\ \frac{\partial u_2}{\partial x_1} & \frac{\partial u_2}{\partial x_2} . \end{array}\right)$

◆ setupDivDiv()

template<class F >

void hp2D::setupDivDiv	(	vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &	bf,
		const concepts::ElementFormulaContainer< F, typename concepts::Realtype< F >::type >	frm = `concepts::ElementFormulaContainer< F, typename concepts::Realtype< F >::type >()`
	)

Function to setup a bilinear form.

$\int_K f(x)\mathrm{div}\underline{u} \mathrm{div}\underline{v}\mathrm{d}x$

on vectorial spaces.

Examples: elasticity2D_tutorial.cc.

◆ setupGradLinearForm()

template<class F >

void hp2D::setupGradLinearForm	(	vectorial::LinearForm< F, typename concepts::Realtype< F >::type > &	lf,
		const concepts::ElementFormulaContainer< concepts::Point< F, 2 > >	frm1,
		const concepts::ElementFormulaContainer< concepts::Point< F, 2 > >	frm2
	)

Function to setup a linear form related to the vectorial linear form.

$\int_K \underline{f}_1\cdot \mbox{\bf grad}{v_1} + \underline{f}_2\cdot \mbox{\bf grad}{v_2}\mathrm{d}x$

on vectorial spaces, where and are the first and second component of the test function $\underline{v}$ , respectively.

◆ setupIdDiv()

template<class F >

void hp2D::setupIdDiv	(	vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &	bf,
		const concepts::ElementFormulaContainer< F >	frm = `concepts::ElementFormulaContainer< F >()`
	)

Function to setup a bilinear form related to the vector Identity, namely.

$\int_K f(x) u \mathrm{div}\underline{v}\mathrm{d}x$

where the test space is a vectorial one.

◆ setupIdentity() [1/2]

template<class F >

void hp2D::setupIdentity	(	vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &	bf,
		const concepts::ElementFormulaContainer< concepts::Mapping< F, 2 > >	frm,
		bool	transpose = `false`
	)

Function to setup a bilinear form related to the vector Identity, namely.

$\int_K f(x) \underline{u}^\top A\underline{v}\mathrm{d}x$

on vectorial spaces. If transpose is true the transpose of the given matrix is taken.

◆ setupIdentity() [2/2]

template<class F >

void hp2D::setupIdentity	(	vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &	bf,
		const concepts::ElementFormulaContainer< F >	frm = `concepts::ElementFormulaContainer< F >()`
	)

Function to setup a bilinear form related to the vector Identity, namely.

$\int_K f(x) \underline{u}\cdot\underline{v}\mathrm{d}x$

on vectorial spaces.

◆ setupLaplace()

template<class F >

void hp2D::setupLaplace	(	vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &	bf,
		const concepts::ElementFormulaContainer< F, typename concepts::Realtype< F >::type >	frm = `concepts::ElementFormulaContainer< F, typename concepts::Realtype< F >::type >()`
	)

Function to setup a bilinear form related to the vector Laplace, namely.

$\int_K f(x)\mathrm{grad}\underline{u}:\mathrm{grad}\underline{v}\mathrm{d}x$

on vectorial spaces.

◆ setupLinStrainStrain()

template<class F >

void hp2D::setupLinStrainStrain	(	vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &	bf,
		const concepts::ElementFormulaContainer< F, typename concepts::Realtype< F >::type >	frm = `concepts::ElementFormulaContainer< F, typename concepts::Realtype< F >::type >()`
	)

Examples: elasticity2D_tutorial.cc.

◆ setupRiesz()

template<class F >

void hp2D::setupRiesz	(	vectorial::LinearForm< F, typename concepts::Realtype< F >::type > &	lf,
		const concepts::ElementFormulaContainer< concepts::Point< F, 2 > >	frm
	)

Function to setup a linear form related to the vector Riesz, namely.

$\int_K \underline{f}\cdot\underline{v}\mathrm{d}x$

on vectorial spaces.

hp2D Namespace Reference

Namespaces

Classes

Typedefs

Enumerations

Functions

Detailed Description

Typedef Documentation

◆ Adaptivity

◆ hpAdaptiveSpaceH1_DG

Enumeration Type Documentation

◆ partDerivType

Function Documentation

◆ hpAdaptiveSpaceH1_DGFromInput()

◆ hpAdaptiveSpaceH1FromInput()

◆ hpAdaptiveSpaceHCurlFromInput()

◆ hpAdaptiveSpaceL2FromInput()

◆ makeShapeFunction2D()

◆ operator<<() [1/10]

◆ operator<<() [2/10]

◆ operator<<() [3/10]

◆ operator<<() [4/10]

◆ operator<<() [5/10]

◆ operator<<() [6/10]

◆ operator<<() [7/10]

◆ operator<<() [8/10]

◆ operator<<() [9/10]

◆ operator<<() [10/10]

◆ refinehpFull()

◆ setQuadrature()

◆ setupAdvection()

◆ setupDivDiv()

◆ setupGradLinearForm()

◆ setupIdDiv()

◆ setupIdentity() [1/2]

◆ setupIdentity() [2/2]

◆ setupLaplace()

◆ setupLinStrainStrain()

◆ setupRiesz()