3D hp-FEM for H¹-conforming elements. More...

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

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

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

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

class	BilinearFormTwoPartDeriv
	A class to calculate the element matrices for partial derivatives. 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	BuildFaceDofs
	Responsible to build the face degrees of freedom in a space. More...

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

class	BuildFaceDofsLinTrunk
	Responsible to build the face degrees of freedom in a (trunk) space. 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	BuildVertexDofs
	Responsible to build the vertex degrees of freedom in a space. More...

class	DaugeWeight
	Weight implemented by Monique Dauge in Melina. More...

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	Element
	Abstract class for a 3D FEM element. More...

class	ElementFormulaVectorOnTrace
	Class for evaluation of solutions on the `TraceSpace` with an `ElementFunction` that is only given on the whole space. More...

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

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

class	Hexahedron
	A 3D FEM element: a hexahedron. More...

class	HexahedronFaceBase
	Class to construct an quadrilateral element out of an hexahedron. More...

class	HexahedronFaceFirst

class	HexahedronGraphics
	Handles graphics for hexahedral 3D hp FEM elements. More...

class	HexFunctions
	Auxiliary functions for hexahedra. More...

class	Hook
	A function class to calculate element matrices for the Bilinearform of linear Elasticity. More...

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

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

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

class	LinearElasticity
	A class to calculate the element matrices for problems of linear elasticity in 3D. More...

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

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

class	NeumannTraceElement3d
	Element on an edge representing the normal derivatives of neighbouring elements, especially their mean or jump. More...

class	NeumannTraceSpace3d
	A the NeumannTrace space of a given 3D - Finite Element space. More...

class	Postprocess14
	Computes `x` to the power of 1/4. More...

class	Postprocess3
	Computes `x` to the power of 3. More...

class	Postprocess34
	Computes `x` to the power of 3/4. More...

class	Postprocess4
	Computes `x` to the power of 4. More...

class	PostprocessRoot
	Returns the square root of `x`. More...

class	PostprocessRoot4
	Returns the forth root of `x`. More...

class	PostprocessSquare
	Squares the given `x`. More...

class	ProductOfAll
	Computes the product of all distances in the singular set `singularities`. More...

class	RefineOrRaise
	Refines element or raises its polynomial degree. More...

class	Riesz
	Linear form in 3D. More...

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

class	ShapeFunction3D
	Collecting the data of a 3D 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 edges and vertices. More...

class	ShortestDistLimited
	A function class for weighted regularization, which returns the minimum of a value and the square of the shortest distance of a point to the singular edges and vertices. More...

class	SingularEdge
	Class for storing a singular edge with coordinates of its corners. More...

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

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

class	Space
	A 3D hp FEM space with continuous, picewise polynomial basis functions. More...

class	SpaceTransition
	Maps a solution vector from one space to another. More...

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

class	TraceSpace
	Builds the trace space of a FE space consisting of hexahedral elements. More...

class	TransitionPair
	Element pair for the `SpaceTransition`. 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...

class	ZeroTangentialValue
	Sets the outer product of the coefficients and the normal vector to zero in every node on an edge with chosen attribute. More...

Enumerations
enum	partDerivType { NO_DERIV = 0, X_DERIV = 1, Y_DERIV = 2, Z_DERIV = 3 }

Functions
template<class F >
ShapeFunction3D< F >	makeShapeFunction3D (const Hexahedron &elm)

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

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

std::ostream &	operator<< (std::ostream &os, const Postprocess14 &p)

std::ostream &	operator<< (std::ostream &os, const Postprocess3 &p)

std::ostream &	operator<< (std::ostream &os, const Postprocess34 &p)

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

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

std::ostream &	operator<< (std::ostream &os, const PostprocessRoot4 &p)

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

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

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

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

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

template<class F >
void	setupAdvection (vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &bf, const concepts::ElementFormulaContainer< concepts::Point< F, 3 > > frm)
	Function to setup a bilinear form related to the vector Advection, namely. More...

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

Detailed Description

3D 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

Todo:: Three dimensional hp-DGFEM in hexahedra for locally refined meshes.

Enumeration Type Documentation

◆ partDerivType

enum hp3D::partDerivType

Enumerator
NO_DERIV
X_DERIV
Y_DERIV
Z_DERIV

Definition at line 31 of file bf3D_partialDeriv.hh.

Function Documentation

◆ makeShapeFunction3D()

template<class F >

ShapeFunction3D<F> hp3D::makeShapeFunction3D ( const Hexahedron & elm )

◆ operator<<() [1/13]

std::ostream& hp3D::operator<<	(	std::ostream &	os,
		const DaugeWeight &	p
	)

◆ operator<<() [2/13]

template<typename DistClass , typename Function >

std::ostream& hp3D::operator<<	(	std::ostream &	os,
		const DistancePost< DistClass, Function > &	p
	)

inline

Definition at line 175 of file shortestDist.hh.

◆ operator<<() [3/13]

std::ostream& hp3D::operator<<	(	std::ostream &	os,
		const Postprocess14 &	p
	)

◆ operator<<() [4/13]

std::ostream& hp3D::operator<<	(	std::ostream &	os,
		const Postprocess3 &	p
	)

◆ operator<<() [5/13]

std::ostream& hp3D::operator<<	(	std::ostream &	os,
		const Postprocess34 &	p
	)

◆ operator<<() [6/13]

std::ostream& hp3D::operator<<	(	std::ostream &	os,
		const Postprocess4 &	p
	)

◆ operator<<() [7/13]

std::ostream& hp3D::operator<<	(	std::ostream &	os,
		const PostprocessRoot &	p
	)

◆ operator<<() [8/13]

std::ostream& hp3D::operator<<	(	std::ostream &	os,
		const PostprocessRoot4 &	p
	)

◆ operator<<() [9/13]

std::ostream& hp3D::operator<<	(	std::ostream &	os,
		const PostprocessSquare &	p
	)

◆ operator<<() [10/13]

std::ostream& hp3D::operator<<	(	std::ostream &	os,
		const ProductOfAll &	p
	)

◆ operator<<() [11/13]

std::ostream& hp3D::operator<<	(	std::ostream &	os,
		const ShortestDist &	p
	)

◆ operator<<() [12/13]

std::ostream& hp3D::operator<<	(	std::ostream &	os,
		const ShortestDistLimited &	p
	)

◆ operator<<() [13/13]

std::ostream& hp3D::operator<<	(	std::ostream &	os,
		const TrivialWeight &	p
	)

◆ setupAdvection()

template<class F >

void hp3D::setupAdvection	(	vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &	bf,
		const concepts::ElementFormulaContainer< concepts::Point< F, 3 > >	frm
	)

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

$\sum_{i,j=1}^3 \int_K w_j u_i\frac{\partial v_i}{\partial_{x_j}}\mathrm{d}x = \sum_{i=1}^3 \int_K \underline{w}\cdot\nabla v_i u_i \mathrm{d}x = \int_K \underline{w}^\top\nabla\underline{v}\underline{u}\mathrm{d}x$

on vectorial spaces, where $\underline{u}$ and $\underline{v}$ are trial and test functions respectively, $\underline{w}$ is a given vectorial formula, and

$\nabla \underline{v} = \left(\begin{array}{ccc} \frac{\partial u_1}{\partial x_1} & \frac{\partial u_1}{\partial x_2} & \frac{\partial u_1}{\partial x_3} \\ \frac{\partial u_2}{\partial x_1} & \frac{\partial u_2}{\partial x_2} & \frac{\partial u_2}{\partial x_3} \\ \frac{\partial u_3}{\partial x_1} & \frac{\partial u_3}{\partial x_2} & \frac{\partial u_3}{\partial x_3}. \end{array}\right)$

◆ setupIdentity() [1/2]

template<class F >

void hp3D::setupIdentity ( vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > & bf )

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

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

on vectorial spaces.

◆ setupIdentity() [2/2]

template<class F >

void hp3D::setupIdentity	(	vectorial::BilinearForm< F, typename concepts::Realtype< F >::type > &	bf,
		const concepts::ElementFormulaContainer< concepts::Mapping< F, 3 > >	frm,
		bool	transposed = `false`
	)

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

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

wih a matrix function A on vectorial spaces.

If transposed is true then the transposed of A is taken instead.

hp3D Namespace Reference

Classes

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

◆ partDerivType

Function Documentation

◆ makeShapeFunction3D()

◆ operator<<() [1/13]

◆ operator<<() [2/13]

◆ operator<<() [3/13]

◆ operator<<() [4/13]

◆ operator<<() [5/13]

◆ operator<<() [6/13]

◆ operator<<() [7/13]

◆ operator<<() [8/13]

◆ operator<<() [9/13]

◆ operator<<() [10/13]

◆ operator<<() [11/13]

◆ operator<<() [12/13]

◆ operator<<() [13/13]

◆ setupAdvection()

◆ setupIdentity() [1/2]

◆ setupIdentity() [2/2]