hp2D::Space Class Reference

#include <space.hh>

Inheritance diagram for hp2D::Space:

Public Types
typedef concepts::Scan< hp2D::Element< Real > >	Scan
typedef ElementWithCell< Real >	type
typedef Scan< ElementWithCell< Real > >	Scanner

Public Member Functions
	Space (concepts::Mesh2 &msh, uint l, uint p, concepts::BoundaryConditions *bc=0)
	Space (const Space &spc)
virtual uint	dim () const
	Returns the dimension of the space.
virtual uint	nelm () const
	Returns the number of elements in the space.
virtual Scan *	scan () const
	Returns a scanner to iterate over the elements of the space.
Scan *	constScan () const
uint	dim ()
uint	nelm ()
Scan *	scan ()
virtual void	adjust (const concepts::Element< Real > &elm, const concepts::AdaptiveAdjustP< 2 > &a)
Space	rebuild ()
virtual uint	getOutputDimension () const
	Returns the default output dimension, when we consider plotting a real-valued operator on this space.
virtual void	adjust (const Element< Real > &elm, const concepts::AdaptiveAdjustP< 2 > &a)=0

Friends
class	BuildDofsBase

Strategies to Build the Degrees of Freedom
void	buildVertexDofs (const BuildDofsBase &b)
void	buildEdgeDofs (const BuildDofsBase &b)
void	buildInnerDofs (const BuildDofsBase &b)
uint	connectedIdx (const concepts::Attribute &a) const
	Gives the number of connected dofs for one attribute.
void	recomputeShapefunctions ()
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.

Detailed Description

A 2D hp FEM space with continuous, piecewise polynomial basis functions. Currently, only hexahedrons and conforming meshes are possible.

Adaptivity

You can adaptively refine this space by using adjust() on some elements to refine them or increase their polynomial degree. Please note that these extensions can be locally varying (ie. non-uniform) and anisotropic.

Trunk Space

Classically, the whole tensor product polynomial space is used on each element to build the degress of freedom. However, a considerable amount of degrees of freedom can be saved, when only a trunk of this space is used. In fact, only very little is lost in accuracy while the gain in terms of degrees of freedom is noteworthy. The methods buildVertexDofs(), buildEdgeDofs() and buildInnerDofs() can be used to change the way the degrees of freedom on each part of each element are built.

Author

Philipp Frauenfelder, 2001

Test:

test::SpaceTest2D

Examples

BGT_0.cc, hpFEM2d-simple.cc, and hpFEM2d.cc.

Definition at line 85 of file space.hh.

Member Typedef Documentation

Scan

typedef concepts::Scan<hp2D::Element<Real> > hp2D::Space::Scan

Definition at line 92 of file space.hh.

Scanner

typedef Scan<ElementWithCell<Real > > concepts::SpaceOnCells< Real >::Scanner

inherited

Definition at line 84 of file space.hh.

type

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

inherited

Definition at line 83 of file space.hh.

Constructor & Destructor Documentation

Space() [1/2]

hp2D::Space::Space	(	concepts::Mesh2 &	msh,
		uint	l,
		uint	p,
		concepts::BoundaryConditions *	bc = 0
	)

Constructor. Scans the mesh and sets the cells in the mesh active and the level of refinement and the polynomial degree in all cells to the given values. rebuild_ is set to true, ie. if the mesh is used it will firstly be rebuilt.

Parameters

msh	The domain of interest partitioned into a mesh.
l	Level of refinement
p	Degree of the polynomials to be used.
bc	Boundary conditions

Space() [2/2]

hp2D::Space::Space

(

const Space &

spc

)

Copy constructor. Copies mesh, boundary conditions and ctrl2_ (information about refinements and polynomial degrees of the elements).

Member Function Documentation

adjust()

virtual void concepts::AdaptiveSpace< Real , concepts::AdaptiveAdjustP< 2 > >::adjust ( const Element< Real > &  elm, const concepts::AdaptiveAdjustP< 2 > &  a  )

pure virtualinherited

Adjusts the space in the next rebuild step for this element.

buildEdgeDofs()

void hp2D::Space::buildEdgeDofs

(

const BuildDofsBase &

b

)

Change the strategy how the degrees of freedom for the edge are built. The default strategy is BuildEdgeDofs. You can change this strategy any time you chose.

buildEdgeDofs_ is reset with a clone of b.

Parameters

b	New strategy

buildInnerDofs()

void hp2D::Space::buildInnerDofs

(

const BuildDofsBase &

b

)

Change the strategy how the degrees of freedom for the interior are built. The default strategy is BuildInnerDofsLinTrunk. You can change this strategy any time you chose.

buildInnerDofs_ is reset with a clone of b.

Parameters

b	New strategy

buildVertexDofs()

void hp2D::Space::buildVertexDofs

(

const BuildDofsBase &

b

)

Change the strategy how the degrees of freedom for the vertices are built. The default strategy is BuildVertexDofs. You can change this strategy any time you chose.

buildVertexDofs_ is reset with a clone of b.

Parameters

b	New strategy

constScan()

Space::Scan * hp2D::Space::constScan ( ) const

inline

Returns constant scanner over elements of last build, In contrast to scan(), this method also workes, if the space would need a rebuild, * i.e. rebuild is true.

Definition at line 408 of file space.hh.

dim() [1/2]

uint hp2D::Space::dim ( )

inline

Definition at line 412 of file space.hh.

dim() [2/2]

uint hp2D::Space::dim ( ) const

inlinevirtual

Returns the dimension of the space.

Implements concepts::SpaceOnCells< Real >.

Examples

BGT_0.cc, and hpFEM2d.cc.

Definition at line 393 of file space.hh.

getOutputDimension()

template<class F >

virtual uint concepts::Space< F >::getOutputDimension ( ) const

inlinevirtualinherited

Returns the default output dimension, when we consider plotting a real-valued operator on this space.

Reimplemented in hp2D::hpAdaptiveSpaceHCurl, and hp2Dedge::Space.

Definition at line 50 of file space.hh.

info()

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

protectedvirtual

Returns information in an output stream.

Reimplemented from concepts::SpaceOnCells< Real >.

nelm() [1/2]

uint hp2D::Space::nelm ( )

inline

Definition at line 417 of file space.hh.

nelm() [2/2]

uint hp2D::Space::nelm ( ) const

inlinevirtual

Returns the number of elements in the space.

Implements concepts::SpaceOnCells< Real >.

Definition at line 398 of file space.hh.

rebuild()

Space hp2D::Space::rebuild

(

)

Rebuilds the space. First the old list of Finite Elements in the space is removed (not the elements in the topology!). Then the control information for the vertices, edges and faces is cleared (the information on the 2D elements is retained). For every cell in the original mesh, rebuild0_ and rebuild1_ are called. From the mesh, they build the space and store the elements in elm_. An essential part of the generated information are the T matrices. They describe how the local shape functions are glued together to form the global shape functions.

rebuild0_ marks the elements with the right values and rebuild1_ really does the work.

See also

TMatrix for more information on T matrices and how they are stored.

Returns

Copy of the space on the old level

Examples

BGT_0.cc, hpFEM2d-simple.cc, and hpFEM2d.cc.

recomputeShapefunctions()

void hp2D::Space::recomputeShapefunctions

(

)

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

Examples

BGT_0.cc.

scan() [1/2]

Space::Scan * hp2D::Space::scan ( )

inline

Definition at line 422 of file space.hh.

scan() [2/2]

Space::Scan * hp2D::Space::scan ( ) const

inlinevirtual

Returns a scanner to iterate over the elements of the space.

Implements concepts::SpaceOnCells< Real >.

Definition at line 403 of file space.hh.

Friends And Related Symbol Documentation

BuildDofsBase

friend class BuildDofsBase

friend

Definition at line 90 of file space.hh.

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

• hp2D/space.hh