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

#include <space.hh>

Inheritance diagram for hp2D::Space:

Public Types
typedef concepts::Scan< hp2D::Element< Real > >	Scan

typedef Scan< ElementWithCell< Real > >	Scanner

typedef ElementWithCell< Real >	type

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

virtual void	adjust (const Element< Real > &elm, const concepts::AdaptiveAdjustP< 2 > &a)=0
	Adjusts the space in the next rebuild step for this element. More...

Scan *	constScan () const
	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. More...

uint	dim ()
	Returns the dimension of the space. More...

virtual uint	dim () const

virtual uint	getOutputDimension () const
	Returns the default output dimension, when we consider plotting a real-valued operator on this space. More...

uint	nelm ()
	Returns the number of elements in the space. More...

virtual uint	nelm () const

Space	rebuild ()
	Rebuilds the space. More...

Scan *	scan ()
	Returns a scanner to iterate over the elements of the space. More...

virtual Scan *	scan () const

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

	Space (const Space &spc)
	Copy constructor. More...

virtual	~Space ()

Friends
class	BuildDofsBase

Strategies to Build the Degrees of Freedom
concepts::Mesh2 &	msh_
	Mesh. More...

concepts::BoundaryConditions *	bc_
	Boundary conditions. More...

bool	rebuild_
	If true: the elements have to be rebuilt. More...

uint	dim_
	Dimension of the FE space. More...

uint	nelm_
	Number of elements currently active in the mesh. More...

concepts::Joiner< Element< Real > , 1 >	elm_
	Linked list of the elements. More...

std::unordered_map< uint, concepts::AdaptiveControl<> >	ctrl0_
	Hash table of the control information for the vertices. More...

std::unique_ptr< std::unordered_map< uint, concepts::AdaptiveControlP< 1 > > >	ctrl1_
	Hash table of the control information for the edges. More...

std::unordered_map< uint, concepts::AdaptiveControlP< 2 > >	ctrl2_
	Hash table of the control information for the 2D elements. More...

std::unordered_map< uint, concepts::AdaptiveControl<> >	ctrlc0_
	Hash table for connected vertex dofs (mapping from attribute) More...

std::unordered_map< uint, const concepts::Attribute * >	vtxConnect_
	Hash table for connected vertex dofs (mapping from cell key) More...

std::map< uint, concepts::CellData >	cellList_
	List of cells. More...

std::map< uint, concepts::EdgeData >	edgeList_
	List of edges. More...

std::map< uint, concepts::VertexData >	vertexList_
	List of vertices. More...

std::unordered_map< uint, concepts::AdaptiveAdjustP< 2 > >	adj_
	Hash table of the adjustment information of the elements. More...

std::unique_ptr< concepts::SMatrix1D >	S1left_
	S matrices in 1D. More...

std::unique_ptr< concepts::SMatrix1D >	S1right_
	Mesh. More...

std::unique_ptr< concepts::SMatrixBase< Real > >	Smatrices2H_ [2]
	S matrices for horizontal subdivision. More...

std::unique_ptr< concepts::SMatrixBase< Real > >	Smatrices2V_ [2]
	S matrices for vertical subdivision. More...

std::unique_ptr< concepts::SMatrixBase< Real > >	Smatrices4_ [4]
	S matrices for subdivision into 4 quads. More...

std::unique_ptr< BuildDofsBase >	buildVertexDofs_
	Strategy to build the vertex degrees of freedom. More...

std::unique_ptr< BuildDofsBase >	buildEdgeDofs_
	Strategy to build the edge degrees of freedom. More...

std::unique_ptr< BuildDofsBase >	buildInnerDofs_
	Strategy to build the inner degrees of freedom. More...

void	buildVertexDofs (const BuildDofsBase &b)
	Change the strategy how the degrees of freedom for the vertices are built. More...

void	buildEdgeDofs (const BuildDofsBase &b)
	Change the strategy how the degrees of freedom for the edge are built. More...

void	buildInnerDofs (const BuildDofsBase &b)
	Change the strategy how the degrees of freedom for the interior are built. More...

uint	connectedIdx (const concepts::Attribute &a) const
	Gives the number of connected dofs for one attribute. More...

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

virtual std::ostream &	info (std::ostream &os) const
	Mesh. More...

void	meshAndPoly_ (concepts::Quad2d &cell, concepts::Level< 2 > &L, int *P)
	Adjusts the mesh and the polynomial degree. More...

void	enforceBC_ (const concepts::Connector2 &cell)
	Enforce Dirichlet boundary conditions. More...

void	createCellList_ (const concepts::Connector &cntr, const concepts::CellData *father)
	Initially fills `cellList_` (recusively) More...

void	createVtxEdgList_ (const concepts::Connector2 &cell)
	Initially fills `edgeListVtx_` and `vertexList_`. More...

void	enrichElm_ (const concepts::Quad2d &cell, int *p)
	Enriches the polynomial degrees. More...

void	minimumRule_ (const concepts::Connector2 &cntr, const concepts::Connector1 &edge)
	Used to enforce the minimum rule. More...

void	buildElements_ (concepts::Quad2d &cell, ushort Pmax, concepts::TColumn< Real > T0=0)
	Creates the elements and their T matrices. More...

void	buildEmptyElements_ (concepts::Quad2d &cell)
	Mesh. More...

void	computePmax_ (const concepts::Connector2 &cntr, ushort Pmax[2]) const
	Computes the maximal polynomial degree of `cell` in each direction. More...

void	recomputeSmatrices_ (const Quad< Real > &elm)
	Checks if the S matrices need to be recomputed and does so if necessary. More...

void	deactivate_ (const concepts::Edge &edg)
	Mesh. More...

void	deactivate_ (const concepts::Vertex &vtx)
	Mesh. More...

bool	activeCell_ (concepts::Cell &cell)
	Checks if a cell is in active region. More...

void	status_ ()
	Gives the cells and edges with given polynomial degree (for debugging) More...

void	matlabstatus_ ()
	Mesh. More...

	Space (const Space &spc, uint i)
	Copy constructor used to return a snapshot of the old space from rebuild() More...

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() [1/3]

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() [2/3]

hp2D::Space::Space ( const Space & spc )

Copy constructor.

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

◆ ~Space()

virtual hp2D::Space::~Space ( )

virtual

◆ Space() [3/3]

hp2D::Space::Space	(	const Space &	spc,
		uint	i
	)

private

Copy constructor used to return a snapshot of the old space from rebuild()

Parameters

spc	To be copied
i	Dummy argument to select this copy constructor

Member Function Documentation

◆ activeCell_()

bool hp2D::Space::activeCell_ ( concepts::Cell & cell )

private

Checks if a cell is in active region.

A whole region can be deactivated by setting the attribute of the cells in the region to be of Dirichlet boundary condition. In this region empty elements. Thats necessary for vectorial spaces, which live on the same mesh, so that the spaces in all dimension have the same number of elements.

The edges of the nonactive regions could be active, that means that the shape functions lie only on one side of the edge. The edges of the region can be deactivated by usual setting of Dirichlet boundary condition.

◆ adjust() [1/2]

virtual void hp2D::Space::adjust	(	const concepts::Element< Real > &	elm,
		const concepts::AdaptiveAdjustP< 2 > &	a
	)

virtual

◆ adjust() [2/2]

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

◆ buildElements_()

void hp2D::Space::buildElements_	(	concepts::Quad2d &	cell,
		ushort *	Pmax,
		concepts::TColumn< Real > *	T0 = `0`
	)

private

Creates the elements and their T matrices.

This routine is called recursively until the finest level is reached. If there have degrees of freedom to be assigned on higher level, the according T columns are adapted using the S matrices. On the finest level, the elements are created and the T matrix is created from the T columns.

Parameters

cell	The current cell
Pmax	Request for maximal polynomial degree, array with 2 entries
T0	Precomputed T columns which belong to a parent of the cell

Precondition: Pmax is an array of 2 integers

◆ buildEmptyElements_()

void hp2D::Space::buildEmptyElements_ ( concepts::Quad2d & cell )

private

Mesh.

◆ 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

◆ computePmax_()

void hp2D::Space::computePmax_	(	const concepts::Connector2 &	cntr,
		ushort	Pmax[2]
	)		const

private

Computes the maximal polynomial degree of cell in each direction.

Takes into account higher polynomial degrees on faces and edges compared to the interior.

◆ connectedIdx()

uint hp2D::Space::connectedIdx ( const concepts::Attribute & a ) const

Gives the number of connected dofs for one attribute.

◆ 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.

◆ createCellList_()

void hp2D::Space::createCellList_	(	const concepts::Connector &	cntr,
		const concepts::CellData *	father
	)

private

Initially fills cellList_ (recusively)

◆ createVtxEdgList_()

void hp2D::Space::createVtxEdgList_ ( const concepts::Connector2 & cell )

private

Initially fills edgeListVtx_ and vertexList_.

◆ deactivate_() [1/2]

void hp2D::Space::deactivate_ ( const concepts::Edge & edg )

private

Mesh.

◆ deactivate_() [2/2]

void hp2D::Space::deactivate_ ( const concepts::Vertex & vtx )

private

Mesh.

◆ dim() [1/2]

uint hp2D::Space::dim ( )

inlinevirtual

Returns the dimension of the space.

Implements concepts::SpaceOnCells< Real >.

Definition at line 412 of file space.hh.

◆ dim() [2/2]

uint hp2D::Space::dim ( ) const

inlinevirtual

Examples: BGT_0.cc, and hpFEM2d.cc.

Definition at line 393 of file space.hh.

◆ enforceBC_()

void hp2D::Space::enforceBC_ ( const concepts::Connector2 & cell )

private

Enforce Dirichlet boundary conditions.

This routine is called by meshAndPoly_ on every cell.

Parameters

cell Cell

◆ enrichElm_()

void hp2D::Space::enrichElm_	(	const concepts::Quad2d &	cell,
		int *	p
	)

private

Enriches the polynomial degrees.

This enrichement is necessary for the edges to be able to create conforming global basis functions.

In refined cells, some of the small edges might have a polynomial degree which is too low to represent a part of a basis function which is defined on a larger element.

To achieve this, the cells are traversed top down until the level of the elements is reached. During the traversal, the needed polynomial degree for the small elements is computed and enforced on the element level (only on the edges).

Precondition: p is an array of 6 integers

◆ getOutputDimension()

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

inlinevirtualinherited

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

Definition at line 50 of file space.hh.

◆ info()

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

protectedvirtual

Mesh.

Reimplemented from concepts::SpaceOnCells< Real >.

◆ matlabstatus_()

void hp2D::Space::matlabstatus_ ( )

private

Mesh.

◆ meshAndPoly_()

void hp2D::Space::meshAndPoly_	(	concepts::Quad2d &	cell,
		concepts::Level< 2 > &	L,
		int *	P
	)

private

Adjusts the mesh and the polynomial degree.

On the old mesh, the adjustment information is taken. This leads to mesh refinements or coarsening and a certain polynomial degree distribution.

The polynomial degree is fixed on the finest level (where the elements are eventually built) and given to the coarser levels (for edges and the interior of the cell). This is done bottom up.

Finally, the boundary conditions are enforced on every cell using enforceBC_

Parameters

cell	Cell
L	The desired level
P	The desired polynomial degree

Precondition: P is an array of 3 integers

See also: enforceBC_

◆ minimumRule_()

void hp2D::Space::minimumRule_	(	const concepts::Connector2 &	cntr,
		const concepts::Connector1 &	edge
	)

private

Used to enforce the minimum rule.

The minimum rule states that the polynomial degree on a edge has to be the minimum of the adjacent elements.

This routine recursively calls itself and asserts that all the elements adjacent to edge enforce their polynomial degree on edge. This is done if the cell is member of the space. Otherwise, minimumRule_ is called with the children of cell.

◆ nelm() [1/2]

uint hp2D::Space::nelm ( )

inlinevirtual

Returns the number of elements in the space.

Implements concepts::SpaceOnCells< Real >.

Definition at line 417 of file space.hh.

◆ nelm() [2/2]

uint hp2D::Space::nelm ( ) const

inlinevirtual

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.

◆ recomputeSmatrices_()

void hp2D::Space::recomputeSmatrices_ ( const Quad< Real > & elm )

private

Checks if the S matrices need to be recomputed and does so if necessary.

Parameters

elm	Element which the S matrices are needed for (the polynomial degrees are important)

◆ scan() [1/2]

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

inlinevirtual

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

Implements concepts::SpaceOnCells< Real >.

Definition at line 422 of file space.hh.

◆ scan() [2/2]

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

inlinevirtual

Definition at line 403 of file space.hh.

◆ status_()

void hp2D::Space::status_ ( )

private

Gives the cells and edges with given polynomial degree (for debugging)

Friends And Related Function Documentation

◆ BuildDofsBase

friend class BuildDofsBase

friend

Definition at line 90 of file space.hh.

Member Data Documentation

◆ adj_

std::unordered_map<uint, concepts::AdaptiveAdjustP<2> > hp2D::Space::adj_

private

Hash table of the adjustment information of the elements.

Definition at line 234 of file space.hh.

◆ bc_

concepts::BoundaryConditions* hp2D::Space::bc_

private

Boundary conditions.

Definition at line 191 of file space.hh.

◆ buildEdgeDofs_

std::unique_ptr<BuildDofsBase> hp2D::Space::buildEdgeDofs_

private

Strategy to build the edge degrees of freedom.

Can be changed with buildEdgeDofs.

Definition at line 258 of file space.hh.

◆ buildInnerDofs_

std::unique_ptr<BuildDofsBase> hp2D::Space::buildInnerDofs_

private

Strategy to build the inner degrees of freedom.

Can be changed with buildInnerDofs.

Definition at line 262 of file space.hh.

◆ buildVertexDofs_

std::unique_ptr<BuildDofsBase> hp2D::Space::buildVertexDofs_

private

Strategy to build the vertex degrees of freedom.

Can be changed with buildVertexDofs.

Definition at line 254 of file space.hh.

◆ cellList_

std::map<uint, concepts::CellData> hp2D::Space::cellList_

private

List of cells.

Definition at line 222 of file space.hh.

◆ ctrl0_

std::unordered_map<uint, concepts::AdaptiveControl<> > hp2D::Space::ctrl0_

private

Hash table of the control information for the vertices.

Definition at line 209 of file space.hh.

◆ ctrl1_

std::unique_ptr<std::unordered_map< uint, concepts::AdaptiveControlP<1> > > hp2D::Space::ctrl1_

private

Hash table of the control information for the edges.

Definition at line 211 of file space.hh.

◆ ctrl2_

std::unordered_map<uint, concepts::AdaptiveControlP<2> > hp2D::Space::ctrl2_

private

Hash table of the control information for the 2D elements.

Definition at line 213 of file space.hh.

◆ ctrlc0_

std::unordered_map<uint, concepts::AdaptiveControl<> > hp2D::Space::ctrlc0_

private

Hash table for connected vertex dofs (mapping from attribute)

Definition at line 216 of file space.hh.

◆ dim_

uint hp2D::Space::dim_

private

Dimension of the FE space.

Definition at line 200 of file space.hh.

◆ edgeList_

std::map<uint, concepts::EdgeData> hp2D::Space::edgeList_

private

List of edges.

Definition at line 224 of file space.hh.

◆ elm_

concepts::Joiner<Element<Real>*, 1>* hp2D::Space::elm_

private

Linked list of the elements.

Definition at line 206 of file space.hh.

◆ msh_

concepts::Mesh2& hp2D::Space::msh_

private

Mesh.

Definition at line 189 of file space.hh.

◆ nelm_

uint hp2D::Space::nelm_

private

Number of elements currently active in the mesh.

Definition at line 203 of file space.hh.

◆ rebuild_

bool hp2D::Space::rebuild_

private

If true: the elements have to be rebuilt.

Some elements have been marked for refinement or for coarsening and the elements are outdated.

Definition at line 197 of file space.hh.

◆ S1left_

std::unique_ptr<concepts::SMatrix1D> hp2D::Space::S1left_

private

S matrices in 1D.

Definition at line 237 of file space.hh.

◆ S1right_

std::unique_ptr<concepts::SMatrix1D> hp2D::Space::S1right_

private

Mesh.

Definition at line 237 of file space.hh.

◆ Smatrices2H_

std::unique_ptr<concepts::SMatrixBase<Real> > hp2D::Space::Smatrices2H_[2]

private

S matrices for horizontal subdivision.

See also: concepts::Quad2dSubdiv2H

Definition at line 241 of file space.hh.

◆ Smatrices2V_

std::unique_ptr<concepts::SMatrixBase<Real> > hp2D::Space::Smatrices2V_[2]

private

S matrices for vertical subdivision.

See also: concepts::Quad2dSubdiv2V

Definition at line 245 of file space.hh.

◆ Smatrices4_

std::unique_ptr<concepts::SMatrixBase<Real> > hp2D::Space::Smatrices4_[4]

private

S matrices for subdivision into 4 quads.

See also: concepts::Quad2dSubdiv4

Definition at line 249 of file space.hh.

◆ vertexList_

std::map<uint, concepts::VertexData> hp2D::Space::vertexList_

private

List of vertices.

Definition at line 226 of file space.hh.

◆ vtxConnect_

std::unordered_map<uint, const concepts::Attribute*> hp2D::Space::vtxConnect_

private

Hash table for connected vertex dofs (mapping from cell key)

Definition at line 219 of file space.hh.

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

hp2D/space.hh

hp2D::Space Class Referenceabstract

Public Types

Public Member Functions

Friends

Strategies to Build the Degrees of Freedom

Detailed Description

Member Typedef Documentation

◆ Scan

◆ Scanner

◆ type

Constructor & Destructor Documentation

◆ Space() [1/3]

◆ Space() [2/3]

◆ ~Space()

◆ Space() [3/3]

Member Function Documentation

◆ activeCell_()

◆ adjust() [1/2]

◆ adjust() [2/2]

◆ buildEdgeDofs()

◆ buildElements_()

◆ buildEmptyElements_()

◆ buildInnerDofs()

◆ buildVertexDofs()

◆ computePmax_()

◆ connectedIdx()

◆ constScan()

◆ createCellList_()

◆ createVtxEdgList_()

◆ deactivate_() [1/2]

◆ deactivate_() [2/2]

◆ dim() [1/2]

◆ dim() [2/2]

◆ enforceBC_()

◆ enrichElm_()

◆ getOutputDimension()

◆ info()

◆ matlabstatus_()

◆ meshAndPoly_()

◆ minimumRule_()

◆ nelm() [1/2]

◆ nelm() [2/2]

◆ rebuild()

◆ recomputeShapefunctions()

◆ recomputeSmatrices_()

◆ scan() [1/2]

◆ scan() [2/2]

◆ status_()

Friends And Related Function Documentation

◆ BuildDofsBase

Member Data Documentation

◆ adj_

◆ bc_

◆ buildEdgeDofs_

◆ buildInnerDofs_

◆ buildVertexDofs_

◆ cellList_

◆ ctrl0_

◆ ctrl1_

◆ ctrl2_

◆ ctrlc0_

◆ dim_

◆ edgeList_

◆ elm_

◆ msh_

◆ nelm_

◆ rebuild_

◆ S1left_

◆ S1right_

◆ Smatrices2H_

◆ Smatrices2V_

◆ Smatrices4_

◆ vertexList_

◆ vtxConnect_