A 2D hp FEM space of edge elements with piecewise polynomial basis functions with two components, where the tangential component is continuous Currently, only quadrilaterials and conforming meshes are possible. More...

#include <space.hh>

Inheritance diagram for hp2Dedge::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...

concepts::BoundaryConditions *	boundary ()

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

uint	dim () const

virtual uint	getOutputDimension () const

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

concepts::Scan< const concepts::Quad > *	interScan ()
	scanner over the intermediate cells More...

concepts::Scan< const concepts::Quad > *	interScan () const
	scanner over the intermediate cells More...

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

uint	nelm () const

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

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

Scan *	scan ()
	scanner over the cells of the coarsest mesh More...

Scan *	scan () const
	scanner over the cells of the coarsest mesh More...

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

virtual	~Space ()

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

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

concepts::TColumn< Real > *	buildEdge_ (concepts::TColumn< Real > T1, const concepts::Quad &cntr, const uint nn)
	Builds the T columns for the edge degrees of freedom. More...

void	buildElements_ (concepts::Quad2d &cell)
	Creates the elements and their T matrices. More...

concepts::TColumn< Real > *	buildInterior_ (concepts::TColumn< Real > T1, const concepts::Quad &cntr, const uint nn)
	Builds the T columns for the interior degrees of freedom. More...

void	buildTColumns_ (const concepts::Quad &cntr, ushort Pmax, concepts::TColumn< Real > T0=0)
	Builds the T columns, stores them together with the neccessary polynomial degrees in a list T_. More...

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

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

void	createEdgList_ (const concepts::Cell2 &cell)
	Initially fills `edgeList_`. More...

void	deactivate_ (concepts::Edge &edg)

void	deactivate_ (concepts::Vertex &vtx)

void	edgeOrientation_ (const concepts::Connector2 &cntr, const uint i, uint &pIndex) const
	Helps distributing the polynomial degree to the edges. More...

void	enforceBC_ (concepts::Quad2d &cell)
	Enforce Dirichlet boundary conditions. More...

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

void	matlabstatus_ ()

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

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

void	nonactiveRegion_ ()
	Set that cells in nonactive region to passive. More...

void	recomputeSmatrices_ (const ushort p, const uint nn)
	Checks if the S matrices need to be recomputed and does so if necessary. More...

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

Private Attributes
concepts::DynArray< concepts::AdaptiveAdjustP< 2 > >	adj_
	Hash table of the adjustment information of the elements. More...

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

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

concepts::DynArray< concepts::AdaptiveControl<> >	ctrl0_
	Hash table of the control information for the vertices. More...

concepts::DynArray< 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...

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

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

concepts::Joiner< hp2D::Element< Real > , 1 >	elm_
	Linked list of the elements. More...

concepts::Joiner< const concepts::Quad , 1 >	interCells_

std::set< uint >	interEdges_

concepts::Mesh2 &	msh_
	Mesh. More...

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

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

std::unique_ptr< concepts::SMatrix1D >	S1left_n_

std::unique_ptr< concepts::SMatrix1D >	S1left_t_
	S matrices in 1D. More...

std::unique_ptr< concepts::SMatrix1D >	S1right_n_

std::unique_ptr< concepts::SMatrix1D >	S1right_t_

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

std::unique_ptr< concepts::SMatrixBase< Real > >	Smatrices2H_X_ [2]
	S matrices for tangential and normal component for different subdivisions. More...

std::unique_ptr< concepts::SMatrixBase< Real > >	Smatrices2H_Y_ [2]

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

std::unique_ptr< concepts::SMatrixBase< Real > >	Smatrices2V_X_ [2]

std::unique_ptr< concepts::SMatrixBase< Real > >	Smatrices2V_Y_ [2]

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

concepts::TColumnSet< Real, 2 >	T_
	List of TColumns (for the member of the space cells) More...

bool	trunk_
	Build trunk space. More...

Detailed Description

A 2D hp FEM space of edge elements with piecewise polynomial basis functions with two components, where the tangential component is continuous Currently, only quadrilaterials and conforming meshes are possible.

Author: Kersten Schmidt, 2004

Definition at line 50 of file space.hh.

Member Typedef Documentation

◆ Scan

typedef concepts::Scan<hp2D::Element<Real> > hp2Dedge::Space::Scan

Definition at line 54 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()

hp2Dedge::Space::Space	(	concepts::Mesh2 &	msh,
		uint	l,
		uint	p,
		concepts::BoundaryConditions *	bc = `0`,
		bool	trunk = `false`
	)

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
trunk	Create trunk space ie., use the the rules `p+q <= pIntMax + 1` in the interior instead of allowing all `p, q` combinations.

◆ ~Space()

virtual hp2Dedge::Space::~Space ( )

virtual

Member Function Documentation

◆ activeCell_()

bool hp2Dedge::Space::activeCell_ ( concepts::Cell & cell )

private

Checks if a cell is in active region.

◆ adjust() [1/2]

virtual void hp2Dedge::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.

◆ boundary()

concepts::BoundaryConditions* hp2Dedge::Space::boundary ( )

inline

Definition at line 95 of file space.hh.

◆ buildEdge_()

concepts::TColumn<Real>* hp2Dedge::Space::buildEdge_	(	concepts::TColumn< Real > *	T1,
		const concepts::Quad &	cntr,
		const uint *	nn
	)

private

Builds the T columns for the edge degrees of freedom.

◆ buildElements_()

void hp2Dedge::Space::buildElements_ ( concepts::Quad2d & cell )

private

Creates the elements and their T matrices.

This routine is called recursively until the finest level is reached. With the TColumns and polynomial degrees, which are taken from T_, the elements are created and the T matrix is created on the finest level.

◆ buildInterior_()

concepts::TColumn<Real>* hp2Dedge::Space::buildInterior_	(	concepts::TColumn< Real > *	T1,
		const concepts::Quad &	cntr,
		const uint *	nn
	)

private

Builds the T columns for the interior degrees of freedom.

◆ buildTColumns_()

void hp2Dedge::Space::buildTColumns_	(	const concepts::Quad &	cntr,
		ushort *	Pmax,
		concepts::TColumn< Real > *	T0 = `0`
	)

private

Builds the T columns, stores them together with the neccessary polynomial degrees in a list T_.

  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 T columns and polynomial degrees are stored.

Parameters

cntr	The current cell (geometric)
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

◆ computePmax_()

void hp2Dedge::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.

◆ createCellList_()

void hp2Dedge::Space::createCellList_	(	const concepts::Connector &	cntr,
		const concepts::CellData *	father
	)

private

Initially fills cellList_ (recursively)

◆ createEdgList_()

void hp2Dedge::Space::createEdgList_ ( const concepts::Cell2 & cell )

private

Initially fills edgeList_.

◆ deactivate_() [1/2]

void hp2Dedge::Space::deactivate_ ( concepts::Edge & edg )

private

◆ deactivate_() [2/2]

void hp2Dedge::Space::deactivate_ ( concepts::Vertex & vtx )

private

◆ dim() [1/2]

uint hp2Dedge::Space::dim ( )

inlinevirtual

Returns the dimension of the space.

Implements concepts::SpaceOnCells< Real >.

Definition at line 366 of file space.hh.

◆ dim() [2/2]

uint hp2Dedge::Space::dim ( ) const

inline

Definition at line 346 of file space.hh.

◆ edgeOrientation_()

void hp2Dedge::Space::edgeOrientation_	(	const concepts::Connector2 &	cntr,
		const uint	i,
		uint &	pIndex
	)		const

private

Helps distributing the polynomial degree to the edges.

Parameters

cntr	Connector
i	Index of the face [0..5]
pIndex	Return value, the index of the polynomial degree of this edge in the array of the element

◆ enforceBC_()

void hp2Dedge::Space::enforceBC_ ( concepts::Quad2d & cell )

private

Enforce Dirichlet boundary conditions.

This routine is called by meshAndPoly_ on every cell.

Parameters

cell Cell

◆ enrichElm_()

void hp2Dedge::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() [1/2]

virtual uint hp2Dedge::Space::getOutputDimension ( ) const

inlinevirtual

Definition at line 74 of file space.hh.

◆ getOutputDimension() [2/2]

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& hp2Dedge::Space::info ( std::ostream & os ) const

protectedvirtual

Reimplemented from concepts::SpaceOnCells< Real >.

◆ interScan() [1/2]

concepts::Scan< const concepts::Quad > * hp2Dedge::Space::interScan ( )

inline

scanner over the intermediate cells

Definition at line 381 of file space.hh.

◆ interScan() [2/2]

concepts::Scan< const concepts::Quad > * hp2Dedge::Space::interScan ( ) const

inline

scanner over the intermediate cells

Definition at line 361 of file space.hh.

◆ matlabstatus_()

void hp2Dedge::Space::matlabstatus_ ( )

private

◆ meshAndPoly_()

void hp2Dedge::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_

  @param cell Cell

Parameters

L	The desired level
P	The desired polynomial degree

Precondition: P is an array of 3 integers

See also: enforceBC_

◆ minimumRule_()

void hp2Dedge::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 hp2Dedge::Space::nelm ( )

inlinevirtual

Returns the number of elements in the space.

Implements concepts::SpaceOnCells< Real >.

Definition at line 371 of file space.hh.

◆ nelm() [2/2]

uint hp2Dedge::Space::nelm ( ) const

inline

Definition at line 351 of file space.hh.

◆ nonactiveRegion_()

void hp2Dedge::Space::nonactiveRegion_ ( )

private

Set that cells in nonactive region to passive.

A whole region can be deactivated by setting the attribute of the cells in the region to be of Dirichlet boundary condition. That not includes the edges of the region.

If the edges of the region can be deactivated by usual setting of Dirichlet boundary condition.

◆ rebuild()

void hp2Dedge::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.

◆ recomputeShapefunctions()

void hp2Dedge::Space::recomputeShapefunctions ( )

Recompute shape functions, e.g.

for other abscissas redefined through setIntegrationRule

◆ recomputeSmatrices_()

void hp2Dedge::Space::recomputeSmatrices_	(	const ushort *	p,
		const uint *	nn
	)

private

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

Parameters

p	polynomial degrees of the element
nn	maximal polynomial degree (in x- and y-direction) for the two vector components, i.e. array with 4 entries, 1st and 2nd are for first vector component, 3rd and 4th are for the second vector component.

◆ scan() [1/2]

Space::Scan * hp2Dedge::Space::scan ( )

inlinevirtual

scanner over the cells of the coarsest mesh

Implements concepts::SpaceOnCells< Real >.

Definition at line 376 of file space.hh.

◆ scan() [2/2]

Space::Scan * hp2Dedge::Space::scan ( ) const

inline

scanner over the cells of the coarsest mesh

Definition at line 356 of file space.hh.

◆ status_()

void hp2Dedge::Space::status_ ( )

private

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

Member Data Documentation

◆ adj_

concepts::DynArray<concepts::AdaptiveAdjustP<2> > hp2Dedge::Space::adj_

private

Hash table of the adjustment information of the elements.

Definition at line 169 of file space.hh.

◆ bc_

concepts::BoundaryConditions* hp2Dedge::Space::bc_

private

Boundary conditions.

Definition at line 124 of file space.hh.

◆ cellList_

std::map<uint, concepts::CellData> hp2Dedge::Space::cellList_

private

List of cells.

Definition at line 151 of file space.hh.

◆ ctrl0_

concepts::DynArray<concepts::AdaptiveControl<> > hp2Dedge::Space::ctrl0_

private

Hash table of the control information for the vertices.

Definition at line 144 of file space.hh.

◆ ctrl1_

concepts::DynArray<concepts::AdaptiveControlP<1> > hp2Dedge::Space::ctrl1_

private

Hash table of the control information for the edges.

Definition at line 146 of file space.hh.

◆ ctrl2_

std::unordered_map<uint, concepts::AdaptiveControlP<2> > hp2Dedge::Space::ctrl2_

private

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

Definition at line 148 of file space.hh.

◆ dim_

uint hp2Dedge::Space::dim_

private

Dimension of the FE space.

Definition at line 135 of file space.hh.

◆ edgeList_

std::map<uint, concepts::EdgeData> hp2Dedge::Space::edgeList_

private

List of edges.

Definition at line 153 of file space.hh.

◆ elm_

concepts::Joiner<hp2D::Element<Real>*, 1>* hp2Dedge::Space::elm_

private

Linked list of the elements.

Definition at line 141 of file space.hh.

◆ interCells_

concepts::Joiner<const concepts::Quad*, 1>* hp2Dedge::Space::interCells_

private

Definition at line 161 of file space.hh.

◆ interEdges_

std::set<uint> hp2Dedge::Space::interEdges_

private

Definition at line 166 of file space.hh.

◆ msh_

concepts::Mesh2& hp2Dedge::Space::msh_

private

Mesh.

Definition at line 122 of file space.hh.

◆ nelm_

uint hp2Dedge::Space::nelm_

private

Number of elements currently active in the mesh.

Definition at line 138 of file space.hh.

◆ rebuild_

bool hp2Dedge::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 132 of file space.hh.

◆ S1left_n_

std::unique_ptr<concepts::SMatrix1D> hp2Dedge::Space::S1left_n_

private

Definition at line 173 of file space.hh.

◆ S1left_t_

std::unique_ptr<concepts::SMatrix1D> hp2Dedge::Space::S1left_t_

private

S matrices in 1D.

Definition at line 173 of file space.hh.

◆ S1right_n_

std::unique_ptr<concepts::SMatrix1D> hp2Dedge::Space::S1right_n_

private

Definition at line 173 of file space.hh.

◆ S1right_t_

std::unique_ptr<concepts::SMatrix1D> hp2Dedge::Space::S1right_t_

private

Definition at line 173 of file space.hh.

◆ Smatrices2H_

std::unique_ptr<concepts::SMatrixBase<Real> > hp2Dedge::Space::Smatrices2H_[2]

private

S matrices for horizontal subdivision.

See also: concepts::Quad2dSubdiv2H

Definition at line 187 of file space.hh.

◆ Smatrices2H_X_

std::unique_ptr<concepts::SMatrixBase<Real> > hp2Dedge::Space::Smatrices2H_X_[2]

private

S matrices for tangential and normal component for different subdivisions.

Definition at line 179 of file space.hh.

◆ Smatrices2H_Y_

std::unique_ptr<concepts::SMatrixBase<Real> > hp2Dedge::Space::Smatrices2H_Y_[2]

private

Definition at line 180 of file space.hh.

◆ Smatrices2V_

std::unique_ptr<concepts::SMatrixBase<Real> > hp2Dedge::Space::Smatrices2V_[2]

private

S matrices for vertical subdivision.

See also: concepts::Quad2dSubdiv2V

Definition at line 191 of file space.hh.

◆ Smatrices2V_X_

std::unique_ptr<concepts::SMatrixBase<Real> > hp2Dedge::Space::Smatrices2V_X_[2]

private

Definition at line 181 of file space.hh.

◆ Smatrices2V_Y_

std::unique_ptr<concepts::SMatrixBase<Real> > hp2Dedge::Space::Smatrices2V_Y_[2]

private

Definition at line 182 of file space.hh.

◆ Smatrices4_

std::unique_ptr<concepts::SMatrixBase<Real> > hp2Dedge::Space::Smatrices4_[4]

private

S matrices for subdivision into 4 quads.

See also: concepts::Quad2dSubdiv4

Definition at line 195 of file space.hh.

◆ T_

concepts::TColumnSet<Real,2> hp2Dedge::Space::T_

private

List of TColumns (for the member of the space cells)

Definition at line 156 of file space.hh.

◆ trunk_

bool hp2Dedge::Space::trunk_

private

Build trunk space.

Definition at line 126 of file space.hh.

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

hp2Dedge/space.hh

hp2Dedge::Space Class Referenceabstract

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ Scan

◆ Scanner

◆ type

Constructor & Destructor Documentation

◆ Space()

◆ ~Space()

Member Function Documentation

◆ activeCell_()

◆ adjust() [1/2]

◆ adjust() [2/2]

◆ boundary()

◆ buildEdge_()

◆ buildElements_()

◆ buildInterior_()

◆ buildTColumns_()

◆ computePmax_()

◆ createCellList_()

◆ createEdgList_()

◆ deactivate_() [1/2]

◆ deactivate_() [2/2]

◆ dim() [1/2]

◆ dim() [2/2]

◆ edgeOrientation_()

◆ enforceBC_()

◆ enrichElm_()

◆ getOutputDimension() [1/2]

◆ getOutputDimension() [2/2]

◆ info()

◆ interScan() [1/2]

◆ interScan() [2/2]

◆ matlabstatus_()

◆ meshAndPoly_()

◆ minimumRule_()

◆ nelm() [1/2]

◆ nelm() [2/2]

◆ nonactiveRegion_()

◆ rebuild()

◆ recomputeShapefunctions()

◆ recomputeSmatrices_()

◆ scan() [1/2]

◆ scan() [2/2]

◆ status_()

Member Data Documentation

◆ adj_

◆ bc_

◆ cellList_

◆ ctrl0_

◆ ctrl1_

◆ ctrl2_

◆ dim_

◆ edgeList_

◆ elm_

◆ interCells_

◆ interEdges_

◆ msh_

◆ nelm_

◆ rebuild_

◆ S1left_n_

◆ S1left_t_

◆ S1right_n_

◆ S1right_t_

◆ Smatrices2H_

◆ Smatrices2H_X_

◆ Smatrices2H_Y_

◆ Smatrices2V_

◆ Smatrices2V_X_

◆ Smatrices2V_Y_

◆ Smatrices4_

◆ T_

◆ trunk_