Space for linear triangular and bilinear quadrilateral FEM in 2D. More...

#include <space2D.hh>

Inheritance diagram for linearFEM::Linear2d:

Public Types
typedef concepts::Scan< Element >	Scan

typedef Scan< Element< Real > >	Scanner

typedef void(*	SMap) (const concepts::TColumn< Real > &, concepts::TColumn< Real > &)

typedef Element< Real >	type

Public Member Functions
void	adjust (const Quad &elm, const short level)
	Adjusts an element in the space. More...

virtual uint	dim () const

virtual uint	dim () const=0
	Returns the dimension of the space. More...

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

	Linear2d (concepts::Mesh2 &msh, uint level, concepts::BoundaryConditions *bc=0)
	Constructor. More...

virtual uint	nelm () const

virtual uint	nelm () const=0
	Returns the number of elements in the space. More...

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

const SMap &	S (uint i) const
	Returns the ith S matrix. More...

virtual Scan *	scan () const

virtual Scanner *	scan () const=0
	Returns a scanner to iterate over the elements of the space. More...

virtual	~Linear2d ()

Static Public Member Functions
static void	S0 (const concepts::TColumn< Real > &src, concepts::TColumn< Real > &dst)

static void	S1 (const concepts::TColumn< Real > &src, concepts::TColumn< Real > &dst)

static void	S2 (const concepts::TColumn< Real > &src, concepts::TColumn< Real > &dst)

static void	S3 (const concepts::TColumn< Real > &src, concepts::TColumn< Real > &dst)

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

Private Member Functions
void	deactivate_ (concepts::Connector1 &edg)
	Deactives children of this edge and the new vertex. More...

void	rebuild0_ (concepts::Connector2 &cntr, const int l, int &L)
	Determines maximal level and sets control information. More...

void	rebuild1_ (concepts::Quad2d &cell, concepts::TColumn< Real > *T0=0)
	Builds the elements for quads. More...

void	rebuild1_ (concepts::Triangle2d &cell, concepts::TColumn< Real > *T0=0)
	Builds the elements for triangles. More...

Private Attributes
std::unordered_map< uint, short >	adj_
	Adjustements (ie. level changes) for the elements. More...

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

std::unordered_map< uint, short >	ctrl0_
	Control information for vertices: active, member of space, valid index. More...

std::unordered_map< uint, short >	ctrl0L_
	Level information for vertices. More...

std::unordered_map< uint, short >	ctrl1_
	Control information for edges: active, member of space. More...

std::unordered_map< uint, short >	ctrl1L_
	Level information for edges. More...

std::unordered_map< uint, short >	ctrl2_
	Control information for elements. More...

uint	dim_
	Number of degrees of freedom. More...

std::unordered_map< uint, uint >	dof_
	Degree of freedom map. More...

concepts::Joiner< Element , 1 >	elm_
	List of elements. More...

concepts::Mesh2 &	msh_
	Mesh which this space is based on. More...

uint	nelm_
	Number of elements. More...

bool	rebuild_
	Flag for rebuilding the space. More...

Static Private Attributes
static SMap	S_ [4]

Detailed Description

Space for linear triangular and bilinear quadrilateral FEM in 2D.

Author: Philipp Frauenfelder, 2002

Definition at line 44 of file space2D.hh.

Member Typedef Documentation

◆ Scan

typedef concepts::Scan<Element> linearFEM::Linear2d::Scan

Definition at line 46 of file space2D.hh.

◆ Scanner

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

inherited

Definition at line 47 of file space.hh.

◆ SMap

typedef void(* linearFEM::Linear2d::SMap) (const concepts::TColumn< Real > &, concepts::TColumn< Real > &)

Definition at line 47 of file space2D.hh.

◆ type

typedef Element<Real > concepts::Space< Real >::type

inherited

Definition at line 46 of file space.hh.

Constructor & Destructor Documentation

◆ Linear2d()

linearFEM::Linear2d::Linear2d	(	concepts::Mesh2 &	msh,
		uint	level,
		concepts::BoundaryConditions *	bc = `0`
	)

Constructor.

Parameters

msh	Mesh
level	Number levels for initial refinement
bc	Boundary conditions

◆ ~Linear2d()

virtual linearFEM::Linear2d::~Linear2d ( )

virtual

Member Function Documentation

◆ adjust()

void linearFEM::Linear2d::adjust	(	const Quad &	elm,
		const short	level
	)

Adjusts an element in the space.

Only quads have S matrices, therefore, only quads can be refined.

Parameters

elm	Element to refine
level	Number of refinements

◆ deactivate_()

void linearFEM::Linear2d::deactivate_ ( concepts::Connector1 & edg )

private

Deactives children of this edge and the new vertex.

◆ dim() [1/2]

virtual uint linearFEM::Linear2d::dim ( ) const

inlinevirtual

Definition at line 58 of file space2D.hh.

◆ dim() [2/2]

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

pure virtualinherited

Returns the dimension of the space.

Implemented in concepts::SpaceOnCells< Real >, concepts::DummySpace< Real >, hp2D::hpAdaptiveSpace< Real >, hp3D::Space, hp2Dedge::Space, hp2D::Space, hp2D::hpAdaptiveSpace< Real >, and hp1D::Space.

◆ 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& linearFEM::Linear2d::info ( std::ostream & os ) const

protectedvirtual

Reimplemented from concepts::Space< Real >.

◆ nelm() [1/2]

virtual uint linearFEM::Linear2d::nelm ( ) const

inlinevirtual

Definition at line 59 of file space2D.hh.

◆ nelm() [2/2]

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

pure virtualinherited

Returns the number of elements in the space.

Implemented in concepts::SpaceOnCells< Real >, concepts::DummySpace< Real >, hp2D::hpAdaptiveSpace< Real >, hp3D::Space, hp2Dedge::Space, hp2D::Space, hp2D::hpAdaptiveSpace< Real >, and hp1D::Space.

◆ rebuild()

void linearFEM::Linear2d::rebuild ( )

Rebuilds the space.

◆ rebuild0_()

void linearFEM::Linear2d::rebuild0_	(	concepts::Connector2 &	cntr,
		const int	l,
		int &	L
	)

private

Determines maximal level and sets control information.

rebuild0_ is called recursively.

Parameters

cntr	Support of the element
l	Current level
L	Maximal level

◆ rebuild1_() [1/2]

void linearFEM::Linear2d::rebuild1_	(	concepts::Quad2d &	cell,
		concepts::TColumn< Real > *	T0 = `0`
	)

private

Builds the elements for quads.

This routine assigns degress of freedom to vertices, creates T matrices, applies S matrices. rebuild1_ is called recursively.

Parameters

cell	Cell of the element
T0	T columns from element on a higher level

◆ rebuild1_() [2/2]

void linearFEM::Linear2d::rebuild1_	(	concepts::Triangle2d &	cell,
		concepts::TColumn< Real > *	T0 = `0`
	)

private

Builds the elements for triangles.

This routines assigns degress of freedom to vertices, creates T matrices. rebuild1_ is called recursively.

Precondition: T0 is 0 as there are no S matrices for triangles up to now.

Todo:: S matrices for triangles

Parameters

cell	Cell of the element
T0	T columns from element on a higher level

◆ S()

const SMap& linearFEM::Linear2d::S ( uint i ) const

Returns the ith S matrix.

The S matrices are used for the irregular refinement of a mesh. An S matrix is independent of the geometry but it depends on the topological relation of the children with the parent: the bottom left child has a different S matrix than the top right etc.

◆ S0()

static void linearFEM::Linear2d::S0	(	const concepts::TColumn< Real > &	src,
		concepts::TColumn< Real > &	dst
	)

static

◆ S1()

static void linearFEM::Linear2d::S1	(	const concepts::TColumn< Real > &	src,
		concepts::TColumn< Real > &	dst
	)

static

◆ S2()

static void linearFEM::Linear2d::S2	(	const concepts::TColumn< Real > &	src,
		concepts::TColumn< Real > &	dst
	)

static

◆ S3()

static void linearFEM::Linear2d::S3	(	const concepts::TColumn< Real > &	src,
		concepts::TColumn< Real > &	dst
	)

static

◆ scan() [1/2]

virtual Scan* linearFEM::Linear2d::scan ( ) const

virtual

◆ scan() [2/2]

virtual Scanner* concepts::Space< Real >::scan ( ) const

pure virtualinherited

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

Implemented in concepts::SpaceOnCells< Real >, concepts::DummySpace< Real >, hp2D::hpAdaptiveSpace< Real >, hp3D::Space, hp2Dedge::Space, hp2D::Space, hp2D::hpAdaptiveSpace< Real >, and hp1D::Space.

Member Data Documentation

◆ adj_

std::unordered_map<uint, short> linearFEM::Linear2d::adj_

private

Adjustements (ie. level changes) for the elements.

Definition at line 103 of file space2D.hh.

◆ bc_

concepts::BoundaryConditions* linearFEM::Linear2d::bc_

private

Boundary conditions.

Definition at line 99 of file space2D.hh.

◆ ctrl0_

std::unordered_map<uint, short> linearFEM::Linear2d::ctrl0_

private

Control information for vertices: active, member of space, valid index.

Definition at line 105 of file space2D.hh.

◆ ctrl0L_

std::unordered_map<uint, short> linearFEM::Linear2d::ctrl0L_

private

Level information for vertices.

Definition at line 107 of file space2D.hh.

◆ ctrl1_

std::unordered_map<uint, short> linearFEM::Linear2d::ctrl1_

private

Control information for edges: active, member of space.

Definition at line 109 of file space2D.hh.

◆ ctrl1L_

std::unordered_map<uint, short> linearFEM::Linear2d::ctrl1L_

private

Level information for edges.

Definition at line 111 of file space2D.hh.

◆ ctrl2_

std::unordered_map<uint, short> linearFEM::Linear2d::ctrl2_

private

Control information for elements.

Definition at line 113 of file space2D.hh.

◆ dim_

uint linearFEM::Linear2d::dim_

private

Number of degrees of freedom.

Definition at line 91 of file space2D.hh.

◆ dof_

std::unordered_map<uint, uint> linearFEM::Linear2d::dof_

private

Degree of freedom map.

Definition at line 115 of file space2D.hh.

◆ elm_

concepts::Joiner<Element*, 1>* linearFEM::Linear2d::elm_

private

List of elements.

Definition at line 101 of file space2D.hh.

◆ msh_

concepts::Mesh2& linearFEM::Linear2d::msh_

private

Mesh which this space is based on.

Definition at line 97 of file space2D.hh.

◆ nelm_

uint linearFEM::Linear2d::nelm_

private

Number of elements.

Definition at line 93 of file space2D.hh.

◆ rebuild_

bool linearFEM::Linear2d::rebuild_

private

Flag for rebuilding the space.

Definition at line 95 of file space2D.hh.

◆ S_

SMap linearFEM::Linear2d::S_[4]

staticprivate

Definition at line 117 of file space2D.hh.

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

linearFEM/space2D.hh

linearFEM::Linear2d Class Referenceabstract

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ Scan

◆ Scanner

◆ SMap

◆ type

Constructor & Destructor Documentation

◆ Linear2d()

◆ ~Linear2d()

Member Function Documentation

◆ adjust()

◆ deactivate_()

◆ dim() [1/2]

◆ dim() [2/2]

◆ getOutputDimension()

◆ info()

◆ nelm() [1/2]

◆ nelm() [2/2]

◆ rebuild()

◆ rebuild0_()

◆ rebuild1_() [1/2]

◆ rebuild1_() [2/2]

◆ S()

◆ S0()

◆ S1()

◆ S2()

◆ S3()

◆ scan() [1/2]

◆ scan() [2/2]

Member Data Documentation

◆ adj_

◆ bc_

◆ ctrl0_

◆ ctrl0L_

◆ ctrl1_

◆ ctrl1L_

◆ ctrl2_

◆ dim_

◆ dof_

◆ elm_

◆ msh_

◆ nelm_

◆ rebuild_

◆ S_