A 2D cell: quadrilateral in thin sheet of constant thickness. More...

#include <thinSheetGeom.hh>

Inheritance diagram for concepts::ThinSheetQuad2d:

Collaboration diagram for concepts::ThinSheetQuad2d:

Public Member Functions
Real3d	center () const
	Returns the center of the cell.
Real2d	chi (Real xi, Real eta) const
	Evaluates the element map.
virtual Quad2d *	child (uint i)
	Returns a child.
virtual const Quad2d *	child (uint i) const
	Returns a child.
const Quad2d *	child (uint i, Real xi, Real eta, Real &xiC, Real &etaC) const
	Returns a child.
Quad2d *	clone (Quad &cntr, MappingQuad2d *map) const
	Returns a copy of itself.
Quad &	connector () const
	Returns the quadrilateral connector (topology)
virtual const bool	constThickness () const
	Returns true, if the thickness is constant in the cell.
const Real	curvature (const Real xi, uint n=0) const
virtual const Real	d (const Real &xi) const
	Returns a child.
const MappingEdge2d *	edge (uint i) const
	Returns the mapping of the i-th edge, where i in {0,2}.
const MappingEdge2d *	edgeMap (uint edge) const
	Returns the mapping of an edge.
Real3d	elemMap (const Real2d &coord_local) const
	Element map from point local coordinates in 2D.
virtual Real3d	elemMap (const Real3d &coord_local) const
	Element map from point local coordinates in 3D.
virtual Real3d	elemMap (const Real coord_local) const
	Element map from point local coordinates in 1D.
const ThinSheetQuad2d *	father () const
	Returns the father cell.
const Quad2dSubdivision *	getStrategy () const
	Returns the subdivision strategy of this quad.
bool	hasChildren () const
	Returns true if there is a least one child.
MapReal2d	jacobian (const Real xi, const Real eta) const
	Computes the Jacobian for `xi`, `eta` $\in [0,1]$ .
Real	jacobianDeterminant (const Real xi, const Real eta) const
	Returns the determinant of the Jacobian for `xi`, `eta` $\in [0,1]$ .
MapReal2d	jacobianInverse (const Real xi, const Real eta) const
	Returns the inverse of the Jacobian for `xi`, `eta` $\in [0,1]$ .
Level< 2 >	level () const
	Returns the level of the cell.
Real	lineElement (const Real xi, const uint edge) const
	Computes the differential element on an edge.
const MappingQuad2d *	map () const
	Returns the stored element map (same for all family related to one ancestor).
const MappingEdge2d *	midline () const
void	neighbour (uint i, const ThinSheetQuad2d *neigbour)
const ThinSheetQuad2d *	neighbour (uint i) const
	Returns one of the neighbouring cells.
virtual void	setStrategy (const Quad2dSubdivision *strategy=0) throw (StrategyChange)
	Sets the subdivision strategy of this quad.
	ThinSheetQuad2d (Quad &cntr, const MappingEdge2d &midline, const Real d)
	Constructor.
Real3d	vertex (uint i) const
	Returns the coordinates of the ith vertex.
virtual	~ThinSheetQuad2d ()
Protected Member Functions
Quad2d *	createChild_ (Quad &cntr, const Index &idx, bool flag) const
	Non-virtual form of the private createChild_() method.
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Protected Attributes
Index	idx_
	Index of this element.
MappingQuad2d *	map_
	Pointer to the element map.
Private Member Functions
virtual Quad2d *	createChild_ (Quad &cntr, const Index &idx) const
	Creates and returns a child.
	ThinSheetQuad2d (Quad &cntr, const ThinSheetQuad2d &father, const Index &idx)
	Pointer to the first child.
Private Attributes
const Real	d_
	Thickness.
const MappingEdge2d *	edges_ [2]
	Edge parametrisation of lower and upper edge (0 and 2), parallel to midline.
const ThinSheetQuad2d *	father_
	Pointer to ancestor.
const MappingEdge2d *	midline_
	Parametrisation of mid line.
const ThinSheetQuad2d *	neighbour_ [2]
	Pointer to a sibling.
Friends
std::ostream &	operator<< (std::ostream &os, const Quad2d::Index &i)

Detailed Description

A 2D cell: quadrilateral in thin sheet of constant thickness.

Only subdivision along the sheet is alowed. Then the quad is subdivided, two new quads are created. This happens automatically, if a child is requested.

Author:: Kersten Schmidt, 2006

Definition at line 294 of file thinSheetGeom.hh.

Constructor & Destructor Documentation

concepts::ThinSheetQuad2d::ThinSheetQuad2d	(	Quad &	cntr,
		const MappingEdge2d &	midline,
		const Real	d
	)

Constructor.

Takes the connector cntr and the element map map and creates a cell.

Parameters:

cntr	Topological information of the quadrilateral
midline	mapping to the mid line
d	thickness

virtual concepts::ThinSheetQuad2d::~ThinSheetQuad2d ( ) [virtual]

concepts::ThinSheetQuad2d::ThinSheetQuad2d	(	Quad &	cntr,
		const ThinSheetQuad2d &	father,
		const Index &	idx
	)		`[private]`

Pointer to the first child.

The children are stored in a linked list. Private copy constructor.

Parameters:

cntr	The edge which should be represented
map	Element map of the edge
l	Level
i	Index (0 or 1), ie. the left or right child

Member Function Documentation

Real3d concepts::Quad2d::center ( ) const [inline, virtual, inherited]

Returns the center of the cell.

Implements concepts::Cell2.

Definition at line 432 of file cell2D.hh.

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Real2d concepts::Quad2d::chi	(	Real	xi,
		Real	eta
	)		const `[inherited]`

Evaluates the element map.

Maps a point from the the reference coordinates in [0,1]² onto the physical coordinates.

Returns:: Point in 2D in physical coordinates.

Parameters:

xi	$\in [0,1]$
eta	$\in [0,1]$

virtual Quad2d* concepts::Quad2d::child ( uint i ) [virtual, inherited]

Returns a child.

If no children exist, four new children are created. The quadrilateral is cut into four new quadrilaterals by joining the midpoints of its edges.

Parameters:

i	Index of the child to be returned.

Implements concepts::Cell2.

virtual const Quad2d* concepts::Quad2d::child ( uint i ) const [virtual, inherited]

Returns a child.

If no children exist, none are created and 0 is returned.

Parameters:

i	Index of the child to be returned.

Implements concepts::Cell2.

const Quad2d* concepts::Quad2d::child	(	uint	i,
		Real	xi,
		Real	eta,
		Real &	xiC,
		Real &	etaC
	)		const `[inline, inherited]`

Returns a child.

If not a valid children exist, none are created and 0 is returned.

Parameters:

i	Index of the child to be returned.
xi,eta	local coordinates, where the child is located
xiC,etaC	local coordinates in the child

Definition at line 345 of file cell2D.hh.

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Quad2d* concepts::Quad2d::clone	(	Quad &	cntr,
		MappingQuad2d *	map
	)		const `[inline, inherited]`

Returns a copy of itself.

Definition at line 451 of file cell2D.hh.

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Quad & concepts::Quad2d::connector ( ) const [inline, virtual, inherited]

Returns the quadrilateral connector (topology)

Implements concepts::Cell2.

Definition at line 518 of file cell2D.hh.

virtual const bool concepts::ThinSheetQuad2d::constThickness ( ) const [inline, virtual]

Returns true, if the thickness is constant in the cell.

Implements concepts::ThinSheetCell< 2 >.

Definition at line 318 of file thinSheetGeom.hh.

Quad2d* concepts::Quad2d::createChild_	(	Quad &	cntr,
		const Index &	idx,
		bool	flag
	)		const `[protected, inherited]`

Non-virtual form of the private createChild_() method.

Can be called by inheritated classes.

virtual Quad2d* concepts::ThinSheetQuad2d::createChild_	(	Quad &	cntr,
		const Index &	idx
	)		const `[private, virtual]`

Creates and returns a child.

Reimplemented from concepts::Quad2d.

const Real concepts::ThinSheetQuad2d::curvature	(	const Real	xi,
		uint	n = `0`
	)		const

virtual const Real concepts::ThinSheetQuad2d::d ( const Real & xi ) const [inline, virtual]

Returns a child.

If no children exist, four new children are created. The quadrilateral is cut into four new quadrilaterals by joining the midpoints of its edges.

Parameters:

i	Index of the child to be returned. Returns a child. If no children exist, none are created and 0 is returned.
i	Index of the child to be returned.

Implements concepts::ThinSheetCell< 2 >.

Definition at line 317 of file thinSheetGeom.hh.

const MappingEdge2d* concepts::ThinSheetQuad2d::edge ( uint i ) const

Returns the mapping of the i-th edge, where i in {0,2}.

i = 0, lower edge i = 2, upper edge

const MappingEdge2d* concepts::Quad2d::edgeMap ( uint edge ) const [inherited]

Returns the mapping of an edge.

Construct an cell for an edge of quad with

				Edge2d edge(quad.connector(), quad.edgeMap(0));

The edgeMap can be useful for egde integrals in a 2D quadrilateral mesh.

Real3d concepts::Quad2d::elemMap ( const Real2d & coord_local ) const [inline, virtual, inherited]

Element map from point local coordinates in 2D.

Implements concepts::Cell2.

Definition at line 375 of file cell2D.hh.

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virtual Real3d concepts::Cell2::elemMap ( const Real3d & coord_local ) const [inline, virtual, inherited]

Element map from point local coordinates in 3D.

Reference element is 2D, third component is omitted.

Reimplemented from concepts::Cell.

Definition at line 100 of file cell.hh.

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virtual Real3d concepts::Cell::elemMap ( const Real coord_local ) const [virtual, inherited]

Element map from point local coordinates in 1D.

Reimplemented in concepts::Edge1d, and concepts::Edge2d.

const ThinSheetQuad2d* concepts::ThinSheetQuad2d::father ( ) const [inline]

Returns the father cell.

Definition at line 330 of file thinSheetGeom.hh.

const Quad2dSubdivision* concepts::Quad2d::getStrategy ( ) const [inline, inherited]

Returns the subdivision strategy of this quad.

If you want to find check against another strategy use

quad.getStrategy() == QuadSubdiv2V::instance()

Definition at line 474 of file cell2D.hh.

bool concepts::Quad2d::hasChildren ( ) const [inline, inherited]

Returns true if there is a least one child.

Reimplemented from concepts::Cell.

Definition at line 335 of file cell2D.hh.

virtual std::ostream& concepts::ThinSheetQuad2d::info ( std::ostream & os ) const [protected, virtual]

Returns information in an output stream.

Reimplemented from concepts::Quad2d.

MapReal2d concepts::Quad2d::jacobian	(	const Real	xi,
		const Real	eta
	)		const `[inherited]`

Computes the Jacobian for xi, eta $\in [0,1]$ .

The Jacobian of a cell in the initial mesh is computed by the element map. The Jacobian of a subdivided cell is computed as follows. Let $H : \hat K \rightarrow \hat K'$ be the subdivision map in the reference coordinates (0,1)² and $F_K : \hat K \rightarrow K$ , $F_{K'} : \hat K \rightarrow K'$ the element maps of K and K' respectively. Then,

$F_K : \hat K' \rightarrow K' \quad \text{and} \quad F_K \circ H = F_{K'}.$

The subdivision map H in reference coordinates is

$H : \vec\xi \mapsto \begin{pmatrix} a & 0 \\ 0 & b \end{pmatrix} \vec \xi$

where $a = 2^{-l_0}$ , $b = 2^{-l_1}$ . $\vec l = (l_0, l_1)$ is the level of the cell with respect to the cell in the initial mesh. The derivative of H is $dH = \begin{pmatrix} a & 0 \\ 0 & b \end{pmatrix}$ .

Then, the Jacobian of $F_{K'}$ is

$dF_{K'} = dF_K \circ H \cdot dH.$

The part $dF_K \circ H$ (without H) is computed by the element map and the part $\cdot dH$ is computed in jacobian().

Real concepts::Quad2d::jacobianDeterminant	(	const Real	xi,
		const Real	eta
	)		const `[inline, inherited]`

Returns the determinant of the Jacobian for xi, eta $\in [0,1]$ .

Definition at line 413 of file cell2D.hh.

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MapReal2d concepts::Quad2d::jacobianInverse	(	const Real	xi,
		const Real	eta
	)		const `[inline, inherited]`

Returns the inverse of the Jacobian for xi, eta $\in [0,1]$ .

Definition at line 406 of file cell2D.hh.

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Level<2> concepts::Quad2d::level ( ) const [inline, inherited]

Returns the level of the cell.

The level describes the refinements in both directions with respect to the parent cell in the initial mesh. This level information is taken into account when evaluating the element map or the Jacobian.

Definition at line 429 of file cell2D.hh.

Real concepts::Quad2d::lineElement	(	const Real	xi,
		const uint	edge
	)		const `[inherited]`

Computes the differential element on an edge.

xi stand for one of the variables

$\xi$

,

$\eta$

depending on the edge.

const MappingQuad2d* concepts::Quad2d::map ( ) const [inline, inherited]

Returns the stored element map (same for all family related to one ancestor).

Definition at line 437 of file cell2D.hh.

const MappingEdge2d* concepts::ThinSheetQuad2d::midline ( ) const

const ThinSheetQuad2d* concepts::ThinSheetQuad2d::neighbour ( uint i ) const

Returns one of the neighbouring cells.

For i = 0 the cell which is adjacent to edge 3 (xi = 0). For i = 1 the cell which is adjacent to edge 1 (xi = 1).

void concepts::ThinSheetQuad2d::neighbour	(	uint	i,
		const ThinSheetQuad2d *	neigbour
	)

virtual void concepts::Quad2d::setStrategy ( const Quad2dSubdivision * strategy = 0 ) throw (StrategyChange) [virtual, inherited]

Sets the subdivision strategy of this quad.

If the parameter is set to 0 (or if the method is called without parameter) the strategy is set to the default (if not already set). The default subdivision strategy is subdivision into 4 children.

Parameters:

strategy Pointer to an instance of a subdivision strategy.

Exceptions:

StrategyChange if the change is not allowed (the change is not allowed if there are children present or the topological strategy is set).

Real3d concepts::Quad2d::vertex ( uint i ) const [virtual, inherited]

Returns the coordinates of the ith vertex.

Implements concepts::Cell2.