A quadrilateral cell in 3D. More...

#include <cell2D.hh>

Inheritance diagram for concepts::Quad3d:

Public Types
typedef uint	index_type

Public Member Functions
Real3d	center () const
	Returns the center of the cell. More...

Real3d	chi (Real xi, Real eta) const
	Evaluates the element map. More...

virtual Quad3d *	child (uint i)
	Returns a child. More...

virtual const Quad3d *	child (uint i) const
	Returns a child. More...

Quad3d *	clone (Quad &cntr, MappingQuad3d *map) const
	Returns a copy of itself. More...

Quad &	connector () const
	Returns the quadrilateral connector (topology) More...

virtual uint	dim () const
	Sets the subdivision strategy of this quad. More...

Z2	dir () const
	Returns the direction of the normal vector. More...

virtual Real3d	elemMap (const Real coord_local) const
	Element map from point local coordinates in 1D. More...

Real3d	elemMap (const Real2d &coord_local) const
	Element map from point local coordinates in 2D. More...

virtual Real3d	elemMap (const Real3d &coord_local) const
	Element map from point local coordinates in 3D. More...

Real	faceElement (const Real xi, const Real eta) const
	Returns the face element for the transformation at `xi`, `eta` $\in [0,1]$ . More...

virtual Real	gramDeterminantRoot (const Real xi, const Real eta) const
	Returns the square root of the Gram determinant. More...

bool	hasChildren () const

Real3d	jacobianColumn (uint i, const Real xi, const Real eta) const
	Computes the Jacobian for `xi`, `eta` $\in [0,1]$ . More...

Level< 2 >	level () const
	Returns the level of the cell. More...

virtual Real	lineElement (const Real xi, const uint edge) const

const MappingQuad3d *	map () const
	Returns the stored element map (same for all family related to one ancestor). More...

Real3d	n0 (Real xi, Real eta) const
	Returns the normal vector on a point of the quad. More...

	Quad3d (Quad &cntr, const MappingQuad3d &map, const Z2 dir=0)
	Constructor. More...

Real3d	vertex (uint i) const
	Returns the coordinates of the ith vertex. More...

virtual	~Quad3d ()

Static Public Attributes
static uint	MAX_LEVEL

Protected Member Functions
Quad3d *	createChild_ (Quad &cntr, const Index &idx, bool flag) const
	Non-virtual form of the private createChild_() method. More...

virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream. More...

Protected Attributes
Quad &	cntr_
	Reference to the quadrilateral connector (topology) More...

Index	idx_
	Index of this element. More...

MappingQuad3d *	map_
	Pointer to the element map. More...

Private Member Functions
virtual Quad3d *	createChild_ (Quad &cntr, const Index &idx) const
	Subdivision strategy for the quadrilateral. More...

Quad3d &	operator= (const Quad3d &other)

	Quad3d (const Quad3d &other)

	Quad3d (Quad &cntr, MappingQuad3d *map, const Index &idx, const Z2 dir=0)

Private Attributes
Quad3d *	chld_
	Pointer to the first child. More...

Z2	dir_
	Direction of the normal vector. More...

Quad3d *	lnk_
	Pointer to a sibling. More...

Detailed Description

A quadrilateral cell in 3D.

If a quad is subdivided, two or four new quads are created. This happens automatically, if a child is requested, depending on the strategy that has been set. If two or four children are created depends on the chosen strategy. The default strategy is the create four children.

The directions of the edges in the quadrilateral on the coarsest level are externally defined, see Quad::rho(). The edges of quadrilaterals which are created by subdivision are always counter-clockwise.

Definition at line 850 of file cell2D.hh.

Member Typedef Documentation

◆ index_type

typedef uint concepts::QuadNd::index_type

inherited

Definition at line 194 of file cell2D.hh.

Constructor & Destructor Documentation

◆ Quad3d() [1/3]

concepts::Quad3d::Quad3d	(	Quad &	cntr,
		const MappingQuad3d &	map,
		const Z2	dir = `0`
	)

Constructor.

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

Parameters

cntr	Topological information of the quadrilateral
map	Element map of the quadrilateral
dir	Direction of the normal vector when looking at the quad from the side that the counterclockwise orientation of the nodes can be seen (dir = 0: normal points back to the point of view, dir = 1: normal points in view direction).

◆ ~Quad3d()

virtual concepts::Quad3d::~Quad3d ( )

virtual

◆ Quad3d() [2/3]

concepts::Quad3d::Quad3d	(	Quad &	cntr,
		MappingQuad3d *	map,
		const Index &	idx,
		const Z2	dir = `0`
	)

private

◆ Quad3d() [3/3]

concepts::Quad3d::Quad3d ( const Quad3d & other )

private

Member Function Documentation

◆ center()

Real3d concepts::Quad3d::center ( ) const

inlinevirtual

Returns the center of the cell.

Implements concepts::Cell2.

Definition at line 947 of file cell2D.hh.

◆ chi()

Real3d concepts::Quad3d::chi	(	Real	xi,
		Real	eta
	)		const

Evaluates the element map.

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

Returns: Point in 3D in physical coordinates.

Parameters

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

◆ child() [1/2]

virtual Quad3d* concepts::Quad3d::child ( uint i )

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.

Implements concepts::Cell2.

◆ child() [2/2]

virtual const Quad3d* concepts::Quad3d::child ( uint i ) const

virtual

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.

◆ clone()

Quad3d* concepts::Quad3d::clone	(	Quad &	cntr,
		MappingQuad3d *	map
	)		const

inline

Returns a copy of itself.

Definition at line 955 of file cell2D.hh.

◆ connector()

Quad& concepts::QuadNd::connector ( ) const

inlinevirtualinherited

Returns the quadrilateral connector (topology)

Implements concepts::Cell2.

Definition at line 234 of file cell2D.hh.

◆ createChild_() [1/2]

virtual Quad3d* concepts::Quad3d::createChild_	(	Quad &	cntr,
		const Index &	idx
	)		const

privatevirtual

Subdivision strategy for the quadrilateral.

Creates and returns a child.

Can only called by the object itself or friend classes. Its virtual, so that inheritated classes with additional properties can create a child of the same kind.

◆ createChild_() [2/2]

Quad3d* concepts::Quad3d::createChild_	(	Quad &	cntr,
		const Index &	idx,
		bool	flag
	)		const

protected

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

Can be called by inheritated classes.

◆ dim()

virtual uint concepts::Quad3d::dim ( ) const

inlinevirtual

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). Returns the subdivision strategy of this quad.

If you want to find check against another strategy use

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

Implements concepts::QuadNd.

Definition at line 980 of file cell2D.hh.

◆ dir()

Z2 concepts::Quad3d::dir ( ) const

inline

Returns the direction of the normal vector.

Definition at line 984 of file cell2D.hh.

◆ elemMap() [1/3]

virtual Real3d concepts::Cell::elemMap ( const Real coord_local ) const

virtualinherited

Element map from point local coordinates in 1D.

Reimplemented in concepts::Edge2d, concepts::Edge1d, concepts::Sphere3d, and concepts::SphericalSurface3d.

◆ elemMap() [2/3]

Real3d concepts::Quad3d::elemMap ( const Real2d & coord_local ) const

inlinevirtual

Element map from point local coordinates in 2D.

Implements concepts::Cell2.

Definition at line 898 of file cell2D.hh.

◆ elemMap() [3/3]

virtual Real3d concepts::Cell2::elemMap ( const Real3d & coord_local ) const

inlinevirtualinherited

Element map from point local coordinates in 3D.

Reference element is 2D, third component is omitted.

Reimplemented from concepts::Cell.

Definition at line 104 of file cell.hh.

◆ faceElement()

Real concepts::Quad3d::faceElement	(	const Real	xi,
		const Real	eta
	)		const

Returns the face element for the transformation at xi, eta $\in [0,1]$ .

◆ gramDeterminantRoot()

virtual Real concepts::Quad3d::gramDeterminantRoot	(	const Real	xi,
		const Real	eta
	)		const

inlinevirtual

Returns the square root of the Gram determinant.

The Gram determinant is given by

$\det(A^\top A) \,,$

where A is the Jacobian of the mapping. Note that for a Quad2d this is the same as the determinant of the Jacobian.

Implements concepts::QuadNd.

Definition at line 935 of file cell2D.hh.

◆ hasChildren()

bool concepts::Quad3d::hasChildren ( ) const

inline

Definition at line 887 of file cell2D.hh.

◆ info()

virtual std::ostream& concepts::Quad3d::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Implements concepts::Cell.

◆ jacobianColumn()

Real3d concepts::Quad3d::jacobianColumn	(	uint	i,
		const Real	xi,
		const Real	eta
	)		const

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().

TODO: improve/revise comment

◆ level()

Level<2> concepts::QuadNd::level ( ) const

inlineinherited

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 257 of file cell2D.hh.

◆ lineElement()

virtual Real concepts::Quad3d::lineElement	(	const Real	xi,
		const uint	edge
	)		const

virtual

Implements concepts::QuadNd.

◆ map()

const MappingQuad3d* concepts::Quad3d::map ( ) const

inline

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

Definition at line 952 of file cell2D.hh.

◆ n0()

Real3d concepts::Quad3d::n0	(	Real	xi,
		Real	eta
	)		const

Returns the normal vector on a point of the quad.

◆ operator=()

Quad3d& concepts::Quad3d::operator= ( const Quad3d & other )

private

◆ vertex()

Real3d concepts::Quad3d::vertex ( uint i ) const

virtual

Returns the coordinates of the ith vertex.

Implements concepts::Cell2.

Member Data Documentation

◆ chld_

Quad3d* concepts::Quad3d::chld_

private

Pointer to the first child.

The children are stored in a linked list.

Definition at line 1004 of file cell2D.hh.

◆ cntr_

Quad& concepts::QuadNd::cntr_

protectedinherited

Reference to the quadrilateral connector (topology)

Definition at line 261 of file cell2D.hh.

◆ dir_

Z2 concepts::Quad3d::dir_

private

Direction of the normal vector.

Definition at line 1007 of file cell2D.hh.

◆ idx_

Index concepts::QuadNd::idx_

protectedinherited

Index of this element.

Definition at line 263 of file cell2D.hh.

◆ lnk_

Quad3d* concepts::Quad3d::lnk_

private

Pointer to a sibling.

Definition at line 999 of file cell2D.hh.

◆ map_

MappingQuad3d* concepts::Quad3d::map_

protected

Pointer to the element map.

Definition at line 990 of file cell2D.hh.

◆ MAX_LEVEL

uint concepts::QuadNd::MAX_LEVEL

staticinherited

Definition at line 198 of file cell2D.hh.

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

geometry/cell2D.hh

concepts::Quad3d Class ReferenceGeometry

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ index_type

Constructor & Destructor Documentation

◆ Quad3d() [1/3]

◆ ~Quad3d()

◆ Quad3d() [2/3]

◆ Quad3d() [3/3]

Member Function Documentation

◆ center()

◆ chi()

◆ child() [1/2]

◆ child() [2/2]

◆ clone()

◆ connector()

◆ createChild_() [1/2]

◆ createChild_() [2/2]

◆ dim()

◆ dir()

◆ elemMap() [1/3]

◆ elemMap() [2/3]

◆ elemMap() [3/3]

◆ faceElement()

◆ gramDeterminantRoot()

◆ hasChildren()

◆ info()

◆ jacobianColumn()

◆ level()

◆ lineElement()

◆ map()

◆ n0()

◆ operator=()

◆ vertex()

Member Data Documentation

◆ chld_

◆ cntr_

◆ dir_

◆ idx_

◆ lnk_

◆ map_

◆ MAX_LEVEL

concepts::Quad3d Class Reference
Geometry