Dune::AxisAlignedCubeGeometry< CoordType, dim, coorddim > Class Template Reference

A geometry implementation for axis-aligned hypercubes. More...

#include <dune/geometry/axisalignedcubegeometry.hh>

Public Types
typedef CoordType	ctype
	Type used for single coordinate coefficients.
typedef FieldVector< ctype, dim >	LocalCoordinate
	Type used for a vector of element coordinates.
typedef FieldVector< ctype, coorddim >	GlobalCoordinate
	Type used for a vector of world coordinates.
typedef ctype	Volume
	Type used for volume.
typedef std::conditional< dim==coorddim, DiagonalMatrix< ctype, dim >, FieldMatrix< ctype, dim, coorddim > >::type	JacobianTransposed
	Return type of jacobianTransposed. More...
typedef std::conditional< dim==coorddim, DiagonalMatrix< ctype, dim >, FieldMatrix< ctype, coorddim, dim > >::type	JacobianInverseTransposed
	Return type of jacobianInverseTransposed. More...
using	Jacobian = std::conditional_t< dim==coorddim, DiagonalMatrix< ctype, dim >, FieldMatrix< ctype, coorddim, dim > >
	Return type of jacobian. More...
using	JacobianInverse = std::conditional_t< dim==coorddim, DiagonalMatrix< ctype, dim >, FieldMatrix< ctype, dim, coorddim > >
	Return type of jacobianInverse. More...

Public Member Functions
	AxisAlignedCubeGeometry ()=default
	Constructs an empty geometry. More...
	AxisAlignedCubeGeometry (const Dune::FieldVector< ctype, coorddim > lower, const Dune::FieldVector< ctype, coorddim > upper)
	Constructor from a lower left and an upper right corner. More...
	AxisAlignedCubeGeometry (const Dune::FieldVector< ctype, coorddim > lower, const Dune::FieldVector< ctype, coorddim > upper, const std::bitset< coorddim > &axes)
	Constructor from a lower left and an upper right corner. More...
	AxisAlignedCubeGeometry (const Dune::FieldVector< ctype, coorddim > lower)
	Constructor from a single point only. More...
GeometryType	type () const
	Type of the cube. Here: a hypercube of the correct dimension.
GlobalCoordinate	global (const LocalCoordinate &local) const
	Map a point in local (element) coordinates to world coordinates.
LocalCoordinate	local (const GlobalCoordinate &global) const
	Map a point in global (world) coordinates to element coordinates.
JacobianTransposed	jacobianTransposed (const LocalCoordinate &local) const
	Jacobian transposed of the transformation from local to global coordinates.
JacobianInverseTransposed	jacobianInverseTransposed (const LocalCoordinate &local) const
	Inverse Jacobian transposed of the transformation from local to global coordinates.
Jacobian	jacobian (const LocalCoordinate &local) const
	Jacobian of the transformation from local to global coordinates.
JacobianInverse	jacobianInverse (const LocalCoordinate &local) const
	Inverse Jacobian of the transformation from local to global coordinates.
Volume	integrationElement (const LocalCoordinate &local) const
	Return the integration element, i.e., the determinant term in the integral transformation formula.
GlobalCoordinate	center () const
	Return center of mass of the element.
int	corners () const
	Return the number of corners of the element.
GlobalCoordinate	corner (int k) const
	Return world coordinates of the k-th corner of the element.
Volume	volume () const
	Return the element volume.
bool	affine () const
	Return if the element is affine. Here: yes.

Static Public Attributes
static constexpr int	mydimension = dim
	Dimension of the cube element.
static constexpr int	coorddimension = coorddim
	Dimension of the world space that the cube element is embedded in.

Detailed Description

template<class CoordType, unsigned int dim, unsigned int coorddim>
class Dune::AxisAlignedCubeGeometry< CoordType, dim, coorddim >

A geometry implementation for axis-aligned hypercubes.

This code is much faster than a generic implementation for hexahedral elements. All methods use the fact that a geometry for axis-aligned cubes is basically just a(n affine) scaling in the coordinate directions.

If dim < coorddim then local coordinates need to be suitably mapped to global ones. AxisAlignedCubeGeometry uses a special std::bitset 'axes' for this. 'axes' has coorddim entries, of which precisely 'dim' need to be set. Each set entry marks a local coordinate, i.e., a coordinate in which the cube has extension. The cube is flat in all other directions. Its coordinates in these directions is taking from the array called 'lower', which specifies the lower left corner of the hypercube.

In the case of dim==coorddim, the code goes into overdrive. Then special code path's are taken (statically) which omit the conditionals needed to sort out the embedding of local into global coordinates. Aggressive compiler/scheduler optimization becomes possible. Additionally, the types returned by the methods jacobianTransposed and jacobianInverseTransposed are dedicated types for diagonal matrices (DiagonalMatrix).

Template Parameters

CoordType	Type used for single coordinate coefficients
dim	Dimension of the cube
coorddim	Dimension of the space that the cube lives in

Member Typedef Documentation

Jacobian

template<class CoordType , unsigned int dim, unsigned int coorddim>

using Dune::AxisAlignedCubeGeometry< CoordType, dim, coorddim >::Jacobian = std::conditional_t<dim==coorddim, DiagonalMatrix<ctype,dim>, FieldMatrix<ctype,coorddim,dim> >

Return type of jacobian.

This is a fast DiagonalMatrix if dim==coorddim, and a FieldMatrix otherwise. The FieldMatrix will never contain more than one entry per row, hence it could be replaced by something more efficient.

JacobianInverse

template<class CoordType , unsigned int dim, unsigned int coorddim>

using Dune::AxisAlignedCubeGeometry< CoordType, dim, coorddim >::JacobianInverse = std::conditional_t<dim==coorddim, DiagonalMatrix<ctype,dim>, FieldMatrix<ctype,dim,coorddim> >

Return type of jacobianInverse.

This is a fast DiagonalMatrix if dim==coorddim, and a FieldMatrix otherwise. The FieldMatrix will never contain more than one entry per row, hence it could be replaced by something more efficient.

JacobianInverseTransposed

template<class CoordType , unsigned int dim, unsigned int coorddim>

typedef std::conditional<dim==coorddim,DiagonalMatrix<ctype,dim>,FieldMatrix<ctype,coorddim,dim>>::type Dune::AxisAlignedCubeGeometry< CoordType, dim, coorddim >::JacobianInverseTransposed

Return type of jacobianInverseTransposed.

This is a fast DiagonalMatrix if dim==coorddim, and a FieldMatrix otherwise. The FieldMatrix will never contain more than one entry per column, hence it could be replaced by something more efficient.

JacobianTransposed

template<class CoordType , unsigned int dim, unsigned int coorddim>

typedef std::conditional<dim==coorddim,DiagonalMatrix<ctype,dim>,FieldMatrix<ctype,dim,coorddim>>::type Dune::AxisAlignedCubeGeometry< CoordType, dim, coorddim >::JacobianTransposed

Return type of jacobianTransposed.

This is a fast DiagonalMatrix if dim==coorddim, and a FieldMatrix otherwise. The FieldMatrix will never contain more than one entry per row, hence it could be replaced by something more efficient.

Constructor & Destructor Documentation

AxisAlignedCubeGeometry() [1/4]

template<class CoordType , unsigned int dim, unsigned int coorddim>

Dune::AxisAlignedCubeGeometry< CoordType, dim, coorddim >::AxisAlignedCubeGeometry ( )

default

Constructs an empty geometry.

This constructor creates an empty (invalid) axis-aligned cube geometry. It may not be used in any way except for assigning other axis-aligned cube geometries to it. After assigning a valid geometry, it may be used without restrictions.

AxisAlignedCubeGeometry() [2/4]

template<class CoordType , unsigned int dim, unsigned int coorddim>

Dune::AxisAlignedCubeGeometry< CoordType, dim, coorddim >::AxisAlignedCubeGeometry ( const Dune::FieldVector< ctype, coorddim >  lower, const Dune::FieldVector< ctype, coorddim >  upper  )

inline

Constructor from a lower left and an upper right corner.

Note

Only for dim==coorddim

AxisAlignedCubeGeometry() [3/4]

template<class CoordType , unsigned int dim, unsigned int coorddim>

Dune::AxisAlignedCubeGeometry< CoordType, dim, coorddim >::AxisAlignedCubeGeometry ( const Dune::FieldVector< ctype, coorddim >  lower, const Dune::FieldVector< ctype, coorddim >  upper, const std::bitset< coorddim > &  axes  )

inline

Constructor from a lower left and an upper right corner.

Parameters

lower	Coordinates for the lower left corner.
upper	Coordinates for the upper right corner.
axes	Each bit set to 'true' here corresponds to a local coordinate axis. In other words, precisely 'dim' bits must be set here.

AxisAlignedCubeGeometry() [4/4]

template<class CoordType , unsigned int dim, unsigned int coorddim>

Dune::AxisAlignedCubeGeometry< CoordType, dim, coorddim >::AxisAlignedCubeGeometry ( const Dune::FieldVector< ctype, coorddim >  lower )

inline

Constructor from a single point only.

Note

Only for dim==0

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

• dune/geometry/axisalignedcubegeometry.hh