DUNE PDELab (git)

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
CoordTypeType used for single coordinate coefficients
dimDimension of the cube
coorddimDimension 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
lowerCoordinates for the lower left corner.
upperCoordinates for the upper right corner.
axesEach 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

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