dune-grid
2.1.1
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Public Types | |
enum | |
export grid dimension More... | |
enum | |
export geometry dimension More... | |
enum | |
export coordinate dimension More... | |
enum | |
export dimension of world More... | |
typedef GridImp::ctype | ctype |
define type used for coordinates in grid module | |
typedef FieldVector< ctype, mydim > | LocalCoordinate |
type of local coordinates | |
typedef FieldVector< ctype, cdim > | GlobalCoordinate |
type of the global coordinates | |
typedef FieldMatrix< ctype, cdim, mydim > | Jacobian |
type of jacobian (also of jacobian inverse transposed) | |
typedef FieldMatrix< ctype, mydim, cdim > | JacobianTransposed |
type of jacobian transposed | |
Public Member Functions | |
MakeableGeometry (int level) | |
void | make (const FieldVector< int, mydimension > &origin, int kuhnIndex) |
GeometryType | type () const |
Return the name of the reference element. The type can be used to access the Dune::GenericReferenceElement. | |
bool | affine () const |
Return true if the geometry mapping is affine and false otherwise. | |
int | corners () const |
Return the number of corners of the reference element. | |
GlobalCoordinate | corner (int i) const |
Obtain a corner of the geometry. | |
GlobalCoordinate | global (const LocalCoordinate &local) const |
Evaluate the map ![]() | |
LocalCoordinate | local (const GlobalCoordinate &global) const |
Evaluate the inverse map ![]() | |
ctype | integrationElement (const LocalCoordinate &local) const |
Return the factor appearing in the integral transformation formula. | |
ctype | volume () const |
return volume of geometry | |
GlobalCoordinate | center () const |
return center of geometry | |
const JacobianTransposed & | jacobianTransposed (const LocalCoordinate &local) const |
Return the transposed of the Jacobian. | |
const Jacobian & | jacobianInverseTransposed (const LocalCoordinate &local) const |
Return inverse of transposed of Jacobian. | |
Protected Types | |
typedef Geometry< mydim, cdim, GridImp > | ImplementationType |
Protected Member Functions | |
Geometry< mydim, cdim, GridImp > & | getRealImp () |
return reference to the real implementation | |
const Geometry< mydim, cdim, GridImp > & | getRealImp () const |
return reference to the real implementation | |
Protected Attributes | |
Geometry< mydim, cdim, GridImp > | realGeometry |
Friends | |
class | GridDefaultImplementation< GridImp::dimension, GridImp::dimensionworld, typename GridImp::ctype, typename GridImp::GridFamily > |
typedef GridImp::ctype Dune::Geometry< mydim, cdim, GridImp, Geometry >::ctype [inherited] |
define type used for coordinates in grid module
typedef FieldVector< ctype, cdim > Dune::Geometry< mydim, cdim, GridImp, Geometry >::GlobalCoordinate [inherited] |
type of the global coordinates
typedef Geometry <mydim,cdim,GridImp> Dune::Geometry< mydim, cdim, GridImp, Geometry >::ImplementationType [protected, inherited] |
typedef FieldMatrix<ctype,cdim,mydim> Dune::Geometry< mydim, cdim, GridImp, Geometry >::Jacobian [inherited] |
type of jacobian (also of jacobian inverse transposed)
typedef FieldMatrix< ctype, mydim, cdim > Dune::Geometry< mydim, cdim, GridImp, Geometry >::JacobianTransposed [inherited] |
type of jacobian transposed
typedef FieldVector<ctype, mydim> Dune::Geometry< mydim, cdim, GridImp, Geometry >::LocalCoordinate [inherited] |
type of local coordinates
anonymous enum [inherited] |
export grid dimension
anonymous enum [inherited] |
export geometry dimension
anonymous enum [inherited] |
export coordinate dimension
anonymous enum [inherited] |
export dimension of world
Dune::RefinementImp::Simplex::MakeableGeometry< mydimension, GridImp >::MakeableGeometry | ( | int | level | ) | [inline] |
bool Dune::Geometry< mydim, cdim, GridImp, Geometry >::affine | ( | ) | const [inline, inherited] |
Return true if the geometry mapping is affine and false otherwise.
GlobalCoordinate Dune::Geometry< mydim, cdim, GridImp, Geometry >::center | ( | ) | const [inline, inherited] |
return center of geometry
Note that this method is still subject to a change of name and semantics. At the moment, the center is not required to be the centroid of the geometry, or even the centroid of its corners. This makes the current default implementation acceptable, which maps the centroid of the reference element to the geometry. We may change the name (and semantic) of the method to centroid() if we find reasonably efficient ways to implement it properly.
GlobalCoordinate Dune::Geometry< mydim, cdim, GridImp, Geometry >::corner | ( | int | i | ) | const [inline, inherited] |
Obtain a corner of the geometry.
This method is for convenient access to the corners of the geometry. The same result could be achieved by by calling
global( genericReferenceElement.position( i, mydimension )
[in] | i | number of the corner (with respect to the generic reference element) |
int Dune::Geometry< mydim, cdim, GridImp, Geometry >::corners | ( | ) | const [inline, inherited] |
Return the number of corners of the reference element.
Since a geometry is a convex polytope the number of corners is a well-defined concept. The method is redundant because this information is also available via the reference element. It is here for efficiency and ease of use.
Geometry <mydim,cdim,GridImp>& Dune::Geometry< mydim, cdim, GridImp, Geometry >::getRealImp | ( | ) | [inline, protected, inherited] |
return reference to the real implementation
const Geometry <mydim,cdim,GridImp>& Dune::Geometry< mydim, cdim, GridImp, Geometry >::getRealImp | ( | ) | const [inline, protected, inherited] |
return reference to the real implementation
GlobalCoordinate Dune::Geometry< mydim, cdim, GridImp, Geometry >::global | ( | const LocalCoordinate & | local | ) | const [inline, inherited] |
Evaluate the map .
[in] | local | Position in the reference element ![]() |
ctype Dune::Geometry< mydim, cdim, GridImp, Geometry >::integrationElement | ( | const LocalCoordinate & | local | ) | const [inline, inherited] |
Return the factor appearing in the integral transformation formula.
Let denote the transformation described by the Geometry. Then the jacobian of the transformation is defined as the
matrix
Here we abbreviated and
for ease of readability.
The integration element for any
is then defined as
[in] | local | Position ![]() |
const Jacobian& Dune::Geometry< mydim, cdim, GridImp, Geometry >::jacobianInverseTransposed | ( | const LocalCoordinate & | local | ) | const [inline, inherited] |
Return inverse of transposed of Jacobian.
The Jacobian is defined in the documentation of integrationElement.
[in] | local | position ![]() |
The use of this function is to compute the gradient of some function at some position
, where
and
the transformation of the Geometry. When we set
and apply the chain rule we obtain
const JacobianTransposed& Dune::Geometry< mydim, cdim, GridImp, Geometry >::jacobianTransposed | ( | const LocalCoordinate & | local | ) | const [inline, inherited] |
Return the transposed of the Jacobian.
The Jacobian is defined in the documentation of integrationElement.
[in] | local | position ![]() |
LocalCoordinate Dune::Geometry< mydim, cdim, GridImp, Geometry >::local | ( | const GlobalCoordinate & | global | ) | const [inline, inherited] |
Evaluate the inverse map .
[in] | global | Position in ![]() |
void Dune::RefinementImp::Simplex::MakeableGeometry< mydimension, GridImp >::make | ( | const FieldVector< int, mydimension > & | origin, |
int | kuhnIndex | ||
) | [inline] |
GeometryType Dune::Geometry< mydim, cdim, GridImp, Geometry >::type | ( | ) | const [inline, inherited] |
Return the name of the reference element. The type can be used to access the Dune::GenericReferenceElement.
ctype Dune::Geometry< mydim, cdim, GridImp, Geometry >::volume | ( | ) | const [inline, inherited] |
return volume of geometry
friend class GridDefaultImplementation< GridImp::dimension, GridImp::dimensionworld,typename GridImp::ctype,typename GridImp::GridFamily > [friend, inherited] |
Geometry <mydim,cdim,GridImp> Dune::Geometry< mydim, cdim, GridImp, Geometry >::realGeometry [protected, inherited] |