Transformation of coordinates between ancestor and child. More...
#include <mllgeometry.hh>
Detailed Description
class Kaskade::MultiLevelLocalGeometry< Grid >
Transformation of coordinates between ancestor and child.
Provides a convenient transfer between a cell and its (possibly higher degree) ancestor.
This defines a mapping \( g:L\to G \), where \( L \) is the "local" grid cell and \( G \) the "global" grid cell. The evaluation of the Jacobian \( J = g'(x) \) is also supported.
It is possible to choose, which of child and ancestor are to be considered as "global". Moreover, it is possible to provide a flag that decides if (chained) transformations should be performed via geometry.global/local, or via localGeometry.global/local. The first option is more efficient for high degree ancestors, but it is only sensible, if the child is actually geometrically a subset of the father. This requirement might be violated in some special cases. In general the transformation from child to father is more efficient than the other way round. This has to do with the data structures in the grid.
- Todo:
- : implement pull-back and pull-forward operation for gradients
Definition at line 50 of file mllgeometry.hh.
Public Types | |
| enum | Direction { ChildIsGlobal , FatherIsGlobal } |
| typedef Grid::template Codim< 0 >::Entity | Entity |
| The entity type between which this geometry object maps. More... | |
Public Member Functions | |
| MultiLevelLocalGeometry (Grid const &grid, Cell const &child_, Cell const &ancestor_, MultiLevelLocalGeometry< Grid >::Direction direction_, bool geometricallyNested_=(dim==dimw), ctype tol_=-100) | |
| Constructor. More... | |
| Entity const & | localEntity () const |
| A reference to the local entity. More... | |
| void | global (std::vector< Dune::FieldVector< ctype, dim > > &x, std::vector< int > &componentsInside) const |
| Transformation from local to global. More... | |
| void | local (std::vector< Dune::FieldVector< ctype, dim > > &x, std::vector< int > &componentsInside) const |
| Transformation from global to local. More... | |
| Dune::FieldMatrix< ctype, dim, dim > | jacobianInverseTransposed (Dune::FieldVector< ctype, dim > const &xLocal) const |
| inverse of transposed Jacobian. More... | |
Protected Attributes | |
| Cell | child |
| Cell | ancestor |
Member Typedef Documentation
◆ Entity
| typedef Grid::template Codim<0>::Entity Kaskade::MultiLevelLocalGeometry< Grid >::Entity |
The entity type between which this geometry object maps.
Definition at line 74 of file mllgeometry.hh.
Member Enumeration Documentation
◆ Direction
| enum Kaskade::MultiLevelLocalGeometry::Direction |
| Enumerator | |
|---|---|
| ChildIsGlobal | |
| FatherIsGlobal | |
Definition at line 68 of file mllgeometry.hh.
Constructor & Destructor Documentation
◆ MultiLevelLocalGeometry()
|
inline |
Constructor.
- Parameters
-
grid Grid in which everthing takes place child_ Pointer to the child entity ancestor_ Pointer to the ancestor entity direction_ determine, which of both entities is seen as the global entitiy geometricallyNested_ true: assume that father and child are geometrically nested. This allows sometimes more efficient transformation, but is not alwasy feasible to assume this (for example in boundary adaptation). tol_ geometric tolerance for checking points to be inside cells or not. Use this to make sure that points inside are detected as such, even if by rounding errors they appear to be outside (by some negligible margin). Defaults to \( 100 \epsilon \).
- Todo:
- : (i) Simplify code by using entity pointer's comparison operator instead of ids (caveat: can ids lead to shorter hierarchies? Remember that entities copied to higher grid levels have the same id. If the comparison operators between entity pointers evaluate to "not equal" in this case, comparing ids may be more efficient. (ii) Check whether spanwidth can be computed as difference of the entity levels instead of using the loop. The same consideration as for (i) applies.
Definition at line 110 of file mllgeometry.hh.
Member Function Documentation
◆ global()
|
inline |
Transformation from local to global.
Definition at line 138 of file mllgeometry.hh.
Referenced by Kaskade::LocalGeometryInCoarseGridAncestor< Grid >::global().
◆ jacobianInverseTransposed()
|
inline |
inverse of transposed Jacobian.
The Jacobian is just the derivative of the local to global map \( g \). This methhod returns the transpose of its inverse.
Definition at line 188 of file mllgeometry.hh.
◆ local()
|
inline |
Transformation from global to local.
Only those points are returned that lie inside the local entity. All others are deleted during the process.
- Parameters
-
x a sequence of global positions. On return, only those are retained and transformed to local positions that are inside the local cell. componentsInside a sequence of the same length as x. Only the elements corresponding to retained positions are retained.
Usually, componentsInside contains an index list 0,1,...,size(x)-1 on entry. This way, on exit the vector contains the original indices of the retained positions.
Note that "insideness" can be controlled by setting the tol_ parameter on construction.
Definition at line 169 of file mllgeometry.hh.
Referenced by Kaskade::localProlongationMatrix(), and Kaskade::LocalTransfer< Space, CoarseningPolicy >::LocalTransfer().
◆ localEntity()
|
inline |
A reference to the local entity.
Definition at line 134 of file mllgeometry.hh.
Member Data Documentation
◆ ancestor
|
protected |
Definition at line 56 of file mllgeometry.hh.
Referenced by Kaskade::LocalGeometryInCoarseGridAncestor< Grid >::getFather(), Kaskade::MultiLevelLocalGeometry< Grid >::jacobianInverseTransposed(), Kaskade::MultiLevelLocalGeometry< Grid >::localEntity(), and Kaskade::MultiLevelLocalGeometry< Grid >::MultiLevelLocalGeometry().
◆ child
|
protected |
Definition at line 56 of file mllgeometry.hh.
Referenced by Kaskade::MultiLevelLocalGeometry< Grid >::jacobianInverseTransposed(), Kaskade::MultiLevelLocalGeometry< Grid >::localEntity(), and Kaskade::MultiLevelLocalGeometry< Grid >::MultiLevelLocalGeometry().
The documentation for this class was generated from the following file:
