concepts::PartMappingHexahedron3d Class Reference
A 3D element map for a restriction of a given hexahedron element mapping. More...
#include <elementMaps3D.hh>
Public Member Functions | |
| PartMappingHexahedron3d * | clone () const override |
| Returns a copy of the map. More... | |
| MappingQuad3d * | face (const uint face) const override |
| Returns the mapping of the given face. More... | |
| MapReal3d | hessian (uint i, const Real x, const Real y, const Real z) const override |
| Returns the Hessian, the integer indicates which 3x3 submap of the 3x3xi (i=1..3) tensor is required. More... | |
| MapReal3d | jacobian (const Real x, const Real y, const Real z) const override |
| Returns the jacobian of the element map. More... | |
| virtual Real | jacobianDeterminant (const Real x, const Real y, const Real z) const |
| Returns the determinant of the Jacobian. More... | |
| virtual MapReal3d | jacobianInverse (const Real x, const Real y, const Real z) const |
| Computes the inverse of the jacobian: More... | |
| Real3d | operator() (Real x, Real y, Real z) const override |
| Returns a point in 3D mapped from the unit cube [0,1]3 onto the element in physical 3d space. More... | |
| PartMappingHexahedron3d * | part (const Real3d x0, const Real3d x1) const override |
| Returns a part of the mapping. More... | |
| PartMappingHexahedron3d (const MappingHexahedron3d &map, const Real3d x0, const Real3d x1) | |
| Constructor. More... | |
| PartMappingHexahedron3d (const PartMappingHexahedron3d &other) | |
| ~PartMappingHexahedron3d () override | |
Protected Member Functions | |
| std::ostream & | info (std::ostream &os) const override |
| Returns information in an output stream. More... | |
Private Member Functions | |
| const Real3d | xi_ (const Real x, const Real y, const Real z) const |
| Embedding of local coordinates to parent hexahedron reference domain. More... | |
Private Attributes | |
| const Real3d | d_ |
| Widths of the restricted hexahedron in coordinates of the parent map. More... | |
| std::unique_ptr< MappingHexahedron3d > | map_ |
| Parent hexahedron map. More... | |
| const Real3d | x0_ |
| Coordinate of the lower left front vertex in the reference domain of the parent map. More... | |
Detailed Description
A 3D element map for a restriction of a given hexahedron element mapping.
Let 
be the parent hexahedron. Then this element mapping is defined by
![\[ F_K(s,t,u) = F^p_K(x_{0,0} (1-s) + x_{1,0} s, x_{0,1} (1-t) + x_{1,1} t, x_{0,2} (1-u) + x_{1,2} u). \]](form_387.png)
- Todo:
- Possibly avoid copying the parent element (switch from unique_ptr to shared_ptr internally)
Definition at line 313 of file elementMaps3D.hh.
Constructor & Destructor Documentation
◆ PartMappingHexahedron3d() [1/2]
| concepts::PartMappingHexahedron3d::PartMappingHexahedron3d | ( | const MappingHexahedron3d & | map, |
| const Real3d | x0, | ||
| const Real3d | x1 | ||
| ) |
Constructor.
- Parameters
-
map Parent hexahedron element map x0,x1 lower left front and upper right back corner of the restricted domain in coordinates of the parent hexahedron
◆ PartMappingHexahedron3d() [2/2]
| concepts::PartMappingHexahedron3d::PartMappingHexahedron3d | ( | const PartMappingHexahedron3d & | other | ) |
◆ ~PartMappingHexahedron3d()
|
inlineoverride |
Definition at line 323 of file elementMaps3D.hh.
Member Function Documentation
◆ clone()
|
overridevirtual |
Returns a copy of the map.
Implements concepts::MappingHexahedron3d.
◆ face()
|
overridevirtual |
Returns the mapping of the given face.
Implements concepts::MappingHexahedron3d.
◆ hessian()
|
overridevirtual |
Returns the Hessian, the integer indicates which 3x3 submap of the 3x3xi (i=1..3) tensor is required.
Implements concepts::MappingHexahedron3d.
◆ info()
|
overrideprotectedvirtual |
Returns information in an output stream.
Implements concepts::MappingHexahedron3d.
◆ jacobian()
![\[ \left(\frac{\partial F_K}{\partial\vec\xi}\right) = \left\{\frac{\partial x^i}{\partial \xi_j}\right\}_{i,j=1}^3 \]](form_395.png)
◆ jacobianDeterminant()
|
inlinevirtualinherited |
Returns the determinant of the Jacobian.
Reimplemented in concepts::MapHexahedron3d.
Definition at line 200 of file elementMaps3D.hh.
◆ jacobianInverse()
|
inlinevirtualinherited |
Computes the inverse of the jacobian:
![\[ \left(\frac{\partial F_K}{\partial\vec\xi}\right)^{-1} = \left\{\frac{\partial \xi_i}{\partial x^j}\right\}_{i,j=1}^3 \]](form_396.png)
Reimplemented in concepts::MapHexahedron3d.
Definition at line 196 of file elementMaps3D.hh.
◆ operator()()
|
overridevirtual |
Returns a point in 3D mapped from the unit cube [0,1]3 onto the element in physical 3d space.
- Returns
Implements concepts::MappingHexahedron3d.
◆ part()
|
overridevirtual |
Returns a part of the mapping.
Implements concepts::MappingHexahedron3d.
◆ xi_()
|
inlineprivate |
Embedding of local coordinates to parent hexahedron reference domain.
Definition at line 341 of file elementMaps3D.hh.
Member Data Documentation
◆ d_
|
private |
Widths of the restricted hexahedron in coordinates of the parent map.
Definition at line 338 of file elementMaps3D.hh.
◆ map_
|
private |
Parent hexahedron map.
Definition at line 334 of file elementMaps3D.hh.
◆ x0_
|
private |
Coordinate of the lower left front vertex in the reference domain of the parent map.
Definition at line 336 of file elementMaps3D.hh.
The documentation for this class was generated from the following file:
- geometry/elementMaps3D.hh