Reference documentation for deal.II version Git 6dcd437 2017-07-22 22:48:07 +0200
Classes | Enumerations
Mappings between reference and real cell
Collaboration diagram for Mappings between reference and real cell:

Classes

class  Mapping< dim, spacedim >
 Abstract base class for mapping classes. More...
 
class  Mapping< dim, spacedim >::InternalDataBase
 
class  MappingC1< dim, spacedim >
 
class  MappingC1< dim, spacedim >::MappingC1Generic
 
class  MappingCartesian< dim, spacedim >
 
class  MappingCartesian< dim, spacedim >::InternalData
 
class  MappingFEField< dim, spacedim, VectorType, DoFHandlerType >
 
class  MappingFEField< dim, spacedim, VectorType, DoFHandlerType >::InternalData
 
class  MappingManifold< dim, spacedim >
 
class  MappingManifold< dim, spacedim >::InternalData
 
class  MappingQ< dim, spacedim >
 
class  MappingQ< dim, spacedim >::InternalData
 
class  MappingQ1< dim, spacedim >
 
struct  StaticMappingQ1< dim, spacedim >
 
class  MappingQ1Eulerian< dim, VectorType, spacedim >
 
class  MappingQEulerian< dim, VectorType, spacedim >
 
class  MappingQEulerian< dim, VectorType, spacedim >::MappingQEulerianGeneric::SupportQuadrature
 
class  MappingQEulerian< dim, VectorType, spacedim >::MappingQEulerianGeneric
 
class  MappingQGeneric< dim, spacedim >
 
class  MappingQGeneric< dim, spacedim >::InternalData
 

Enumerations

enum  MappingType {
  mapping_none = 0x0000, mapping_covariant = 0x0001, mapping_contravariant = 0x0002, mapping_covariant_gradient = 0x0003,
  mapping_contravariant_gradient = 0x0004, mapping_piola = 0x0100, mapping_piola_gradient = 0x0101, mapping_nedelec = 0x0200,
  mapping_raviart_thomas = 0x0300, mapping_bdm = mapping_raviart_thomas, mapping_covariant_hessian, mapping_contravariant_hessian,
  mapping_piola_hessian
}
 

Detailed Description

The classes in this module are used to map from unit coordinates to the coordinates of a cell in real cell. Most commonly, one uses the MappingQ1 class that provides a Q1 (bi-/trilinear) mapping (i.e. a mapping that is isoparametric for the usual Q1 elements). However, there are other classes that implement higher-order mappings as well to provide for curvilinear elements. These are discussed in the step-11 and step-12 tutorial programs.

The MappingQ1Eulerian class is an extension to the MappingQ1 class in that it accepts a vector that describes a displacement field for each position of the domain. This is used in Eulerian computations without the need to actually move vertices after each time step.

In addition, the MappingC1 class provides for a boundary of the computational domain that is not only curved, but also has a continuous derivative at the interface between two cells on the boundary.

Finally, the MappingCartesian class is an optimization for elements that are brick-shaped and with edges parallel to the coordinate axes.

Enumeration Type Documentation

The transformation type used for the Mapping::transform() functions.

Special finite elements may need special Mapping from the reference cell to the actual mesh cell. In order to be most flexible, this enum provides an extensible interface for arbitrary transformations. Nevertheless, these must be implemented in the transform() functions of inheriting classes in order to work.

Enumerator
mapping_none 

No mapping, i.e., shape functions are not mapped from a reference cell but instead are defined right on the real-space cell.

mapping_covariant 

Covariant mapping (see Mapping::transform() for details).

mapping_contravariant 

Contravariant mapping (see Mapping::transform() for details).

mapping_covariant_gradient 

Mapping of the gradient of a covariant vector field (see Mapping::transform() for details).

mapping_contravariant_gradient 

Mapping of the gradient of a contravariant vector field (see Mapping::transform() for details).

mapping_piola 

The Piola transform usually used for Hdiv elements. Piola transform is the standard transformation of vector valued elements in Hdiv. It amounts to a contravariant transformation scaled by the inverse of the volume element.

mapping_piola_gradient 

Transformation for the gradient of a vector field corresponding to a mapping_piola transformation (see Mapping::transform() for details).

mapping_nedelec 

The mapping used for Nedelec elements.

Curl-conforming elements are mapped as covariant vectors. Nevertheless, we introduce a separate mapping type, such that we can use the same flag for the vector and its gradient (see Mapping::transform() for details).

mapping_raviart_thomas 

The mapping used for Raviart-Thomas elements.

mapping_bdm 

The mapping used for BDM elements.

mapping_covariant_hessian 

The mappings for 2-forms and third order tensors.

These are mappings typpically applied to hessians transformed to the reference cell.

Mapping of the hessian of a covariant vector field (see Mapping::transform() for details).

mapping_contravariant_hessian 

Mapping of the hessian of a contravariant vector field (see Mapping::transform() for details).

mapping_piola_hessian 

Mapping of the hessian of a piola vector field (see Mapping::transform() for details).

Definition at line 50 of file mapping.h.