Reference documentation for deal.II version Git ca6ed5c 2017-11-20 14:53:00 +0100
Modules | Namespaces | Classes | Enumerations | Functions
Finite element access/FEValues classes
Collaboration diagram for Finite element access/FEValues classes:

Modules

 Handling vector valued problems
 

Namespaces

 CellSimilarity
 
 internal
 
 FEValuesViews
 
 FEValuesExtractors
 

Classes

class  internal::FEValues::MappingRelatedData< dim, spacedim >
 
class  internal::FEValues::FiniteElementRelatedData< dim, spacedim >
 
struct  FEValuesViews::Scalar< dim, spacedim >::OutputType< Number >
 
struct  FEValuesViews::Scalar< dim, spacedim >::ShapeFunctionData
 
class  FEValuesViews::Scalar< dim, spacedim >
 
struct  FEValuesViews::Vector< dim, spacedim >::OutputType< Number >
 
struct  FEValuesViews::Vector< dim, spacedim >::ShapeFunctionData
 
class  FEValuesViews::Vector< dim, spacedim >
 
struct  FEValuesViews::SymmetricTensor< 2, dim, spacedim >::OutputType< Number >
 
struct  FEValuesViews::SymmetricTensor< 2, dim, spacedim >::ShapeFunctionData
 
class  FEValuesViews::SymmetricTensor< 2, dim, spacedim >
 
struct  FEValuesViews::Tensor< 2, dim, spacedim >::OutputType< Number >
 
struct  FEValuesViews::Tensor< 2, dim, spacedim >::ShapeFunctionData
 
class  FEValuesViews::Tensor< 2, dim, spacedim >
 
class  FEValuesBase< dim, spacedim >
 
class  FEValues< dim, spacedim >
 
class  FEFaceValuesBase< dim, spacedim >
 
class  FEFaceValues< dim, spacedim >
 
class  FESubfaceValues< dim, spacedim >
 
struct  FEValuesExtractors::Scalar
 
struct  FEValuesExtractors::Vector
 
struct  FEValuesExtractors::SymmetricTensor< rank >
 
struct  FEValuesExtractors::Tensor< rank >
 

Enumerations

enum  UpdateFlags {
  update_default = 0, update_values = 0x0001, update_gradients = 0x0002, update_hessians = 0x0004,
  update_3rd_derivatives = 0x0008, update_boundary_forms = 0x0010, update_quadrature_points = 0x0020, update_JxW_values = 0x0040,
  update_normal_vectors = 0x0080, update_face_normal_vectors = update_normal_vectors, update_cell_normal_vectors = update_normal_vectors, update_jacobians = 0x0100,
  update_jacobian_grads = 0x0200, update_inverse_jacobians = 0x0400, update_covariant_transformation = 0x0800, update_contravariant_transformation = 0x1000,
  update_transformation_values = 0x2000, update_transformation_gradients = 0x4000, update_volume_elements = 0x10000, update_jacobian_pushed_forward_grads = 0x100000,
  update_jacobian_2nd_derivatives = 0x200000, update_jacobian_pushed_forward_2nd_derivatives = 0x400000, update_jacobian_3rd_derivatives = 0x800000, update_jacobian_pushed_forward_3rd_derivatives = 0x1000000,
  update_q_points = update_quadrature_points, update_second_derivatives = update_hessians, update_piola = update_volume_elements | update_contravariant_transformation, update_mapping
}
 
enum  CellSimilarity::Similarity { CellSimilarity::none, CellSimilarity::translation, CellSimilarity::inverted_translation, CellSimilarity::invalid_next_cell }
 

Functions

template<class StreamType >
StreamType & operator<< (StreamType &s, const UpdateFlags u)
 
UpdateFlags operator| (const UpdateFlags f1, const UpdateFlags f2)
 
UpdateFlagsoperator|= (UpdateFlags &f1, const UpdateFlags f2)
 
UpdateFlags operator& (const UpdateFlags f1, const UpdateFlags f2)
 
UpdateFlagsoperator&= (UpdateFlags &f1, const UpdateFlags f2)
 

Detailed Description

The classes in this module are used when one wants to assemble matrices or vectors. They link finite elements, quadrature objects, and mappings: the finite element classes describe a finite element space on a unit cell (i.e. the unit line segment, square, or cube [0,1]^d), the quadrature classes describe where quadrature points are located and what weight they have, and the mapping classes describe how to map a point from the unit cell to a real cell and back. Since integration happens at quadrature points on the real cell, and needs to know their location as well as the values and gradients of finite element shape functions at these points. The FEValues class coordinates getting this information. For integrations on faces (for example for integration on the boundary, or interfaces between cells), the FEFaceValues class offers similar functionality as the FEValues class does for cells. Finally, the FESubfaceValues class offers the possibility to ingrate on parts of faces if the neighboring cell is refined and the present cell shares only a part of its face with the neighboring cell. If vector-valued elements are used, the FEValues and related classes allow access to all vector components; if one wants to pick individual components, there are extractor classes that make this task simpler, as described in the Handling vector valued problems module.

The last member of this group, the UpdateFlags enumeration, is used as an optimization: instead of letting the FEValues class compute every possible piece of data relating to a given finite element on a cell, you have to specify up front which information you are actually interested in. The UpdateFlags enumeration is used to offer symbolic names denoting what you want the FEValues class to compute.

All these classes are used in all tutorial programs from step-3 onward, and are described there in significant detail.

The actual workings of the FEValues class and friends is complicated because it has to be general yet efficient. The page on The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues attempts to give an overview of how this works.

Enumeration Type Documentation

The enum type given to the constructors of FEValues, FEFaceValues and FESubfaceValues, telling those objects which data will be needed on each mesh cell.

Selecting these flags in a restrictive way is crucial for the efficiency of FEValues::reinit(), FEFaceValues::reinit() and FESubfaceValues::reinit(). Therefore, only the flags actually needed should be selected. It is the responsibility of the involved Mapping and FiniteElement to add additional flags according to their own requirements. For instance, most finite elements will add update_covariant_transformation if update_gradients is selected. By default, all flags are off, i.e. no reinitialization will be done.

You can select more than one flag by concatenation using the bitwise or operator|(UpdateFlags,UpdateFlags).

Use of these flags flags

More information on the use of this type both in user code as well as internally can be found in the documentation modules on The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues and How Mapping, FiniteElement, and FEValues work together.

Enumerator
update_default 

No update.

update_values 

Shape function values.

Compute the values of the shape functions at the quadrature points on the real space cell. For the usual Lagrange elements, these values are equal to the values of the shape functions at the quadrature points on the unit cell, but they are different for more complicated elements, such as FE_RaviartThomas elements.

update_gradients 

Shape function gradients.

Compute the gradients of the shape functions in coordinates of the real cell.

update_hessians 

Second derivatives of shape functions.

Compute the second derivatives of the shape functions in coordinates of the real cell.

update_3rd_derivatives 

Third derivatives of shape functions.

Compute the third derivatives of the shape functions in coordinates of the real cell

update_boundary_forms 

Outer normal vector, not normalized.

Vector product of tangential vectors, yielding a normal vector with a length corresponding to the surface element; may be more efficient than computing both.

update_quadrature_points 

Transformed quadrature points.

Compute the quadrature points transformed into real cell coordinates.

update_JxW_values 

Transformed quadrature weights.

Compute the quadrature weights on the real cell, i.e. the weights of the quadrature rule multiplied with the determinant of the Jacobian of the transformation from reference to real cell.

update_normal_vectors 

Normal vectors.

Compute the normal vectors, either for a face or for a cell of codimension one. Setting this flag for any other object will raise an error.

update_face_normal_vectors 
Deprecated:
Use update_normal_vectors instead.
update_cell_normal_vectors 
Deprecated:
Use update_normal_vectors instead.
update_jacobians 

Volume element.

Compute the Jacobian of the transformation from the reference cell to the real cell.

update_jacobian_grads 

Gradient of volume element.

Compute the derivatives of the Jacobian of the transformation.

update_inverse_jacobians 

Volume element.

Compute the inverse Jacobian of the transformation from the reference cell to the real cell.

update_covariant_transformation 

Covariant transformation.

Compute all values the Mapping needs to perform a contravariant transformation of vectors. For special mappings like MappingCartesian this may be simpler than update_inverse_jacobians.

update_contravariant_transformation 

Contravariant transformation.

Compute all values the Mapping needs to perform a contravariant transformation of vectors. For special mappings like MappingCartesian this may be simpler than update_jacobians.

update_transformation_values 

Shape function values of transformation.

Compute the shape function values of the transformation defined by the Mapping.

update_transformation_gradients 

Shape function gradients of transformation.

Compute the shape function gradients of the transformation defined by the Mapping.

update_volume_elements 

Determinant of the Jacobian.

Compute the volume element in each quadrature point.

update_jacobian_pushed_forward_grads 

Compute the derivatives of the Jacobian of the transformation pushed forward to the real cell coordinates.

update_jacobian_2nd_derivatives 

Compute the second derivatives of the Jacobian of the transformation.

update_jacobian_pushed_forward_2nd_derivatives 

Compute the second derivatives of the Jacobian of the transformation pushed forward to the real cell coordinates.

update_jacobian_3rd_derivatives 

Compute the third derivatives of the Jacobian of the transformation.

update_jacobian_pushed_forward_3rd_derivatives 

Compute the third derivatives of the Jacobian of the transformation pushed forward to the real cell coordinates.

update_q_points 
Deprecated:
Use update_quadrature_points instead.
update_second_derivatives 
Deprecated:
Use update_hessians instead.
update_piola 

Values needed for Piola transform.

Combination of the flags needed for Piola transform of Hdiv elements.

update_mapping 

Combination of the flags that require a mapping calculation

Definition at line 62 of file fe_update_flags.h.

Enumerator
none 

The cells differ by something besides a translation or inverted translations.

translation 

The cells differ by a translation.

inverted_translation 

The cells differ by an inverted translation.

invalid_next_cell 

The next cell is not valid.

Definition at line 361 of file fe_update_flags.h.

Function Documentation

template<class StreamType >
StreamType& operator<< ( StreamType &  s,
const UpdateFlags  u 
)
inline

Output operator which outputs update flags as a set of or'd text values.

The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues

Definition at line 245 of file fe_update_flags.h.

UpdateFlags operator| ( const UpdateFlags  f1,
const UpdateFlags  f2 
)
inline

Global operator which returns an object in which all bits are set which are either set in the first or the second argument. This operator exists since if it did not then the result of the bit-or operator | would be an integer which would in turn trigger a compiler warning when we tried to assign it to an object of type UpdateFlags.

The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues

Definition at line 285 of file fe_update_flags.h.

UpdateFlags& operator|= ( UpdateFlags f1,
const UpdateFlags  f2 
)
inline

Global operator which sets the bits from the second argument also in the first one.

The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues

Definition at line 304 of file fe_update_flags.h.

UpdateFlags operator& ( const UpdateFlags  f1,
const UpdateFlags  f2 
)
inline

Global operator which returns an object in which all bits are set which are set in the first as well as the second argument. This operator exists since if it did not then the result of the bit-and operator & would be an integer which would in turn trigger a compiler warning when we tried to assign it to an object of type UpdateFlags.

The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues

Definition at line 323 of file fe_update_flags.h.

UpdateFlags& operator&= ( UpdateFlags f1,
const UpdateFlags  f2 
)
inline

Global operator which clears all the bits in the first argument if they are not also set in the second argument.

The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues

Definition at line 340 of file fe_update_flags.h.