Reference documentation for deal.II version Git f0d9923401 2020-09-28 19:47:38 -0600
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Public Types | Public Member Functions | Public Attributes | Static Public Attributes | Private Attributes | List of all members
FiniteElementData< dim > Class Template Reference

#include <deal.II/fe/fe_base.h>

Inheritance diagram for FiniteElementData< dim >:
[legend]

Public Types

enum  Conformity {
  unknown = 0x00, L2 = 0x01, Hcurl = 0x02, Hdiv = 0x04,
  H1 = Hcurl | Hdiv, H2 = 0x0e
}
 

Public Member Functions

 FiniteElementData (const std::vector< unsigned int > &dofs_per_object, const unsigned int n_components, const unsigned int degree, const Conformity conformity=unknown, const BlockIndices &block_indices=BlockIndices())
 
 FiniteElementData (const std::vector< unsigned int > &dofs_per_object, const ReferenceCell::Type cell_type, const unsigned int n_components, const unsigned int degree, const Conformity conformity=unknown, const BlockIndices &block_indices=BlockIndices())
 
 FiniteElementData (const internal::GenericDoFsPerObject &data, const ReferenceCell::Type cell_type, const unsigned int n_components, const unsigned int degree, const Conformity conformity=unknown, const BlockIndices &block_indices=BlockIndices())
 
ReferenceCell::Type reference_cell_type () const
 
unsigned int n_unique_quads () const
 
unsigned int n_unique_faces () const
 
unsigned int n_dofs_per_vertex () const
 
unsigned int n_dofs_per_line () const
 
unsigned int n_dofs_per_quad (unsigned int face_no=0) const
 
unsigned int max_dofs_per_quad () const
 
unsigned int n_dofs_per_hex () const
 
unsigned int n_dofs_per_face (unsigned int face_no=0, unsigned int child=0) const
 
unsigned int max_dofs_per_face () const
 
unsigned int n_dofs_per_cell () const
 
template<int structdim>
unsigned int n_dofs_per_object (const unsigned int i=0) const
 
unsigned int n_components () const
 
unsigned int n_blocks () const
 
const BlockIndicesblock_indices () const
 
unsigned int tensor_degree () const
 
bool conforms (const Conformity) const
 
bool operator== (const FiniteElementData &) const
 
unsigned int get_first_line_index () const
 
unsigned int get_first_quad_index (const unsigned int quad_no=0) const
 
unsigned int get_first_hex_index () const
 
unsigned int get_first_face_line_index (const unsigned int face_no=0) const
 
unsigned int get_first_face_quad_index (const unsigned int face_no=0) const
 

Public Attributes

const unsigned int dofs_per_vertex
 
const unsigned int dofs_per_line
 
const unsigned int dofs_per_quad
 
const unsigned int dofs_per_hex
 
const unsigned int first_line_index
 
const unsigned int first_quad_index
 
const unsigned int first_hex_index
 
const unsigned int first_face_line_index
 
const unsigned int first_face_quad_index
 
const unsigned int dofs_per_face
 
const unsigned int dofs_per_cell
 
const unsigned int components
 
const unsigned int degree
 
const Conformity conforming_space
 
const BlockIndices block_indices_data
 

Static Public Attributes

static const unsigned int dimension = dim
 

Private Attributes

const ReferenceCell::Type cell_type
 
const unsigned int number_unique_quads
 
const unsigned int number_unique_faces
 
const std::vector< unsigned intn_dofs_on_quad
 
const unsigned int dofs_per_quad_max
 
const std::vector< unsigned intfirst_index_of_quads
 
const std::vector< unsigned intfirst_line_index_of_faces
 
const std::vector< unsigned intfirst_quad_index_of_faces
 
const std::vector< unsigned intn_dofs_on_face
 
const unsigned int dofs_per_face_max
 

Detailed Description

template<int dim>
class FiniteElementData< dim >

A class that declares a number of scalar constant variables that describe basic properties of a finite element implementation. This includes, for example, the number of degrees of freedom per vertex, line, or cell; the number of vector components; etc.

The kind of information stored here is computed during initialization of a finite element object and is passed down to this class via its constructor. The data stored by this class is part of the public interface of the FiniteElement class (which derives from the current class). See there for more information.

Definition at line 208 of file fe_base.h.

Member Enumeration Documentation

◆ Conformity

template<int dim>
enum FiniteElementData::Conformity

Enumerator for the different types of continuity a finite element may have. Continuity is measured by the Sobolev space containing the constructed finite element space and is also called this way.

Note that certain continuities may imply others. For instance, a function in H1 is in Hcurl and Hdiv as well.

If you are interested in continuity in the classical sense, then the following relations hold:

  1. H1 implies that the function is continuous over cell boundaries.

  2. H2 implies that the function is continuously differentiable over cell boundaries.

  3. L2 indicates that the element is discontinuous. Since discontinuous elements have no topological couplings between grid cells and code may actually depend on this property, L2 conformity is handled in a special way in the sense that it is not implied by any higher conformity.

In order to test if a finite element conforms to a certain space, use FiniteElementData<dim>::conforms().

Enumerator
unknown 

Indicates incompatible continuities of a system.

L2 

Discontinuous elements. See above!

Hcurl 

Conformity with the space Hcurl (continuous tangential component of a vector field)

Hdiv 

Conformity with the space Hdiv (continuous normal component of a vector field)

H1 

Conformity with the space H1 (continuous)

H2 

Conformity with the space H2 (continuously differentiable)

Definition at line 241 of file fe_base.h.

Constructor & Destructor Documentation

◆ FiniteElementData() [1/3]

template<int dim>
FiniteElementData< dim >::FiniteElementData ( const std::vector< unsigned int > &  dofs_per_object,
const unsigned int  n_components,
const unsigned int  degree,
const Conformity  conformity = unknown,
const BlockIndices block_indices = BlockIndices() 
)

Constructor, computing all necessary values from the distribution of dofs to geometrical objects.

Parameters
[in]dofs_per_objectA vector that describes the number of degrees of freedom on geometrical objects for each dimension. This vector must have size dim+1, and entry 0 describes the number of degrees of freedom per vertex, entry 1 the number of degrees of freedom per line, etc. As an example, for the common \(Q_1\) Lagrange element in 2d, this vector would have elements (1,0,0). On the other hand, for a \(Q_3\) element in 3d, it would have entries (1,2,4,8).
[in]n_componentsNumber of vector components of the element.
[in]degreeThe maximal polynomial degree of any of the shape functions of this element in any variable on the reference element. For example, for the \(Q_1\) element (in any space dimension), this would be one; this is so despite the fact that the element has a shape function of the form \(\hat x\hat y\) (in 2d) and \(\hat x\hat y\hat z\) (in 3d), which, although quadratic and cubic polynomials, are still only linear in each reference variable separately. The information provided by this variable is typically used in determining what an appropriate quadrature formula is.
[in]conformityA variable describing which Sobolev space this element conforms to. For example, the \(Q_p\) Lagrange elements (implemented by the FE_Q class) are \(H^1\) conforming, whereas the Raviart-Thomas element (implemented by the FE_RaviartThomas class) is \(H_\text{div}\) conforming; finally, completely discontinuous elements (implemented by the FE_DGQ class) are only \(L_2\) conforming.
[in]block_indicesAn argument that describes how the base elements of a finite element are grouped. The default value constructs a single block that consists of all dofs_per_cell degrees of freedom. This is appropriate for all "atomic" elements (including non-primitive ones) and these can therefore omit this argument. On the other hand, composed elements such as FESystem will want to pass a different value here.

Definition at line 124 of file fe_data.cc.

◆ FiniteElementData() [2/3]

template<int dim>
FiniteElementData< dim >::FiniteElementData ( const std::vector< unsigned int > &  dofs_per_object,
const ReferenceCell::Type  cell_type,
const unsigned int  n_components,
const unsigned int  degree,
const Conformity  conformity = unknown,
const BlockIndices block_indices = BlockIndices() 
)

The same as above but with the difference that also the type of the underlying geometric entity can be specified.

Definition at line 143 of file fe_data.cc.

◆ FiniteElementData() [3/3]

template<int dim>
FiniteElementData< dim >::FiniteElementData ( const internal::GenericDoFsPerObject data,
const ReferenceCell::Type  cell_type,
const unsigned int  n_components,
const unsigned int  degree,
const Conformity  conformity = unknown,
const BlockIndices block_indices = BlockIndices() 
)

The same as above but instead of passing a vector containing the degrees of freedoms per object a struct of type GenericDoFsPerObject. This allows that 2D objects might have different number of degrees of freedoms, which is particular useful for cells with triangles and quadrilaterals as faces.

Definition at line 159 of file fe_data.cc.

Member Function Documentation

◆ reference_cell_type()

template<int dim>
ReferenceCell::Type FiniteElementData< dim >::reference_cell_type ( ) const

Return type of reference cell.

◆ n_unique_quads()

template<int dim>
unsigned int FiniteElementData< dim >::n_unique_quads ( ) const

Number of unique quads. If all quads have the same type, the value is one; else it equals the number of quads.

◆ n_unique_faces()

template<int dim>
unsigned int FiniteElementData< dim >::n_unique_faces ( ) const

Number of unique faces. If all faces have the same type, the value is one; else it equals the number of faces.

◆ n_dofs_per_vertex()

template<int dim>
unsigned int FiniteElementData< dim >::n_dofs_per_vertex ( ) const

Number of dofs per vertex.

◆ n_dofs_per_line()

template<int dim>
unsigned int FiniteElementData< dim >::n_dofs_per_line ( ) const

Number of dofs per line. Not including dofs on lower dimensional objects.

◆ n_dofs_per_quad()

template<int dim>
unsigned int FiniteElementData< dim >::n_dofs_per_quad ( unsigned int  face_no = 0) const

Number of dofs per quad. Not including dofs on lower dimensional objects.

◆ max_dofs_per_quad()

template<int dim>
unsigned int FiniteElementData< dim >::max_dofs_per_quad ( ) const

Maximum number of dofs per quad. Not including dofs on lower dimensional objects.

◆ n_dofs_per_hex()

template<int dim>
unsigned int FiniteElementData< dim >::n_dofs_per_hex ( ) const

Number of dofs per hex. Not including dofs on lower dimensional objects.

◆ n_dofs_per_face()

template<int dim>
unsigned int FiniteElementData< dim >::n_dofs_per_face ( unsigned int  face_no = 0,
unsigned int  child = 0 
) const

Number of dofs per face, accumulating degrees of freedom of all lower dimensional objects.

◆ max_dofs_per_face()

template<int dim>
unsigned int FiniteElementData< dim >::max_dofs_per_face ( ) const

Maximum number of dofs per face, accumulating degrees of freedom of all lower dimensional objects.

◆ n_dofs_per_cell()

template<int dim>
unsigned int FiniteElementData< dim >::n_dofs_per_cell ( ) const

Number of dofs per cell, accumulating degrees of freedom of all lower dimensional objects.

◆ n_dofs_per_object()

template<int dim>
template<int structdim>
unsigned int FiniteElementData< dim >::n_dofs_per_object ( const unsigned int  i = 0) const

Return the number of degrees per structdim-dimensional object. For structdim==0, the function therefore returns dofs_per_vertex, for structdim==1 dofs_per_line, etc. This function is mostly used to allow some template trickery for functions that should work on all sorts of objects without wanting to use the different names (vertex, line, ...) associated with these objects.

◆ n_components()

template<int dim>
unsigned int FiniteElementData< dim >::n_components ( ) const

Number of components. See the glossary for more information.

◆ n_blocks()

template<int dim>
unsigned int FiniteElementData< dim >::n_blocks ( ) const

Number of blocks. See the glossary for more information.

◆ block_indices()

template<int dim>
const BlockIndices& FiniteElementData< dim >::block_indices ( ) const

Detailed information on block sizes.

◆ tensor_degree()

template<int dim>
unsigned int FiniteElementData< dim >::tensor_degree ( ) const

Maximal polynomial degree of a shape function in a single coordinate direction.

This function can be used to determine the optimal quadrature rule.

◆ conforms()

template<int dim>
bool FiniteElementData< dim >::conforms ( const Conformity  ) const

Test whether a finite element space conforms to a certain Sobolev space.

Note
This function will return a true value even if the finite element space has higher regularity than asked for.

◆ operator==()

template<int dim>
bool FiniteElementData< dim >::operator== ( const FiniteElementData< dim > &  f) const

Comparison operator.

Definition at line 202 of file fe_data.cc.

◆ get_first_line_index()

template<int dim>
unsigned int FiniteElementData< dim >::get_first_line_index ( ) const

Return first index of dof on a line.

◆ get_first_quad_index()

template<int dim>
unsigned int FiniteElementData< dim >::get_first_quad_index ( const unsigned int  quad_no = 0) const

Return first index of dof on a quad.

◆ get_first_hex_index()

template<int dim>
unsigned int FiniteElementData< dim >::get_first_hex_index ( ) const

Return first index of dof on a hexahedron.

◆ get_first_face_line_index()

template<int dim>
unsigned int FiniteElementData< dim >::get_first_face_line_index ( const unsigned int  face_no = 0) const

Return first index of dof on a line for face data.

◆ get_first_face_quad_index()

template<int dim>
unsigned int FiniteElementData< dim >::get_first_face_quad_index ( const unsigned int  face_no = 0) const

Return first index of dof on a quad for face data.

Member Data Documentation

◆ dimension

template<int dim>
const unsigned int FiniteElementData< dim >::dimension = dim
static

The dimension of the finite element, which is the template parameter dim

Definition at line 281 of file fe_base.h.

◆ cell_type

template<int dim>
const ReferenceCell::Type FiniteElementData< dim >::cell_type
private

Reference cell type.

Definition at line 287 of file fe_base.h.

◆ number_unique_quads

template<int dim>
const unsigned int FiniteElementData< dim >::number_unique_quads
private

Number of unique quads. If all quads have the same type, the value is one; else it equals the number of quads.

Definition at line 293 of file fe_base.h.

◆ number_unique_faces

template<int dim>
const unsigned int FiniteElementData< dim >::number_unique_faces
private

Number of unique faces. If all faces have the same type, the value is one; else it equals the number of faces.

Definition at line 299 of file fe_base.h.

◆ dofs_per_vertex

template<int dim>
const unsigned int FiniteElementData< dim >::dofs_per_vertex

Number of degrees of freedom on a vertex.

Definition at line 305 of file fe_base.h.

◆ dofs_per_line

template<int dim>
const unsigned int FiniteElementData< dim >::dofs_per_line

Number of degrees of freedom in a line; not including the degrees of freedom on the vertices of the line.

Definition at line 311 of file fe_base.h.

◆ n_dofs_on_quad

template<int dim>
const std::vector<unsigned int> FiniteElementData< dim >::n_dofs_on_quad
private

Number of degrees of freedom on quads. If all quads have the same number of degrees freedoms the values equal dofs_per_quad.

Definition at line 318 of file fe_base.h.

◆ dofs_per_quad

template<int dim>
const unsigned int FiniteElementData< dim >::dofs_per_quad

Number of degrees of freedom in a quadrilateral; not including the degrees of freedom on the lines and vertices of the quadrilateral.

Definition at line 325 of file fe_base.h.

◆ dofs_per_quad_max

template<int dim>
const unsigned int FiniteElementData< dim >::dofs_per_quad_max
private

Maximum number of degrees of freedom on any quad.

Definition at line 331 of file fe_base.h.

◆ dofs_per_hex

template<int dim>
const unsigned int FiniteElementData< dim >::dofs_per_hex

Number of degrees of freedom in a hexahedron; not including the degrees of freedom on the quadrilaterals, lines and vertices of the hexahedron.

Definition at line 338 of file fe_base.h.

◆ first_line_index

template<int dim>
const unsigned int FiniteElementData< dim >::first_line_index

First index of dof on a line.

Definition at line 343 of file fe_base.h.

◆ first_index_of_quads

template<int dim>
const std::vector<unsigned int> FiniteElementData< dim >::first_index_of_quads
private

First index of a quad. If all quads have the same number of degrees of freedom, only the first index of the first quad is stored since the indices of the others can be simply recomputed.

Definition at line 351 of file fe_base.h.

◆ first_quad_index

template<int dim>
const unsigned int FiniteElementData< dim >::first_quad_index

First index of dof on a quad.

Definition at line 357 of file fe_base.h.

◆ first_hex_index

template<int dim>
const unsigned int FiniteElementData< dim >::first_hex_index

First index of dof on a hexahedron.

Definition at line 362 of file fe_base.h.

◆ first_line_index_of_faces

template<int dim>
const std::vector<unsigned int> FiniteElementData< dim >::first_line_index_of_faces
private

Index of the first line of all faces.

Definition at line 368 of file fe_base.h.

◆ first_face_line_index

template<int dim>
const unsigned int FiniteElementData< dim >::first_face_line_index

First index of dof on a line for face data.

Definition at line 374 of file fe_base.h.

◆ first_quad_index_of_faces

template<int dim>
const std::vector<unsigned int> FiniteElementData< dim >::first_quad_index_of_faces
private

Index of the first quad of all faces.

Definition at line 380 of file fe_base.h.

◆ first_face_quad_index

template<int dim>
const unsigned int FiniteElementData< dim >::first_face_quad_index

First index of dof on a quad for face data.

Definition at line 386 of file fe_base.h.

◆ n_dofs_on_face

template<int dim>
const std::vector<unsigned int> FiniteElementData< dim >::n_dofs_on_face
private

Number of degrees of freedom on faces. If all faces have the same number of degrees freedoms the values equal dofs_per_quad.

Definition at line 393 of file fe_base.h.

◆ dofs_per_face

template<int dim>
const unsigned int FiniteElementData< dim >::dofs_per_face

Number of degrees of freedom on a face. This is the accumulated number of degrees of freedom on all the objects of dimension up to dim-1 constituting a face.

Definition at line 401 of file fe_base.h.

◆ dofs_per_face_max

template<int dim>
const unsigned int FiniteElementData< dim >::dofs_per_face_max
private

Maximum number of degrees of freedom on any face.

Definition at line 407 of file fe_base.h.

◆ dofs_per_cell

template<int dim>
const unsigned int FiniteElementData< dim >::dofs_per_cell

Total number of degrees of freedom on a cell. This is the accumulated number of degrees of freedom on all the objects of dimension up to dim constituting a cell.

Definition at line 415 of file fe_base.h.

◆ components

template<int dim>
const unsigned int FiniteElementData< dim >::components

Number of vector components of this finite element, and dimension of the image space. For vector-valued finite elements (i.e. when this number is greater than one), the number of vector components is in many cases equal to the number of base elements glued together with the help of the FESystem class. However, for elements like the Nedelec element, the number is greater than one even though we only have one base element.

Definition at line 425 of file fe_base.h.

◆ degree

template<int dim>
const unsigned int FiniteElementData< dim >::degree

Maximal polynomial degree of a shape function in a single coordinate direction.

Definition at line 431 of file fe_base.h.

◆ conforming_space

template<int dim>
const Conformity FiniteElementData< dim >::conforming_space

Indicate the space this element conforms to.

Definition at line 436 of file fe_base.h.

◆ block_indices_data

template<int dim>
const BlockIndices FiniteElementData< dim >::block_indices_data

Storage for an object describing the sizes of each block of a compound element. For an element which is not an FESystem, this contains only a single block with length dofs_per_cell.

Definition at line 443 of file fe_base.h.


The documentation for this class was generated from the following files: