Form

class dolfin.cpp.fem.Form(*args)

Bases: dolfin.cpp.fem.HierarchicalForm

Base class for UFC code generated by FFC for DOLFIN with option -l.

A note on the order of trial and test spaces: FEniCS numbers argument spaces starting with the leading dimension of the corresponding tensor (matrix). In other words, the test space is numbered 0 and the trial space is numbered 1. However, in order to have a notation that agrees with most existing finite element literature, in particular

a = a(u, v)

the spaces are numbered from right to

a: V_1 x V_0 -> R

Note

Figure out how to write this in math mode without it getting messed up in the Python version.

This is reflected in the ordering of the spaces that should be supplied to generated subclasses. In particular, when a bilinear form is initialized, it should be initialized as

a(V_1, V_0) = ...

where V_1 is the trial space and V_0 is the test space. However, when a form is initialized by a list of argument spaces (the variable function_spaces in the constructors below, the list of spaces should start with space number 0 (the test space) and then space number 1 (the trial space).

Overloaded versions

• Form(rank, num_coefficients)

  Create form of given rank with given number of coefficients

  Arguments

  rank (int)

  The rank.

  num_coefficients (int)

  The number of coefficients.

• Form(ufc_form, function_spaces, coefficients)

  Create form (shared data)

  Arguments

  ufc_form (ufc::form)

  The UFC form.

  function_spaces (list of FunctionSpace)

  Vector of function spaces.

  coefficients (list of GenericFunction)

  Vector of coefficients.

cell_domains()

Return cell domains (zero pointer if no domains have been specified)

Returns

MeshFunction

The cell domains.

check()

Check function spaces and coefficients

coefficient()

Overloaded versions

• coefficient(i)

  Return coefficient with given number

  Arguments

  i (int)

  Index

  Returns

  GenericFunction

  The coefficient.

• coefficient(name)

  Return coefficient with given name

  Arguments

  name (str)

  The name.

  Returns

  GenericFunction

  The coefficient.

coefficient_name()

Return the name of the coefficient with this number

Arguments

i (int)

The number

Returns

str

The name of the coefficient with the given number.

coefficient_number()

Return the number of the coefficient with this name

Arguments

name (str)

The name.

Returns

int

The number of the coefficient with the given name.

coefficients()

Return all coefficients

Returns

list of GenericFunction

All coefficients.

coloring()

Return coloring type for colored (multi-threaded) assembly of form over a mesh entity of a given dimension

Arguments

entity_dim (int)

Dimension.

Returns

numpy.array(int)

Coloring type.

exterior_facet_domains()

Return exterior facet domains (zero pointer if no domains have been specified)

Returns

MeshFunction

The exterior facet domains.

function_space(i)

Return function space for given argument

Arguments

i (std::size_t)

Index

Returns

_FunctionSpace_

Function space shared pointer.

function_spaces()

Return function spaces for arguments

Returns

list of FunctionSpace

Vector of function space shared pointers.

interior_facet_domains()

Return interior facet domains (zero pointer if no domains have been specified)

Returns

MeshFunction

The interior facet domains.

mesh()

Extract common mesh from form

Returns

Mesh

The mesh.

mesh_shared_ptr()

Return mesh shared pointer (if any)

Returns

Mesh

The mesh shared pointer.

num_coefficients()

Return number of coefficients

Returns

int

The number of coefficients.

rank()

Return rank of form (bilinear form = 2, linear form = 1, functional = 0, etc)

Returns

int

The rank of the form.

set_cell_domains()

Set cell domains

Arguments

cell_domains (MeshFunction)

The cell domains.

set_coefficient()

Overloaded versions

• set_coefficient(i, coefficient)

  Set coefficient with given number (shared pointer version)

  Arguments

  i (int)

  The given number.

  coefficient (GenericFunction)

  The coefficient.

• set_coefficient(name, coefficient)

  Set coefficient with given name (shared pointer version)

  Arguments

  name (str)

  The name.

  coefficient (GenericFunction)

  The coefficient.

set_coefficients()

Set all coefficients in given map. All coefficients in the given map, which may contain only a subset of the coefficients of the form, will be set.

Arguments

coefficients (GenericFunction)

The map of coefficients.

set_exterior_facet_domains()

Set exterior facet domains

Arguments

exterior_facet_domains (MeshFunction)

The exterior facet domains.

set_interior_facet_domains()

Set interior facet domains

Arguments

interior_facet_domains (MeshFunction)

The interior facet domains.

set_mesh()

Set mesh, necessary for functionals when there are no function spaces

Arguments

mesh (Mesh)

The mesh.

set_some_coefficients()

Set some coefficients in given map. Each coefficient in the given map will be set, if the name of the coefficient matches the name of a coefficient in the form.

This is useful when reusing the same coefficient map for several forms, or when some part of the form has been outcommented (for testing) in the UFL file, which means that the coefficient and attaching it to the form does not need to be outcommented in a C++ program using code from the generated UFL file.

Arguments

coefficients (GenericFunction)

The map of coefficients.

set_vertex_domains()

Set vertex domains

Arguments

vertex_domains (MeshFunction)

The vertex domains.

thisown None

The membership flag

ufc_form()

Return UFC form shared pointer

Returns

ufc::form

The UFC form.

vertex_domains()

Return vertex domains (zero pointer if no domains have been specified)

Returns

MeshFunction

The vertex domains.