FunctionSpace

class dolfin.cpp.function.FunctionSpace(*args)

Bases: dolfin.cpp.common.Variable, dolfin.cpp.function.HierarchicalFunctionSpace

This class represents a finite element function space defined by a mesh, a finite element, and a local-to-global mapping of the degrees of freedom (dofmap).

Overloaded versions

• FunctionSpace(mesh, element, dofmap)

  Create function space for given mesh, element and dofmap (shared data)

  Arguments

  mesh (Mesh)

  The mesh.

  element (FiniteElement)

  The element.

  dofmap (GenericDofMap)

  The dofmap.

• FunctionSpace(mesh)

  Create empty function space for later initialization. This constructor is intended for use by any sub-classes which need to construct objects before the initialisation of the base class. Data can be attached to the base class using FunctionSpace::attach(...).

  Arguments

  mesh (Mesh)

  The mesh.

• FunctionSpace(V)

  Copy constructor

  Arguments

  V (FunctionSpace)

  The object to be copied.

assign()

Assignment operator

Arguments

V (FunctionSpace)

Another function space.

child()

Return the child FunctionSpace in the hierarchy

collapse()

Overloaded versions

• collapse()

  Collapse a subspace and return a new function space

  Returns

  FunctionSpace

  The new function space.

• collapse(collapsed_dofs)

  Collapse a subspace and return a new function space and a map from new to old dofs

  Arguments

  collapsed_dofs (std::unordered_map<std::size_t, std::size_t>)

  The map from new to old dofs.

  Returns

  FunctionSpace

  The new function space.

component()

Return component w.r.t. to root superspace, i.e.

W.sub(1).sub(0) == [1, 0].

Returns

numpy.array(int)

The component (w.r.t to root superspace).

contains()

Check whether V is subspace of this, or this itself

Arguments

V (FunctionSpace)

The space to be tested for inclusion.

Returns

bool

True if V is contained or equal to this.

dim()

Return dimension of function space

Returns

int

The dimension of the function space.

dofmap()

Return dofmap

Returns

GenericDofMap

The dofmap.

element()

Return finite element

Returns

FiniteElement

The finite element.

extract_sub_space()

Extract subspace for component

Arguments

component (numpy.array(int))

The component.

Returns

FunctionSpace

The subspace.

has_cell()

Check if function space has given cell

Arguments

cell (Cell)

The cell.

Returns

bool

True if the function space has the given cell.

has_element()

Check if function space has given element

Arguments

element (FiniteElement)

The finite element.

Returns

bool

True if the function space has the given element.

interpolate()

Interpolate function v into function space, returning the vector of expansion coefficients

Arguments

expansion_coefficients (GenericVector)

The expansion coefficients.

v (GenericFunction)

The function to be interpolated.

leaf_node()

Return the finest FunctionSpace in hierarchy

mesh()

Return mesh

Returns

Mesh

The mesh.

parent()

Return the parent FunctionSpace in the hierarchy

print_dofmap()

Print dofmap (useful for debugging)

root_node()

Return the coarsest FunctionSpace in hierarchy

set_x()

Set dof entries in vector to value*x[i], where [x][i] is the coordinate of the dof spatial coordinate. Parallel layout of vector must be consistent with dof map range This function is typically used to construct the null space of a matrix operator, e.g. rigid body rotations.

Arguments

vector (GenericVector)

The vector to set.

value (float)

The value to multiply to coordinate by.

component (int)

The coordinate index.

mesh (Mesh)

The mesh.

sub()

Overloaded versions

• sub(component)

  Extract subspace for component

  Arguments

  component (int)

  Index of the subspace.

  Returns

  FunctionSpace

  The subspace.

• sub(component)

  Extract subspace for component

  Arguments

  component (numpy.array(int))

  The component.

  Returns

  FunctionSpace

  The subspace.

tabulate_dof_coordinates()

Tabulate the coordinates of all dofs on this process. This function is typically used by preconditioners that require the spatial coordinates of dofs, for example for re-partitioning or nullspace computations.

Arguments

mesh (Mesh)

The mesh.

Returns

numpy.array(float)

The dof coordinates (x0, y0, x1, y1, . . .)

thisown

The membership flag