Class FunctionSpace

python/dolfinx/fem/function.py:711–865

A space on which Functions (fields) can be defined.

class FunctionSpace(ufl.FunctionSpace, Generic[Real]):
    """A space on which Functions (fields) can be defined."""

    _cpp_object: _cpp.fem.FunctionSpace_float32 | _cpp.fem.FunctionSpace_float64
    _mesh: Mesh[Real]

    def __init__(
        self,
        mesh: Mesh[Real],
        element: ufl.finiteelement.AbstractFiniteElement,
        cppV: (_cpp.fem.FunctionSpace_float32 | _cpp.fem.FunctionSpace_float64),
    ):
        """Create a finite element function space.

        Note:
            This initialiser is for internal use and not normally called
            in user code. Use :func:`functionspace` to create a function
            space.

        Args:
            mesh: Mesh that space is defined on.
            element: UFL finite element.
            cppV: Compiled C++ function space.
        """
        if mesh._cpp_object is not cppV.mesh:
            raise RuntimeError("Meshes do not match in function space initialisation.")
        ufl_domain = mesh.ufl_domain()
        self._cpp_object = cppV
        self._mesh = mesh
        super().__init__(ufl_domain, element)

    def clone(self) -> FunctionSpace[Real]:
        """Create a FunctionSpace which shares data with this space.

        The new space has a different unique integer ID.

        Create a new FunctionSpace :math:`W` which shares data with this
        FunctionSpace :math:`V`, but with a different unique integer ID.

        This function is helpful for defining mixed problems and using
        blocked linear algebra. For example, a matrix block defined on
        the spaces :math:`V \\times W` where, :math:`V` and :math:`W`
        are defined on the same finite element and mesh can be
        identified as an off-diagonal block whereas the :math:`V \\times
        V` and :math:`V \\times V` matrices can be identified as
        diagonal blocks. This is relevant for the handling of boundary
        conditions.

        Returns:
            A new function space that shares data
        """  # noqa: D301
        try:
            Vcpp = _cpp.fem.FunctionSpace_float64(
                self._cpp_object.mesh, self._cpp_object.element, self._cpp_object.dofmap
            )  # type: ignore
        except TypeError:
            Vcpp = _cpp.fem.FunctionSpace_float32(
                self._cpp_object.mesh, self._cpp_object.element, self._cpp_object.dofmap