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Underlying matrix entry data.

Local representation of the vector.

Create a finite element function space. Args: mesh: Mesh that space is defined on. element: Finite element description. Retu

Interpolate an expression. Args: u0: Callable function, Expression or Function to interpolate. cells0:

TODO: Is there any use for this? In many situations one has to get the topology of a const Mesh, which is done by Mesh::topology_mutable. Note that th

Create a Form or list of Forms. Args: form: A UFL form or iterable of UFL forms. dtype: Scalar type to use for the compiled form.

Index map for the parallel distribution of the mesh entities. Args: dim: Topological dimension. Returns: Ind

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Create a mesh of a unit square. Args: comm: MPI communicator. nx: Number of cells in the "x" direction. ny: Number of cel

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Return a sub-function (a view into the ``Function``). Sub-functions are indexed ``i = 0, ..., N-1``, where ``N`` is the number of sub

@brief Get the links (edges) for given node. @param[in] node Node index. @return Array of outgoing links for the node. The length will be `AdjacencyLi

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Scatter ghost entries to owner. Args: mode: Control how scattered values are set/accumulated by owner.

Mesh geometry.

Create a mesh of a unit cube. Args: comm: MPI communicator. nx: Number of cells in "x" direction. ny: Number of cells in

@brief Create function on given function space. @param[in] V The function space

Build entity connectivity ``d0 -> d1``. Args: d0: Dimension of entities connectivity is from. d1: Dimension of entiti

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@brief Get the number of nodes. @return The number of nodes in the adjacency list

Assemble functional. The returned value is local and not accumulated across processes. Args: M: The functional to compute. c

Return the Basix cell type.

Retrieve the links of a node. Note: This is available only for adjacency lists with no additional link (edge) data.

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@brief Common mesh for the form (the 'integration domain'). @return The integration domain mesh.

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@brief Underlying vector (const version).

Update ghost entries.

@brief Access the function space. @return The function space.

Assemble a bilinear form into a matrix. The following cases are supported: 1. If ``a`` is a single bilinear form, the form is assembled

Return connectivity. Connectivity from entities of dimension ``d0`` to entities of dimension ``d1``. Args: d0: D

Update ghost values of solution vector.

Representation of Dirichlet boundary condition. Args: value: Lifted boundary values function. It must have a ``dtype`` proper

The finite element

@brief Get mesh topology if one really needs the mutable version. @return The topology object associated with the mesh.

Locate degrees-of-freedom belonging to mesh entities topologically. Args: V: Function space(s) in which to search for degree-of-freedom

Function space finite element.

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@brief Degree-of-freedom map associated with each coordinate map element in the geometry. @return A list of dofmap arrays, each with shape `(num_cells

The value of the constant.

Write a functions to file with a given time.

Set array entries that are constrained by a Dirichlet condition. Entries in ``x`` that are constrained by a Dirichlet boundary condit

Get the underlying MPI communicator

Compute mesh entities satisfying a geometric marking function. Args: msh: Mesh to locate entities on. dim: Topological dimension

Create a mesh from topology and geometry arrays. Args: comm: MPI communicator to define the mesh on. cells: Cells of the mesh. ``

Function spaces on which this form is defined.

Write mesh to file for a given time.

@brief Local-to-global mapping of dofs on a cell @param[in] c The cell index @return Local-global dof map for the cell (using process-local indices)

Create entities of given topological dimension. Args: dim: Topological dimension of entities to create. num_threads:

Mesh entities connected to a boundary facet a geometric condition. Compute indices of all mesh entities that are attached to an owned boundar

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Create a function to partition a mesh. Args: part: Partition function. mode: Ghosting mode to use. max_facet_to_cell_link

@brief Number of connections for given node. @param[in] node Node index. @return The number of outgoing links (edges) from the node.

Solve non-linear problem into function ``u``. Returns the number of iterations and if the solver converged.

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Function called before the residual or Jacobian is computed. This is usually used to update ghost values. Args: x: The ve

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@brief DofMap for the geometry. @return A 2D array with shape `(num_cells, dofs_per_cell)`. @deprecated Use dofmaps().front() instead.

Write data to file for a given time.

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Entity types in the topology for all topological dimensions.

@brief Find all entities with a given tag value @param[in] value The value @return Indices of tagged entities. The indices are sorted.

Compute the indices of exterior facets that are owned by the caller. An exterior facet (co-dimension 1) is one that is connected globally to

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Compute the squared Frobenius norm. Note: This operation is collective and requires communication.

Create a copy of the Function. The function space is shared and the degree-of-freedom vector is copied. Returns:

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Blocked problem using a {py:class}`basix.ufl.mixed_element`.

The coordinate maps.

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Add a block of values in the matrix.

Modify a vector to account for Dirichlet boundary conditions. See :func:`dolfinx.fem.apply_lifting` for a mathematical descriptions of the li

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The dofmap

Get a list of all entity indices with a given value. Args: value: Tag value to search for. Returns: Indices

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Assemble simple linear form over a mesh into the array b.

Create a bounding box tree for use in collision detection. Args: mesh: The mesh. dim: Dimension of the mesh entities to build bou

Cell local-global dof map. Args: cell_index: The cell index. Returns: Local-global dof map for the cell (usi

Create a collapsed version of this Function.

Check if a space is contained in, or is the same as, this space. Args: V: The space to check to for inclusion. Returns:

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Mesh topology.