dolfinx.fem
Tools for assembling and manipulating finite element forms.
Functions
Create a sparsity pattern from a bilinear form. |
- class dolfinx.fem.Constant(domain, c: Union[ndarray, Sequence, float, complex])[source]
Bases:
Constant
A constant with respect to a domain.
- Parameters:
domain – DOLFINx or UFL mesh
c – Value of the constant.
- property dtype: dtype
- property value
The value of the constant
- class dolfinx.fem.DirichletBC(bc)[source]
Bases:
object
Representation of Dirichlet boundary condition which is imposed on a linear system.
Note
Dirichlet boundary conditions should normally be constructed using
fem.dirichletbc()
and not using this class initialiser. This class is combined with different base classes that depend on the scalar type of the boundary condition.- Parameters:
value – Lifted boundary values function.
dofs – Local indices of degrees of freedom in function space to which boundary condition applies. Expects array of size (number of dofs, 2) if function space of the problem,
V
is passed. Otherwise assumes function space of the problem is the same of function space of boundary values function.V – Function space of a problem to which boundary conditions are applied.
- property function_space: FunctionSpaceBase
The function space on which the boundary condition is defined
- class dolfinx.fem.DofMap(dofmap: DofMap)[source]
Bases:
object
Degree-of-freedom map
This class handles the mapping of degrees of freedom. It builds a dof map based on a ufcx_dofmap on a specific mesh.
- property bs
Returns the block size of the dofmap
- cell_dofs(cell_index: int)[source]
Cell local-global dof map
- Parameters:
cell – The cell index
- Returns:
Local-global dof map for the cell (using process-local indices)
- property dof_layout
Layout of dofs on an element
- property index_map
Index map that described the parallel distribution of the dofmap
- property index_map_bs
Block size of the index map
- property list
Adjacency list with dof indices for each cell
- class dolfinx.fem.ElementMetaData(family: str, degree: int, shape: Optional[Tuple[int, ...]] = None, symmetry: Optional[bool] = None)[source]
Bases:
NamedTuple
Data for representing a finite element
- Parameters:
family – Element type.
degree – Polynomial degree of the element.
shape – Shape for vector/tensor valued elements that are constructed from blocked scalar elements (e.g., Lagrange).
symmetry – Symmetry option for blocked tensor elements.
Create new instance of ElementMetaData(family, degree, shape, symmetry)
- degree: int
Alias for field number 1
- family: str
Alias for field number 0
- shape: Optional[Tuple[int, ...]]
Alias for field number 2
- symmetry: Optional[bool]
Alias for field number 3
- class dolfinx.fem.Expression(e: ufl.core.expr.Expr, X: np.ndarray, comm: Optional[_MPI.Comm] = None, form_compiler_options: Optional[dict] = None, jit_options: Optional[dict] = None, dtype: Optional[npt.DTypeLike] = None)[source]
Bases:
object
Create DOLFINx Expression.
Represents a mathematical expression evaluated at a pre-defined set of points on the reference cell. This class closely follows the concept of a UFC Expression.
This functionality can be used to evaluate a gradient of a Function at the quadrature points in all cells. This evaluated gradient can then be used as input to a non-FEniCS function that calculates a material constitutive model.
- Parameters:
e – UFL expression.
X – Array of points of shape
(num_points, tdim)
on the reference element.comm – Communicator that the Expression is defined on.
form_compiler_options – Options used in FFCx compilation of this Expression. Run
ffcx --help
in the commandline to see all available options.jit_options – Options controlling JIT compilation of C code.
Note
This wrapper is responsible for the FFCx compilation of the UFL Expr and attaching the correct data to the underlying C++ Expression.
- property argument_function_space: Optional[FunctionSpaceBase]
The argument function space if expression has argument
- property code: str
C code strings
- property dtype: dtype
- eval(mesh: Mesh, cells: np.ndarray, values: Optional[np.ndarray] = None) np.ndarray [source]
Evaluate Expression in cells.
- Parameters:
mesh – Mesh to evaluate Expression on.
cells – Cells of mesh` to evaluate Expression on.
values – Array to fill with evaluated values. If
None
, storage will be allocated. Otherwise must have shape(len(cells), num_points * value_size * num_all_argument_dofs)
- Returns:
Expression evaluated at points for cells`.
- property ufcx_expression
The compiled ufcx_expression object
- property ufl_expression
Original UFL Expression
- property value_size: int
Value size of the expression
- class dolfinx.fem.Form(form, ufcx_form=None, code: Optional[str] = None)[source]
Bases:
object
A finite element form
Note
Forms should normally be constructed using
form()
and not using this class initialiser. This class is combined with different base classes that depend on the scalar type used in the Form.- Parameters:
form – Compiled form object.
ufcx_form – UFCx form
code – Form C++ code
- property code: Optional[str]
C code strings
- property dtype: dtype
Scalar type of this form
- property function_spaces: List[FunctionSpaceBase]
Function spaces on which this form is defined
- property integral_types
Integral types in the form
- property rank: int
- property ufcx_form
The compiled ufcx_form object
- class dolfinx.fem.Function(*args, **kw)[source]
Bases:
Coefficient
A finite element function that is represented by a function space (domain, element and dofmap) and a vector holding the degrees-of-freedom
Initialize a finite element Function.
- Parameters:
V – The function space that the Function is defined on.
x – Function degree-of-freedom vector. Typically required only when reading a saved Function from file.
name – Function name.
dtype – Scalar type. Is not set, the DOLFINx default scalar type is used.
- copy() Function [source]
Create a copy of the Function. The function space is shared and the degree-of-freedom vector is copied.
- property dtype: dtype
- eval(x: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]], cells: Union[_SupportsArray[dtype], _NestedSequence[_SupportsArray[dtype]], bool, int, float, complex, str, bytes, _NestedSequence[Union[bool, int, float, complex, str, bytes]]], u=None) ndarray [source]
Evaluate Function at points x, where x has shape (num_points, 3), and cells has shape (num_points,) and cell[i] is the index of the cell containing point x[i]. If the cell index is negative the point is ignored.
- property function_space: FunctionSpaceBase
The FunctionSpace that the Function is defined on
- interpolate(u: Union[Callable, Expression, Function], cells: Optional[ndarray] = None, nmm_interpolation_data=((), (), (), ())) None [source]
Interpolate an expression
- Parameters:
u – The function, Expression or Function to interpolate.
cells – The cells to interpolate over. If None then all cells are interpolated over.
- property name: str
Name of the Function.
- split() tuple[dolfinx.fem.function.Function, ...] [source]
Extract (any) sub-functions.
A sub-function can be extracted from a discrete function that is in a mixed, vector, or tensor FunctionSpace. The sub-function resides in the subspace of the mixed space.
- Returns:
First level of subspaces of the function space.
- sub(i: int) Function [source]
Return a sub-function.
- Parameters:
i – Index of the sub-function to extract.
Note
The sub-functions are numbered i = 0, …, N-1, where N is the number of sub-spaces.
- property vector
PETSc vector holding the degrees-of-freedom.
Upon first call, this function creates a PETSc
Vec
object that wraps the degree-of-freedom data. TheVec
object is cached and the cachedVec
is returned upon subsequent calls.Note
Prefer :func`x` where possible.
- dolfinx.fem.FunctionSpace(mesh: Mesh, element: Union[ufl.FiniteElementBase, ElementMetaData, Tuple[str, int, Tuple, bool]], form_compiler_options: Optional[dict[str, Any]] = None, jit_options: Optional[dict[str, Any]] = None) FunctionSpaceBase [source]
Create a finite element function space.
Deprecated since version 0.7: Use
functionspace()
(no caps) instead.- Parameters:
mesh – Mesh that space is defined on
element – Finite element description
form_compiler_options – Options passed to the form compiler
jit_options – Options controlling just-in-time compilation
- Returns:
A function space.
- class dolfinx.fem.FunctionSpaceBase(mesh: Mesh, element: ufl.FiniteElementBase, cppV: Union[_cpp.fem.FunctionSpace_float32, _cpp.fem.FunctionSpace_float64])[source]
Bases:
FunctionSpace
A space on which Functions (fields) can be defined.
Create a finite element function space.
Note
This initialiser is for internal use and not normally called in user code. Use
FunctionSpace()
to create a function space.- Parameters:
mesh – Mesh that space is defined on
element – UFL finite element
cppV – Compiled C++ function space.
- clone() FunctionSpaceBase [source]
Create a new FunctionSpace \(W\) which shares data with this FunctionSpace \(V\), 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 \(V \times W\) where, \(V\) and \(W\) are defined on the same finite element and mesh can be identified as an off-diagonal block whereas the \(V \times V\) and \(V \times V\) matrices can be identified as diagonal blocks. This is relevant for the handling of boundary conditions.
- Returns:
A new function space that shares data
- collapse() tuple[dolfinx.fem.function.FunctionSpaceBase, numpy.ndarray] [source]
Collapse a subspace and return a new function space and a map from new to old dofs.
- Returns:
A new function space and the map from new to old degrees-of-freedom.
- contains(V) bool [source]
Check if a space is contained in, or is the same as (identity), this space.
- Parameters:
V – The space to check to for inclusion.
- Returns:
True if
V
is contained in, or is the same as, this space
- property element
Function space finite element.
- property num_sub_spaces: int
Number of sub spaces.
- sub(i: int) FunctionSpaceBase [source]
Return the i-th sub space.
- Parameters:
i – The subspace index
- Returns:
A subspace
- class dolfinx.fem.IntegralType(self: dolfinx.cpp.fem.IntegralType, value: int)
Bases:
pybind11_object
Members:
cell
exterior_facet
interior_facet
vertex
- cell = <IntegralType.cell: 0>
- exterior_facet = <IntegralType.exterior_facet: 1>
- interior_facet = <IntegralType.interior_facet: 2>
- property name
- property value
- vertex = <IntegralType.vertex: 3>
- dolfinx.fem.VectorFunctionSpace(mesh: Mesh, element: Union[ElementMetaData, Tuple[str, int]], dim: Optional[int] = None) FunctionSpaceBase [source]
Create a vector finite element (composition of scalar elements) function space.
Deprecated since version 0.7: Use
FunctionSpace()
with a shape argument instead.- Parameters:
mesh – Mesh that space is defined on
element – Finite element description. Must be a scalar element, e.g. Lagrange.
dim – Dimension of the vector, e.g. number of vector components. It defaults to the geometric dimension of the mesh.
- Returns:
A blocked vector function space.
- dolfinx.fem.apply_lifting(b: ndarray, a: List[Form], bcs: List[List[DirichletBC]], x0: Optional[List[ndarray]] = None, scale: float = 1.0, constants=None, coeffs=None) None [source]
Modify RHS vector b for lifting of Dirichlet boundary conditions.
It modifies b such that:
\[b \leftarrow b - \text{scale} * A_j (g_j - x0_j)\]where j is a block (nest) index. For a non-blocked problem j = 0. The boundary conditions bcs are on the trial spaces V_j. The forms in [a] must have the same test space as L (from which b was built), but the trial space may differ. If x0 is not supplied, then it is treated as zero.
Note
Ghost contributions are not accumulated (not sent to owner). Caller is responsible for calling VecGhostUpdateBegin/End.
- dolfinx.fem.assemble_matrix(a: Any, bcs: Optional[List[DirichletBC]] = None, diagonal: float = 1.0, constants=None, coeffs=None, block_mode: Optional[BlockMode] = None)[source]
- dolfinx.fem.assemble_matrix(A: MatrixCSR, a: Form, bcs: Optional[List[DirichletBC]] = None, diagonal: float = 1.0, constants=None, coeffs=None) MatrixCSR
Assemble bilinear form into a matrix.
- Parameters:
a – The bilinear form assemble.
bcs – Boundary conditions that affect the assembled matrix. Degrees-of-freedom constrained by a boundary condition will have their rows/columns zeroed and the value
diagonal
set on on the matrix diagonal.constants – Constants that appear in the form. If not provided, any required constants will be computed.
coeffs –
- Coefficients that appear in the form. If not provided,
any required coefficients will be computed.
- block_mode: Block size mode for the returned space matrix. If
None
, default is used.
- Returns:
Matrix representation of the bilinear form
a
.
Note
The returned matrix is not finalised, i.e. ghost values are not accumulated.
- dolfinx.fem.assemble_scalar(M: Form, constants=None, coeffs=None)[source]
Assemble functional. The returned value is local and not accumulated across processes.
- Parameters:
M – The functional to compute.
constants – Constants that appear in the form. If not provided, any required constants will be computed.
coeffs – Coefficients that appear in the form. If not provided, any required coefficients will be computed.
- Returns:
The computed scalar on the calling rank.
Note
Passing constants and coefficients is a performance optimisation for when a form is assembled multiple times and when (some) constants and coefficients are unchanged.
To compute the functional value on the whole domain, the output of this function is typically summed across all MPI ranks.
- dolfinx.fem.assemble_vector(L: Any, constants=None, coeffs=None)[source]
- dolfinx.fem.assemble_vector(L: Form, constants=None, coeffs=None) Vector
- dolfinx.fem.assemble_vector(b: ndarray, L: Form, constants=None, coeffs=None)
- dolfinx.fem.bcs_by_block(spaces: Iterable[Optional[FunctionSpaceBase]], bcs: Iterable[DirichletBC]) List[List[DirichletBC]] [source]
Arrange Dirichlet boundary conditions by the function space that they constrain.
Given a sequence of function spaces
spaces
and a sequence of DirichletBC objectsbcs
, return a list where the ith entry is the list of DirichletBC objects whose space is contained inspace[i]
.
- dolfinx.fem.create_matrix(a: Form, block_mode: Optional[BlockMode] = None) MatrixCSR [source]
Create a sparse matrix that is compatible with a given bilinear form. :param a: Bilinear form to assemble. :param block_mode: Block mode of the CSR matrix. If
None
, default :param is used.:- Returns:
Assembled sparse matrix.
- dolfinx.fem.create_nonmatching_meshes_interpolation_data(*args, **kwargs)
Overloaded function.
create_nonmatching_meshes_interpolation_data(mesh0: dolfinx.cpp.mesh.Mesh_float32, element0: dolfinx.cpp.fem.FiniteElement_float32, mesh1: dolfinx.cpp.mesh.Mesh_float32) -> Tuple[List[int], List[int], List[float], List[int]]
create_nonmatching_meshes_interpolation_data(geometry0: dolfinx.cpp.mesh.Geometry_float32, element0: dolfinx.cpp.fem.FiniteElement_float32, mesh1: dolfinx.cpp.mesh.Mesh_float32, cells: numpy.ndarray[numpy.int32]) -> Tuple[List[int], List[int], List[float], List[int]]
create_nonmatching_meshes_interpolation_data(mesh0: dolfinx.cpp.mesh.Mesh_float64, element0: dolfinx.cpp.fem.FiniteElement_float64, mesh1: dolfinx.cpp.mesh.Mesh_float64) -> Tuple[List[int], List[int], List[float], List[int]]
create_nonmatching_meshes_interpolation_data(geometry0: dolfinx.cpp.mesh.Geometry_float64, element0: dolfinx.cpp.fem.FiniteElement_float64, mesh1: dolfinx.cpp.mesh.Mesh_float64, cells: numpy.ndarray[numpy.int32]) -> Tuple[List[int], List[int], List[float], List[int]]
- dolfinx.fem.create_sparsity_pattern(a: Form)[source]
Create a sparsity pattern from a bilinear form.
- Parameters:
a – Bilinear form to build a sparsity pattern for.
- Returns:
Sparsity pattern for the form
a
.
Note
The pattern is not finalised, i.e. the caller is responsible for calling
assemble
on the sparsity pattern.
- dolfinx.fem.create_vector(L: Form) Vector [source]
Create a Vector that is compatible with a given linear form
- dolfinx.fem.dirichletbc(value: Union[Function, Constant, np.ndarray], dofs: numpy.typing.NDArray[np.int32], V: Optional[dolfinx.fem.FunctionSpaceBase] = None) DirichletBC [source]
Create a representation of Dirichlet boundary condition which is imposed on a linear system.
- Parameters:
value – Lifted boundary values function. It must have a
dtype
property. –
dofs – Local indices of degrees of freedom in function space to which boundary condition applies. Expects array of size (number of dofs, 2) if function space of the problem,
V
, is passed. Otherwise assumes function space of the problem is the same of function space of boundary values function.V – Function space of a problem to which boundary conditions are applied.
- Returns:
A representation of the boundary condition for modifying linear systems.
- dolfinx.fem.extract_function_spaces(forms: Union[Iterable[Form], Iterable[Iterable[Form]]], index: int = 0) Iterable[Union[None, function.FunctionSpaceBase]] [source]
Extract common function spaces from an array of forms. If forms is a list of linear form, this function returns of list of the corresponding test functions. If forms is a 2D array of bilinear forms, for index=0 the list common test function space for each row is returned, and if index=1 the common trial function spaces for each column are returned.
- dolfinx.fem.form(form: ~typing.Union[~ufl.form.Form, ~typing.Iterable[~ufl.form.Form]], dtype: ~typing.Union[~numpy.dtype[~typing.Any], None, ~typing.Type[~typing.Any], ~numpy._typing._dtype_like._SupportsDType[~numpy.dtype[~typing.Any]], str, ~typing.Tuple[~typing.Any, int], ~typing.Tuple[~typing.Any, ~typing.Union[~typing.SupportsIndex, ~typing.Sequence[~typing.SupportsIndex]]], ~typing.List[~typing.Any], ~numpy._typing._dtype_like._DTypeDict, ~typing.Tuple[~typing.Any, ~typing.Any]] = <class 'numpy.float64'>, form_compiler_options: ~typing.Optional[dict] = None, jit_options: ~typing.Optional[dict] = None)[source]
Create a Form or an array of Forms.
- Parameters:
- Returns:
Compiled finite element Form.
Note
This function is responsible for the compilation of a UFL form (using FFCx) and attaching coefficients and domains specific data to the underlying C++ form. It dynamically create a
Form
instance with an appropriate base class for the scalar type, e.g._cpp.fem.Form_float64()
.
- dolfinx.fem.functionspace(mesh: Mesh, element: Union[ufl.FiniteElementBase, ElementMetaData, Tuple[str, int, Tuple, bool]], form_compiler_options: Optional[dict[str, Any]] = None, jit_options: Optional[dict[str, Any]] = None) FunctionSpaceBase [source]
Create a finite element function space.
- Parameters:
mesh – Mesh that space is defined on
element – Finite element description
form_compiler_options – Options passed to the form compiler
jit_options – Options controlling just-in-time compilation
- Returns:
A function space.
- dolfinx.fem.locate_dofs_geometrical(V: Union[FunctionSpaceBase, Iterable[FunctionSpaceBase]], marker: Callable) ndarray [source]
Locate degrees-of-freedom geometrically using a marker function.
- Parameters:
V – Function space(s) in which to search for degree-of-freedom indices.
marker – A function that takes an array of points
x
with shape(gdim, num_points)
and returns an array of booleans of lengthnum_points
, evaluating toTrue
for entities whose degree-of-freedom should be returned.
- Returns:
An array of degree-of-freedom indices (local to the process) for degrees-of-freedom whose coordinate evaluates to True for the marker function.
If
V
is a list of two function spaces, then a 2-D array of shape (number of dofs, 2) is returned.Returned degree-of-freedom indices are unique and ordered by the first column.
- dolfinx.fem.locate_dofs_topological(V: Union[FunctionSpaceBase, Iterable[FunctionSpaceBase]], entity_dim: int, entities: ndarray[Any, dtype[int32]], remote: bool = True) ndarray [source]
Locate degrees-of-freedom belonging to mesh entities topologically.
- Parameters:
V – Function space(s) in which to search for degree-of-freedom indices.
entity_dim – Topological dimension of entities where degrees-of-freedom are located.
entities – Indices of mesh entities of dimension
entity_dim
where degrees-of-freedom are located.remote – True to return also “remotely located” degree-of-freedom indices.
- Returns:
An array of degree-of-freedom indices (local to the process) for degrees-of-freedom topologically belonging to mesh entities.
If
V
is a list of two function spaces, then a 2-D array of shape (number of dofs, 2) is returned.Returned degree-of-freedom indices are unique and ordered by the first column.
- dolfinx.fem.set_bc(b: ndarray, bcs: List[DirichletBC], x0: Optional[ndarray] = None, scale: float = 1.0) None [source]
Insert boundary condition values into vector.
Only local (owned) entries are set, hence communication after calling this function is not required unless ghost entries need to be updated to the boundary condition value.