# Source code for dolfinx.fem.bcs

```
# Copyright (C) 2017-2021 Chris N. Richardson, Garth N. Wells and Jørgen S. Dokken
#
# This file is part of DOLFINx (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
"""Support for representing Dirichlet boundary conditions that are enforced
via modification of linear systems."""
from __future__ import annotations
import numbers
import typing
import numpy.typing
if typing.TYPE_CHECKING:
from dolfinx.fem.function import Constant, Function
import numpy as np
import dolfinx
from dolfinx import cpp as _cpp
[docs]def locate_dofs_geometrical(V: typing.Union[dolfinx.fem.FunctionSpace, typing.Iterable[dolfinx.fem.FunctionSpace]],
marker: typing.Callable) -> np.ndarray:
"""Locate degrees-of-freedom geometrically using a marker function.
Args:
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
length ``num_points``, evaluating to ``True`` 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.
"""
try:
return _cpp.fem.locate_dofs_geometrical(V._cpp_object, marker) # type: ignore
except AttributeError:
_V = [space._cpp_object for space in V]
return _cpp.fem.locate_dofs_geometrical(_V, marker)
[docs]def locate_dofs_topological(V: typing.Union[dolfinx.fem.FunctionSpace, typing.Iterable[dolfinx.fem.FunctionSpace]],
entity_dim: int, entities: numpy.typing.NDArray[np.int32],
remote: bool = True) -> np.ndarray:
"""Locate degrees-of-freedom belonging to mesh entities topologically.
Args:
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.
"""
_entities = np.asarray(entities, dtype=np.int32)
try:
return _cpp.fem.locate_dofs_topological(V._cpp_object, entity_dim, _entities, remote) # type: ignore
except AttributeError:
_V = [space._cpp_object for space in V]
return _cpp.fem.locate_dofs_topological(_V, entity_dim, _entities, remote)
[docs]class DirichletBCMetaClass:
def __init__(self, value: typing.Union[Function, Constant, numpy.ndarray],
dofs: numpy.typing.ArrayLike, V: typing.Optional[dolfinx.fem.FunctionSpace] = None):
"""Representation of Dirichlet boundary condition which is imposed on
a linear system.
Notes:
Dirichlet boundary conditions should normally be
constructed using :func:`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.
Args:
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.
"""
# Unwrap value object, if required
if isinstance(value, np.ndarray):
_value = value
else:
try:
_value = value._cpp_object
except AttributeError:
_value = value
if V is not None:
try:
super().__init__(_value, dofs, V) # type: ignore
except TypeError:
super().__init__(_value, dofs, V._cpp_object) # type: ignore
else:
super().__init__(_value, dofs) # type: ignore
@property
def g(self):
"""The boundary condition value(s)"""
return self.value # type: ignore
@property
def function_space(self) -> dolfinx.fem.FunctionSpace:
"""The function space on which the boundary condition is defined"""
return super().function_space # type: ignore
[docs]def dirichletbc(value: typing.Union[Function, Constant, np.ndarray],
dofs: numpy.typing.NDArray[np.int32],
V: typing.Optional[dolfinx.fem.FunctionSpace] = None) -> DirichletBCMetaClass:
"""Create a representation of Dirichlet boundary condition which
is imposed on a linear system.
Args:
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.
"""
if isinstance(value, numbers.Number):
value = np.asarray(value)
try:
dtype = value.dtype
if dtype == np.float32:
bctype = _cpp.fem.DirichletBC_float32
elif dtype == np.float64:
bctype = _cpp.fem.DirichletBC_float64
elif dtype == np.complex64:
bctype = _cpp.fem.DirichletBC_complex64
elif dtype == np.complex128:
bctype = _cpp.fem.DirichletBC_complex128
else:
raise NotImplementedError(f"Type {value.dtype} not supported.")
except AttributeError:
raise AttributeError("Boundary condition value must have a dtype attribute.")
formcls = type("DirichletBC", (DirichletBCMetaClass, bctype), {})
return formcls(value, dofs, V)
[docs]def bcs_by_block(spaces: typing.Iterable[typing.Union[dolfinx.fem.FunctionSpace, None]],
bcs: typing.Iterable[DirichletBCMetaClass]) -> typing.List[typing.List[DirichletBCMetaClass]]:
"""Arrange Dirichlet boundary conditions by the function space that
they constrain.
Given a sequence of function spaces `spaces` and a sequence of
DirichletBC objects `bcs`, return a list where the ith entry is the
list of DirichletBC objects whose space is contained in
`space[i]`."""
def _bc_space(V, bcs):
"Return list of bcs that have the same space as V"
return [bc for bc in bcs if V.contains(bc.function_space)]
return [_bc_space(V, bcs) if V is not None else [] for V in spaces]
```