"""
Finite Element Boundary Conditions and Mesh Tagging Utilities
=============================================================
This module provides functions for creating boundary conditions and handling mesh tagging.
Notes
-----
These functions are useful for defining boundary conditions and subdomains in finite element simulations.
Examples
--------
See individual function documentation for usage examples.
"""
import numpy as np
import dolfinx
import ufl
import petsc4py
[docs]
def bc_phi(facet, V_phi, fdim, value=0.0):
"""
Create a Dirichlet boundary condition for the scalar field `phi` on a specified facet.
Parameters
----------
facet : int
The topological index of the facet on which the boundary condition is applied.
V_phi : dolfinx.FunctionSpace
The function space associated with the scalar field `phi`.
fdim : int
The topological dimension of the facets (e.g., 2 for triangles).
Returns
-------
dolfinx.fem.dirichletbc
A Dirichlet boundary condition for the scalar field `phi`.
Notes
-----
This function is useful for defining Dirichlet boundary conditions for scalar fields in finite element simulations.
The boundary condition enforces `phi` to have a constant value (`phi_D`) on the specified facet.
Example
-------
>>> facet_index = 0
>>> V_phi_space = dolfinx.FunctionSpace(mesh, "CG", 1)
>>> bc_phi_condition = bc_phi(facet_index, V_phi_space, 2)
"""
phi_D = petsc4py.PETSc.ScalarType(value)
boundary_dofs = dolfinx.fem.locate_dofs_topological(V_phi, fdim, facet)
return dolfinx.fem.dirichletbc(phi_D, boundary_dofs, V_phi)
[docs]
def bc_x(facet, V_u, fdim, value=0.0):
"""
Create a Dirichlet boundary condition for the x-component of a vector field `u` on a specified facet.
Parameters
----------
facet : int
The topological index of the facet on which the boundary condition is applied.
V_u : dolfinx.FunctionSpace
The function space associated with the vector field `u`.
fdim : int
The topological dimension of the facets (e.g., 2 for triangles).
Returns
-------
dolfinx.fem.dirichletbc
A Dirichlet boundary condition for the x-component of the vector field `u`.
Notes
-----
This function is useful for defining Dirichlet boundary conditions for the x-component of vector fields in finite element simulations.
The boundary condition enforces the x-component of `u` to have a constant value (`u_x_D`) on the specified facet.
Example
-------
>>> facet_index = 0
>>> V_u_space = dolfinx.VectorFunctionSpace(mesh, "CG", 1)
>>> bc_x_condition = bc_x(facet_index, V_u_space, 2)
"""
u_x_D = petsc4py.PETSc.ScalarType(value)
boundary_dofs = dolfinx.fem.locate_dofs_topological(
V_u.sub(0), fdim, facet)
return dolfinx.fem.dirichletbc(u_x_D, boundary_dofs, V_u.sub(0))
[docs]
def bc_y(facet, V_u, fdim, value=0.0):
"""
Create a Dirichlet boundary condition for the y-component of a vector field `u` on a specified facet.
Parameters
----------
facet : int
The topological index of the facet on which the boundary condition is applied.
V_u : dolfinx.FunctionSpace
The function space associated with the vector field `u`.
fdim : int
The topological dimension of the facets (e.g., 2 for triangles).
Returns
-------
dolfinx.fem.DirichletBC
A Dirichlet boundary condition for the y-component of the vector field `u`.
Notes
-----
This function is useful for defining Dirichlet boundary conditions for the y-component of vector fields in finite element simulations.
The boundary condition enforces the y-component of `u` to have a constant value (`u_y_D`) on the specified facet.
Example
-------
>>> facet_index = 0
>>> V_u_space = dolfinx.VectorFunctionSpace(mesh, "CG", 1)
>>> bc_y_condition = bc_y(facet_index, V_u_space, 2)
"""
u_y_D = petsc4py.PETSc.ScalarType(value)
boundary_dofs = dolfinx.fem.locate_dofs_topological(
V_u.sub(1), fdim, facet)
return dolfinx.fem.dirichletbc(u_y_D, boundary_dofs, V_u.sub(1))
[docs]
def bc_z(facet, V_u, fdim, value=0.0):
"""
Create a Dirichlet boundary condition for the z-component of a vector field `u` on a specified facet.
Parameters
----------
facet : int
The topological index of the facet on which the boundary condition is applied.
V_u : dolfinx.FunctionSpace
The function space associated with the vector field `u`.
fdim : int
The topological dimension of the facets (e.g., 2 for triangles).
Returns
-------
dolfinx.fem.dirichletbc
A Dirichlet boundary condition for the z-component of the vector field `u`.
Notes
-----
This function is useful for defining Dirichlet boundary conditions for the z-component of vector fields in finite element simulations.
The boundary condition enforces the z-component of `u` to have a constant value (`u_z_D`) on the specified facet.
Example
-------
>>> facet_index = 0
>>> V_u_space = dolfinx.VectorFunctionSpace(mesh, "CG", 1)
>>> bc_z_condition = bc_z(facet_index, V_u_space, 2)
"""
u_z_D = petsc4py.PETSc.ScalarType(value)
boundary_dofs = dolfinx.fem.locate_dofs_topological(
V_u.sub(2), fdim, facet)
return dolfinx.fem.dirichletbc(u_z_D, boundary_dofs, V_u.sub(2))
[docs]
def bc_xy(facet, V_u, fdim, value_x=0.0, value_y=0.0):
"""
Create Dirichlet boundary conditions for both x and y components of a vector field `u` on a specified facet.
Parameters
----------
facet : int
The topological index of the facet on which the boundary conditions are applied.
V_u : dolfinx.FunctionSpace
The function space associated with the vector field `u`.
fdim : int
The topological dimension of the facets (e.g., 2 for triangles).
Returns
-------
dolfinx.fem.dirichletbc
Dirichlet boundary conditions for both the x and y components of the vector field `u`.
Notes
-----
This function is useful for defining Dirichlet boundary conditions for both the x and y components of vector fields in finite element simulations.
The boundary conditions enforce constant values (`u_xy_D`) for both the x and y components on the specified facet.
Example
-------
>>> facet_index = 0
>>> V_u_space = dolfinx.VectorFunctionSpace(mesh, "CG", 1)
>>> bc_xy_conditions = bc_xy(facet_index, V_u_space, 2)
"""
u_xy_D = np.array([value_x, value_y], dtype=petsc4py.PETSc.ScalarType)
boundary_dofs = dolfinx.fem.locate_dofs_topological(V_u, fdim, facet)
return dolfinx.fem.dirichletbc(u_xy_D, boundary_dofs, V_u)
[docs]
def bc_xyz(facet, V_u, fdim, value_x=0.0, value_y=0.0, value_z=0.0):
"""
Create Dirichlet boundary conditions for all three components (x, y, and z) of a vector field `u` on a specified facet.
Parameters
----------
facet : int
The topological index of the facet on which the boundary conditions are applied.
V_u : dolfinx.FunctionSpace
The function space associated with the vector field `u`.
fdim : int
The topological dimension of the facets (e.g., 2 for triangles).
Returns
-------
dolfinx.fem.dirichletbc
Dirichlet boundary conditions for all three components (x, y, and z) of the vector field `u`.
Notes
-----
This function is useful for defining Dirichlet boundary conditions for all three components (x, y, and z) of vector fields in finite element simulations.
The boundary conditions enforce constant values (`u_xyz_D`) for all three components on the specified facet.
Example
-------
>>> facet_index = 0
>>> V_u_space = dolfinx.VectorFunctionSpace(mesh, "CG", 1)
>>> bc_xyz_conditions = bc_xyz(facet_index, V_u_space, 2)
"""
u_xyz_D = np.array([value_x, value_y, value_z],
dtype=petsc4py.PETSc.ScalarType)
boundary_dofs = dolfinx.fem.locate_dofs_topological(V_u, fdim, facet)
return dolfinx.fem.dirichletbc(u_xyz_D, boundary_dofs, V_u)
[docs]
def get_ds_bound_from_marker(facet_marker, msh, fdim):
"""
Create a `ufl.Measure` representing the boundary of a specific subdomain based on facet markers.
Parameters
----------
facet_marker : numpy.ndarray
An array of facet markers indicating the desired subdomain.
msh : dolfinx.Mesh
The mesh on which to define the boundary measure.
fdim : int
The topological dimension of the facets (e.g., 2 for triangles).
Returns
-------
ufl.Measure
A UFL Measure object representing the boundary of the specified subdomain.
Notes
-----
This function is useful for defining a UFL Measure representing the boundary of a specific subdomain based on facet markers.
It allows you to create a boundary measure for a subdomain with a specific facet marker value.
Parameters:
- `facet_marker` is an array that specifies which facets belong to the desired subdomain. Facets with marker value 1 are considered part of the subdomain.
- `msh` is the mesh on which the boundary measure is defined.
- `fdim` is the topological dimension of the facets (e.g., 2 for triangles).
Example
-------
>>> facet_markers = np.array([0, 1, 1, 0, 1], dtype=int)
>>> mesh = dolfinx.UnitSquareMesh(MPI.COMM_WORLD, 2, 2)
>>> boundary_measure = get_ds_bound_from_marker(facet_markers, mesh, 1)
"""
marked_facets = np.hstack([facet_marker])
marked_values = np.hstack([np.full_like(facet_marker, 1)])
sorted_facets = np.argsort(marked_facets)
facet_tag = dolfinx.mesh.meshtags(
msh, fdim, marked_facets[sorted_facets], marked_values[sorted_facets])
ds_bound = ufl.Measure(
"ds", domain=msh, subdomain_data=facet_tag, subdomain_id=1)
return ds_bound
