def homogenize_boundaries(bcs):
if isinstance(bcs, dla.DirichletBC):
bcs = [bcs]
hbcs = [dla.DirichletBC(bc) for bc in bcs]
for hbc in hbcs:
hbc.homogenize()
return hbcs
def get_boundary_indices(function_space):
bc_map = dla.Function(function_space)
bc = dla.DirichletBC(function_space, dla.Constant(1.0), 'on_boundary')
bc.apply(bc_map.vector())
indices = np.arange(
bc_map.vector().size())[bc_map.vector().get_local() == 1.0]
return indices
def fenics_solve(f):
u = fa.Function(V, name="State")
v = fn.TestFunction(V)
F = (ufl.inner(ufl.grad(u), ufl.grad(v)) - f * v) * ufl.dx
bcs = [fa.DirichletBC(V, 0.0, "on_boundary")]
fa.solve(F == 0, u, bcs)
return u
def forward(rho):
"""Solve the forward problem for a given fluid distribution rho(x)."""
w = fenics_adjoint.Function(W)
(u, p) = fenics.split(w)
(v, q) = fenics.TestFunctions(W)
inner, grad, dx, div = ufl.inner, ufl.grad, ufl.dx, ufl.div
F = (
alpha(rho) * inner(u, v) * dx
+ inner(grad(u), grad(v)) * dx
+ inner(grad(p), v) * dx
+ inner(div(u), q) * dx
)
bcs = [
fenics_adjoint.DirichletBC(W.sub(0).sub(1), 0, "on_boundary"),
fenics_adjoint.DirichletBC(W.sub(0).sub(0), inflow_outflow_bc, "on_boundary"),
]
fenics_adjoint.solve(F == 0, w, bcs=bcs)
return w
def collect_dirichlet_boundaries(function_space, boundary_conditions,
boundaries):
num_bndrys = len(boundary_conditions)
dirichlet_bcs = []
for ii in range(num_bndrys):
if boundary_conditions[ii][0] == 'dirichlet':
bc_expr = boundary_conditions[ii][2]
#ii must be same marker number as used in mark_boundaries()
dirichlet_bcs.append(
dla.DirichletBC(function_space, bc_expr, boundaries, ii))
return dirichlet_bcs
def solve_fenics(kappa0, kappa1):
f = fa.Expression(
"10*exp(-(pow(x[0] - 0.5, 2) + pow(x[1] - 0.5, 2)) / 0.02)", degree=2)
u = fa.Function(V)
bcs = [fa.DirichletBC(V, fa.Constant(0.0), "on_boundary")]
inner, grad, dx = ufl.inner, ufl.grad, ufl.dx
JJ = 0.5 * inner(kappa0 * grad(u), grad(u)) * dx - kappa1 * f * u * dx
v = fenics.TestFunction(V)
F = fenics.derivative(JJ, u, v)
fa.solve(F == 0, u, bcs=bcs)
return u
def get_num_subdomain_dofs(Vh, subdomain):
"""
Get the number of dofs on a subdomain
"""
temp = dla.Function(Vh)
bc = dla.DirichletBC(Vh, dla.Constant(1.0), subdomain)
# warning applying bc does not just apply subdomain.inside to all coordinates
# it does some boundary points more than once and other inside points not
# at all.
bc.apply(temp.vector())
vec = temp.vector().get_local()
dl.plot(temp)
import matplotlib.pyplot as plt
plt.show()
return np.where(vec > 0)[0].shape[0]
fn.CellType.Type.triangle)
V = fn.VectorFunctionSpace(mesh, "CG", 1) # Displacements
C = fn.FunctionSpace(mesh, "CG", 1) # Control
# Volumetric Load
q = -10.0 / t
b = fa.Constant((0.0, q))
def Left_boundary(x, on_boundary):
return on_boundary and abs(x[0]) < fn.DOLFIN_EPS
u_L = fa.Constant((0.0, 0.0))
bcs = [fa.DirichletBC(V, u_L, Left_boundary)]
@build_jax_fem_eval((fa.Function(C), ))
def forward(x):
u = fn.TrialFunction(V)
w = fn.TestFunction(V)
sigma = lmbda * tr(sym(grad(u))) * Identity(2) + 2 * G * sym(
grad(u)) # Stress
R = simp(x) * inner(sigma, grad(w)) * dx - dot(b, w) * dx
a, L = ufl.lhs(R), ufl.rhs(R)
u = fa.Function(V)
fa.solve(a == L, u, bcs)
return u
