def copy_expression(expr):
if hasattr(expr, 'cppcode'):
# old fenics versions
new_expr = dla.Expression(expr.cppcode, **expr.user_parameters,
degree=expr.ufl_element().degree())
else:
# fenics 2019
new_expr = dla.Expression(expr._cppcode, **expr._user_parameters,
degree=expr.ufl_element().degree())
return new_expr
def get_halfar_shallow_ice_exact_solution(Gamma, mesh, degree, ndim):
import sympy as sp
H, x, y, t = get_halfar_shallow_ice_exact_solution_sympy(Gamma, ndim)
exact_sol = dla.Expression(
sp.printing.ccode(H), cell=mesh.ufl_cell(),
domain=mesh, t=0, degree=degree)
return exact_sol
def assemble_fenics(u, kappa0, kappa1):
f = fa.Expression(
"10*exp(-(pow(x[0] - 0.5, 2) + pow(x[1] - 0.5, 2)) / 0.02)", degree=2)
inner, grad, dx = ufl.inner, ufl.grad, ufl.dx
J_form = 0.5 * inner(kappa0 * grad(u), grad(u)) * dx - kappa1 * f * u * dx
J = fa.assemble(J_form)
return J
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