I'm trying to solve a nonlinear problem in fenics. Instead of knowing the nonlinear function as an expression, I only know the values in the form of data.
In other words, if i am solving nabla(k(u).nabla(u)) = C, I do not know k(u) or cannot write it in terms of x[0] etc, I only know corresponding values of k for all values of u.
At the moment i have written some interpolating function and called it into 'k' which can project it to a function space, but it does not seem to work when i put it into the variational form and solve.
Below is some code to clarify the problem: I was using method of manufactured solutions where u=x^2 with k=1+u^2 as a test, where k_data = list of data for u=[0,(1+xmax^2)].
I've been told i can look into subclasses in Expression but i have no idea how to do this without knowing it in terms of x[0]. please help!
u = Function(V)
v = TestFunction(V)
u.interpolate(Expression("x[0]"))
k = interpolate_table(u,kappa_data)
plot(project(k,V))
C = Expression("-2.0-10.0*x[0]*x[0]*x[0]*x[0]")
diff_part = k*inner(grad(u),grad(v))*dx
source_part = C*v*dx
Res = diff_part - source_part
J = derivative(Res,u)
problem = NonlinearVariationalProblem(Res, u, bcs, J)
solver = NonlinearVariationalSolver(problem)
solver.solve()
prm = solver.parameters['newton_solver']
prm['relative_tolerance'] = 1E-6
prm['absolute_tolerance'] = 1E-6
prm['maximum_iterations'] = 100
