Hi,
I have the problem following nonlinear problems discussed here
http://fenicsproject.org/documentation/tutorial/nonlinear.html
I changed the problem slightly to input sqrt(inner(nabla_grad(u_), nabla_grad(u_))) into the nonlinear function. This is euclidean norm of u_ and I need to work with such nonlinearities. As soon as I try to solve equation with this setting I obtain
[0]PETSC ERROR: Floating point exception!
[0]PETSC ERROR: Infinite or not-a-number generated in norm!
I think there should be no such error since inner(nabla_grad(u_), nabla_grad(u_)) should be non negative number. Moreover if I add some small number to it and compute sqrt(0.0001+inner(nabla_grad(u_), nabla_grad(u_))) it does then converge.
Please could you help me what I am doing wrong?
Thank you,
Vojtech.
Complete code:
from dolfin import *
import numpy
mesh = dolfin.UnitSquareMesh(50, 50)
tol = 1E-14
def left_boundary(x, on_boundary):
return on_boundary and abs(x[0]) < tol
def right_boundary(x, on_boundary):
return on_boundary and abs(x[0]-1) < tol
V = FunctionSpace(mesh, 'Lagrange', 1)
Gamma_0 = DirichletBC(V, Constant(0.0), left_boundary)
Gamma_1 = DirichletBC(V, Constant(1.0), right_boundary)
bcs = [Gamma_0, Gamma_1]
def q(u):#fenics examples
m=2
return (1+u)**m
du = TrialFunction(V)
u_ = Function(V) # most recently computed solution
v = TestFunction(V)
F = inner(q(sqrt(inner(nabla_grad(u_), nabla_grad(u_))))*nabla_grad(u_), nabla_grad(v))*dx
#F = inner(q(sqrt(0.0001+inner(nabla_grad(u_), nabla_grad(u_))))*nabla_grad(u_), nabla_grad(v))*dx#works well
#F = inner(q(u_)*nabla_grad(u_), nabla_grad(v))*dx #works well
J = derivative(F, u_, du) # Gateaux derivative in dir. of du
problem = NonlinearVariationalProblem(F, u_, bcs, J)
solver = NonlinearVariationalSolver(problem)
prm = solver.parameters
prm['newton_solver']['absolute_tolerance'] = 1E-8
prm['newton_solver']['relative_tolerance'] = 1E-7
prm['newton_solver']['maximum_iterations'] = 25
prm['newton_solver']['relaxation_parameter'] = 1.0
solver.solve()
