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[Mikael Mortensen <question156790@xxxxxxxxxxxxxxxxxxxxx>]

Question #156790 on DOLFIN changed:
https://answers.launchpad.net/dolfin/+question/156790

    Status: Open => Answered

Mikael Mortensen proposed the following answer:
Hi,

There is an Eikonal solver in the CBC.RANS project on
https://launchpad.net/cbc.rans.

Basically, you need to declare a nonlinear problem.  Try something like

y = Function(Q)
eps = Constant(0.01)
F = inner(grad(y), grad(y))*v*dx - n**2*v*dx + eps*inner(grad(u),
grad(v))*dx
J = derivative(F, y, u)
bc = DirichletBC(Q, Constant(0), DomainBoundary())
problem = VariationalProblem(J, -F, bcs)
y = problem.solve()

where the last term in F is for stabilization. There are other possibilities
for
stabilizing as well, but this is the one that works for me.

Hope it works. Look up the nonlinear demos if it doesn't. (Never tried it in
1D before)

Best regards

Mikael


On 9 May 2011 21:56, Chaffra <question156790@xxxxxxxxxxxxxxxxxxxxx>
wrote:

> New question #156790 on DOLFIN:
> https://answers.launchpad.net/dolfin/+question/156790
>
> Hi,
>
> I'd like to solve the pde  |grad(u)|**2 = n**2. To start , I tried the
> following example but it does not work. What would be the correct
> variational form for this?
>
> Thanks. Chaffra
>
>
> mesh = UnitInterval(51, )
>
> class RefractiveIndex(Expression):
>    def eval(self, values,x):
>        if x[0]<0.5:
>            values[0] = 2.0
>        else:
>            values[0] = 3.0
>
> Q = FunctionSpace(mesh,'CG',1)
> u = TrialFunction(Q)
> v = TestFunction(Q)
>
> n = RefractiveIndex()
> a = inner(grad(u), grad(u))*v*dx
> L = n**2*v*dx
>
> problem = VariationalProblem(a, L, bcs=[])
> problem.solve()
>
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