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[Martin Sandve Alnæs <question159192@xxxxxxxxxxxxxxxxxxxxx>]

Question #159192 on DOLFIN changed:
https://answers.launchpad.net/dolfin/+question/159192

    Status: Open => Answered

Martin Sandve Alnæs proposed the following answer:
Check your dot(A, grad(v)) term again. Can you write it with index
notation?

Martin
Den 27. mai 2011 01.25 skrev "Graham Rowlands" <
question159192@xxxxxxxxxxxxxxxxxxxxx> følgende:
> New question #159192 on DOLFIN:
> https://answers.launchpad.net/dolfin/+question/159192
>
> Greetings,
>
> I'm solving the Fokker-Planck equation in 2D just fine in the
time-dependent case (Crank-Nicolson using dolfin in the usual manner I've
seen around here.) I'm now trying to find the steady state solution without
waiting for the dynamic simulation to converge. This is apparently much more
difficult for me to wrap my head around.
>
> The equation (with implied summation over repeated indices):
> du/dt = d/dx_i (A_i * u) + d/dx_i (d/dx_j (B_ij * u ) ))
>
> maps to the following ufl code in weak form in the steady state:
> drift = -dot(A,grad(v))*u
> diffusion = -dot(dot(B,div(B)),grad(v))*u +
0.5*dot(dot(B*B.T,grad(u)),grad(v))
>
> a = (drift + diffusion)*dx # bilinear
> L = f*v*dx # Linear, where f is set to 0.0 in the cpp code
>
> I seem to just get the trivial solution when trying the
VariationalProblem(a,L,bcs) approach, and I guess I'm rather unsure how to
work on relaxing this system in a similar way to that seen in the non-linear
approach.
>
> Many thanks to all involved,
> Graham
>
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