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[Graham Rowlands <question159192@xxxxxxxxxxxxxxxxxxxxx>]

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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