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[Martin Sandve Alnæs <question159192@xxxxxxxxxxxxxxxxxxxxx>]

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

Martin Sandve Alnæs proposed the following answer:
Sorry, that was too quick. Since u is scalar, that term is fine.

Martin

On 27 May 2011 08:20, Martin Sandve Alnæs <martinal@xxxxxxxxx> wrote:
> 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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