Question #159192 on DOLFIN changed: https://answers.launchpad.net/dolfin/+question/159192
Graham Rowlands posted a new comment: Nathan, Thanks for your thoughtful response. I've more or less arrived at similar conclusions, and appreciate the suggestion to relax at an elevated diffusion level. I assume the number of available steady states is system dependent, but those I'm working with should have a well defined global energy minimum. All in all it seems like a well-managed time-dependent technique is problem the most promising. I guess I'm slightly unsure how you added the reflective boundary condition. When solving in the time-dependent case I've been using Dirichlet conditions at the boundaries (with seemingly minor loss in overall probability). The Crank-Nicolson scheme uses the following forms: a = v*u*dx + 0.5*( -dt*dot(A*u,grad(v))*dx + dt*( dot(u*dot(B,div(B)),grad(v)) + 0.5*dot(dot(B*B.T,grad(u)),grad(v)) )*dx ) L = v*u0*dx - 0.5*( -dt*dot(A*u0,grad(v))*dx + dt*( dot(u0*dot(B,div(B)),grad(v)) + 0.5*dot(dot(B*B.T,grad(u0)),grad(v)) )*dx ) Where u0 is the result from the previous time step. For the reflective boundaries are you simply taking L += g*v*ds, where g is valued 0.0 along the boundaries? Am I missing your meaning? You are correct though, FPEs seem somewhat confounding to FE solvers in certain respects (though I lack familiarity with both the equations and the solvers.) I'm curious about what systems you are studying, btw. Thanks, Graham -- You received this question notification because you are a member of DOLFIN Team, which is an answer contact for DOLFIN. _______________________________________________ Mailing list: https://launchpad.net/~dolfin Post to : [email protected] Unsubscribe : https://launchpad.net/~dolfin More help : https://help.launchpad.net/ListHelp
