Hi I've been using the signed distance function (Eikonal equation) for some time in various turbulence models. This equation is very stiff so in my approach I have found it necessary to add a stabilization term. I also solve a simpler linear Poisson problem first to get a good initial guess for the nonlinear Newton solver. Otherwise it's pretty straightforward. You could probably use the NonlinearVariational etc classes to wrap this up nicely, but I haven't done that. The code I use is basically (copy and pasted from http://bazaar.launchpad.net/~cbc.rans/cbc.rans/mikael/view/head:/cbc/rans/turbsolvers/Eikonal.py):
V = FunctionSpace(mesh, 'CG', 1) v = TestFunction(V) u = TrialFunction(V) f = Constant(1.0) y = Function(V) # Initialization problem to get good initial guess for nonlinear problem: F1 = inner(grad(u), grad(v))*dx - f*v*dx a1, L1 = lhs(F1), rhs(F1) A1, b1 = assemble_system(a1, L1) # Apply boundary conditions: DirichletBC = 0 on the boundary for bc in bcs: bc.apply(A1, b1) solve(A1, y.vector(), b1) # Stabilized Eikonal equation eps = Constant(0.01) F = sqrt(inner(grad(y), grad(y)))*v*dx - f*v*dx + eps*inner(grad(y), grad(v))*dx J = derivative(F, y, u) etc Solve with Newton iterations This works for me for a range of geometries. Hope it is helpful. Best regards Mikael On 8 August 2011 22:31, Johan Hake <[email protected]> wrote: > Hello! > > Has anyone in the FEniCS comunity used FEniCS to solve for the signed > distance > function? > > http://en.wikipedia.org/wiki/Signed_distance > > This functions gives the distance to the boundary for any given point > inside > the domain. I would like to compute this for the vertices of a mesh. It > looks > like it is a nontrivial problem and I wonder if any of you have put your > teeth > into this one. > > Johan > > _______________________________________________ > Mailing list: https://launchpad.net/~dolfin > Post to : [email protected] > Unsubscribe : https://launchpad.net/~dolfin > More help : https://help.launchpad.net/ListHelp >
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