dolfin team mailing list archive

[Johan Hake <johan.hake@xxxxxxxxx>]

Thanks Mikael!

That worked after I scaled up the stabilizing factor for a larger mesh. See 
attached image :)

Even if this is cool, I am planing to extend the CGAL wrapper so a user can 
compute the closest distance between a vertex and the boundary. This might be 
faster, and less mesh dependent. 

I am also hoping I can make this Boundary marker dependent. Given a 
FacetFunction I should be able to calculate the closest distance to a subset 
of the boundary which is nice for a particular application I have in mind :)

Cheers!

Johan

On Tuesday August 9 2011 01:04:11 Mikael Mortensen wrote:
> 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/t
> urbsolvers/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 <johan.hake@xxxxxxxxx> 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
> > 
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