dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Tue, Aug 09, 2011 at 08:50:39AM -0700, Johan Hake wrote:
> Thanks Mikael!
>
> That worked after I scaled up the stabilizing factor for a larger mesh. See
> attached image :)

Consider adding, and documenting, a demo for the Eikonal equation!

--
Anders


> 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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