dolfin team mailing list archive

[Johan Hake <johan.hake@xxxxxxxxx>]

On Tuesday August 9 2011 09:27:50 Anders Logg wrote:
> 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!

Will do!

Consider I mean ;)

Johan

> --
> 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/ra
> > > ns/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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