[petsc-users] From 1D to 3D problem ? Unstructured mesh ?

Jed Brown jed at jedbrown.org
Fri Feb 21 19:33:36 CST 2014

Christophe Ortiz <christophe.ortiz at ciemat.es> writes:

> Hi all,
> Recently I have implemented a 1D problem of coupled diffusion equations
> using PETSc. I did it using finite differences for diffusion terms and
> F(t,U,U_t) = 0. It works pretty well with ARKIMEX3. I get a nice timestep
> variation and all boundary conditions work well.
> Now I would like to move to 3D problems to simulate the diffusion and
> interaction of species in a "real material". By real material I mean a
> material made of subregions with internal surfaces where species could
> recombine (means Dirichlet). These subregions are distributed in a
> complicated manner, ie not cartesian. A good picture of this would be a
> polycrystal (see attachment to get an idea). Each crystal has a different
> orientation and the boundary between two small crystals forms an internal
> surface.
> I have several questions on how to implement this:
> 1) Since, the problem will not be solved in a cartesian mesh, should I use
> unstructured meshes ? If so, how can this unstructured mesh can be
> generated ( I have no experience with unstructured meshes. I always work in
> 1D).

Are you intending to mesh the boundaries of the crystals?  Will you be
dynamically remeshing?  (That is very complicated and expensive in 3D.)
What formulation will you be using for grain boundary evolution?

I think you should check out phase field models, such as the publication
below.  Perhaps check out the paper below.  The framework (MOOSE) used
for this publication should be released open source on github next week
(check https://github.com/idaholab/).  I don't know if Marmot, the
phase-field component, will be open source any time soon, but they are
typically happy to collaborate.  MOOSE uses PETSc for solvers, but
provides a higher level interface.

  title={An object-oriented finite element framework for multiphysics phase field simulations},
  author={Tonks, M.R. and Gaston, D. and Millett, P.C. and Andrs, D. and Talbot, P.},
  journal={Computational Materials Science},

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