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

Christophe Ortiz christophe.ortiz at ciemat.es
Wed Feb 19 01:50:36 CST 2014

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

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

2) If answer to 1) is yes, what are the steps to follow to use unstructured
mesh with PETSc ?

3) If answer to 1) is yes, ie unstructured meshes should be used, should I
use a finite volume approach instead of a finite differences ?

4) As I mentionned before, there will be internal surfaces between the
subregions, ie there will not only be a unique surface outside the volume.
Do you think the presence of internal surfaces, ie internal boundary
conditions, can be implemented ?

Many thanks in advance for your help.
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