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

Christophe Ortiz christophe.ortiz at ciemat.es
Wed Feb 26 01:56:27 CST 2014


On Sat, Feb 22, 2014 at 6:17 AM, Derek Gaston <friedmud at gmail.com> wrote:

> The phase-field system developed by Michael Tonks (copied on this email)
> will be part of the open-source release of MOOSE (hopefully by the end of
> next week).  Feel free to contact either myself or Mike for more
> information while we all wait...
Thanks a lot for the offer. I checked out the videos of MOOSE and indeed it
seems to be a great tool. However, in my group we prefer to develop our own
home-made simulation tools (except for tools like PETSc of course). I know
that using simulation tools developed by others saves a lot of work, but by
experience I can say that when comes the time to implement new things (new
mechanisms, new conditions), which were not planned, it becomes difficult
and time consuming since you must spend a lot of time to adapt the tool.
Therefore, we adopted the policy to develop our own tools.
Moreover, I already dedicated some time to develop a programming interface
(ie collections of C++ classes) for our purpose, which is the diffusion and
interaction of many species (thousands).

Nevertheless, I am reading the paper about the phase-field model behind
MOOSE. Maybe I will use this approach for our problems, still don't know. I
don't have experience with phase-field models. BTW, thanks Jed for the
link. I could download the paper.


> In the meantime you can also check out some of the youtube videos of MOOSE
> in action (the phase-field system is in use in these videos in the
> microstructure models):
> http://www.youtube.com/watch?v=0oz8FD3H52s
> http://www.youtube.com/watch?v=4xTfQxpGAI4
> http://www.youtube.com/watch?v=V-2VfET8SNw
> Derek
> On Fri, Feb 21, 2014 at 5:33 PM, Jed Brown <jed at jedbrown.org> wrote:
>> 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.
>> @article{tonks2012object,
>>   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},
>>   volume={51},
>>   number={1},
>>   pages={20--29},
>>   year={2012},
>>   publisher={Elsevier}
>> }
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