On Sat, Dec 8, 2012 at 4:26 PM, Adam Stone <[email protected]> wrote:
> Sorry to be asking so many questions, but I've hit yet another hurdle.
> This is sort of a continuation of my laser heating problem. Thanks to the
> mailing list I was able to obtain the correct temperature distribution, but
> the next part of the problem is to use that temperature distribution to
> calculate a thermo-elastic expansion given by
>
>
>
Adam,
Good that you are making some progress. There is a problem here. FiPy
doesn't support creating equations that are both anisotropic and coupled
(or vectorized). To solve the above you need a representation of an
equation as follows,
$ \partial_t q^i = \partial_k \left[ \Gamma^{kli}_j \partial_l \q^j
\right] $
where $ \Gamma^{kli}_j$ is a diffusion tensor and $i$ and $j$ run over the
number of equations and $k$ and $l$ run over the number of dimensions.
Currently, in FiPy you can have either
$ \partial_t q^i = \partial_k \left[ \Gamma^i_j \partial_k \q^j \right] $
or
$ \partial_t q = \partial_k \left[ \Gamma^{kl} \partial_l \q \right] $
but not both. I can't see a way to make it work at present other than just
using an explicit representation.
On an alternative branch, I have a working code for coupled hyperbolic
equations of the form
$ \partial_t q^i = A^{ki}_j \partial_k q^j $
which is similar to what you want. I am sure it is straight forward getting
the $\Gamma^{kli}_j$ tensor notation working given that we have the sub
parts working. I'll file a ticket and hopefully do something on this for
the next release.
Sorry about that.
--
Daniel Wheeler
<<dfdffdga.png>>
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