On Mon, Apr 9, 2012 at 1:02 PM, James Snyder <[email protected]>wrote:
> I'm interested in looking at some problems that involve time harmonic
> versions of Maxwell's equations in looking around at how these have
> been approached in finite element models in the past, I've run into a
> few issues:
>
FiPy is not currently set up to do this effectively. The next release of
FiPy will allow the implementation of hyperbolic vector equations of the
form,
\partial_t \phi^i + \partial_j \left( A^{ij}_k \phi^k \right) = 0
where the $A^{ij}_k$ is a coefficient matrix that might be dependent on
$\phi$. An effective solution to that equation is what is required to solve
Maxwell's correctly. The next version of FiPy will allow the problem to be
posed, but will solve it only in a naive way.
I am currently working on a less naive approach to solving general coupled
hyperbolic equations using Riemann flux updates which will enable an
effective solution of Maxwell's equations in FiPy. Most likely that will be
part of version 3.1 (and we haven't released 3.0 yet). I'm planning on
including a Maxwell's equations example as part of this although I haven't
done so yet. The branch is
<http://matforge.org/fipy/browser/branches/riemann>
You can take a look at progress but I can't provide any support right now.
The first of which is how to represent a curl operator. Presumably it
> might be best to add the functionality, perhaps based on existing
> gradient functionality? I suppose that there are workarounds using
> the existing API, but if they're part of an equation I suspect that
> might get more complex than desirable.
>
You'll have to wait for vector equations to do this correctly. Anything
else will be a hack that probably won't work properly.
Cheers
--
Daniel Wheeler
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