On Mar 20, 2:34 pm, Ondrej Certik <ond...@certik.cz> wrote:
> On Fri, Mar 20, 2009 at 6:58 AM, comer.dun...@gmail.com
>
> <comer.dun...@gmail.com> wrote:
> > Thanks for the suggestion. I have now looked at the relativity.py
> > file and believe it to be a reasonable start. Once I understand more
> > I will make some related changes and let you know what I get. Another
>
> Excelllent. Btw, the way it is currently done is very inneficient ---
> for example for the Riemann tensor I am calculating all the
> coefficients of the Christoffel symbols over and over again. This
> should be cached.
>
> > related area is general relativistic fluid dynamics for which sympy
> > hopefully can be useful in generating eigenvectors and eigenvalues of
> > the Jacobian matrix of the conservative variables with respect to the
> > primitive variables. Also, using sympy to compute the residual of the
> > equations when studying the accuracy of computations based on
> > Einstein's equations (Numerical Relativity) could be useful. These
> > kinds of computations are currently done using Mma. These are just a
> > few things which it would be nice to demonstrate can be handled by
> > sympy.
>
> That is very cool. How are you solving the Einstein's equations?
> Spectral elements? Or finite differences? Or some other method?
Einstein's equations coupled to relativistic fluid. Both are handled
using flavors of Finite Volume methods, not FE.
>
> Is there an application for finite elements? If so, then the whole
> group that I am at could be interested in that, feel free to browse
> what we do here:
>
> http://hpfem.org/http://hpfem.math.unr.edu/
Yeah, I see. I don't think we will be delving into using FE in the
foreseeable future.
I need sympy enhanced with indicial tensor capability. I would use
this facility to help support code development and testing of the
Numerical Relativity codes.
>
> > On a related topic, what do you think is the problem with tensor.py?
> > I can see a need for the approach which seems to be contained therein,
> > namely evaluation of expressions involving products of various tensors
> > of various ranks in things like:
>
> > T^{abcd}_{ef} * Z_{ad} * W_{b} * Q_{bc} where a,b,c, and d run over
> > {0,1,2,3}.
>
> > Such expressions are used in Numerical Relativity codes and are quite
> > unwieldy to generate by hand. Having sympy do this would be cool and
> > maybe even useful.
>
> I started to write code for this in this issue:
>
> http://code.google.com/p/sympy/issues/detail?id=16
I see. I am afraid that I am too new to this business to do much in
the way of developing the indicial stuff. I would be very appreciative
if you or the other developers in the know can get it done !!
>
> as you can see, it is a very old issue. :) So it just needs to be finished.
>
> I am very interested in sympy being useful for your research and maybe
> you'll find other ways that we can collaborate on this, see above.
>
Maybe we can. Let's just see how things go in the coming weeks with my
feeble attempts.
Thanks for your efforts.
Comer
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