Kshitij Kulshreshtha kshitij at math.upb.de
Mon Oct 7 09:51:21 EDT 2013

```Hello,

in such a case you should ask yourself which derivatives do you really
require? Do you require the derivatives of some function computed on the
stencil w.r.t. the areas and the volumes, or do you require the
derivatives of the function on the stencil w.r.t. the coordinates of the
stencil?

In the first case you only need to do variant 2 on each stencil
(depending on the case) this computation requires only tracing for one
stencil and then can be repeated for all others. You will get
per-stencil derivatives.

In the second case you can break the trace into two parts, one that
computes S and V from X,Y,Z globally. And another that does variant 2.
You will get two separate derivatives. One per-stencil as before and the
second global. Then you need to multiply the corresponding stencil
derivatives with the global ones to get the derivatives w.r.t. coordinates.

So the real question is which derivatives do you need?

Best
Kshitij.

As on 2013-10-07 15:37h, Antoine De Blois did write:
> Hi Everyone,
>
>
>
> I would like to know which of the 2 following options is computationally
> better. My current version of the code involves surface areas as
> independent variables. I now have to add the volumes to the independent
> variable, which leads to a dilemma for my implementation. In my
> application, surfaces and volumes are pre-computed on the entire
> computational domain. However, I perform automatic differentiation on a
> smaller stencil. The only thing to remember for you is that the surfaces
> and volumes are already pre-computed on the entire grid.
>
>
>
> Since the surfaces and volumes are in fact dependent on the coordinates
> S=S(X,Y,Z), V=V(X,Y,Z), should I:
>
>
>
> 1.       Use the coordinates as independent variables (Xa << X; Ya << Y;
> Za <<Z;) and then compute the surfaces and volumes as active arrays
>
> 2.       Use the surfaces and volumes as independent variables (Sa <<S;
> Va <<V;), yielding more independent variables, but less computation
> between the trace_on and trace_off.
>
>
>
> I already asked what was the biggest contributing factor for efficient
> process was the amount of computation between the trace_on and
> trace_off, and not the amount of indendent variables. This would lead to
> option 2, right, especially that the volumes calculation involves tests
> at the boundaries.
>
>
>
> Thank you for your time,
>
> Cheers,
>
> Antoine
>
>
>
>
>
> *Antoine DeBlois*
> Aéronautique / Aerospace
>
> T    514-855-5001, x 50862
>
> antoine.deblois at aero.bombardier.com
> <mailto:antoine.deblois at aero.bombardier.com>
>
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> _______________________________________________
>

--
Dr. Kshitij Kulshreshtha

Institut für Mathematik,
Warburger Straße 100,

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