# [aspect-devel] How to grab the radius of every interior sphere made up from cell faces in the domain and some MPI questions

Ian Rose ian.rose at berkeley.edu
Sun Oct 25 09:56:12 PDT 2015

Yes, I am saying that we don't need the index 'i' at all.  It is a natural
way to do things if you already have a grid that has radial slices to pick
out, but it is not necessary (unless I've made an error in thinking here).

On Sun, Oct 25, 2015 at 9:53 AM, Wolfgang Bangerth <bangerth at tamu.edu>
wrote:

> On 10/25/2015 11:49 AM, Ian Rose wrote:
>
>>
>>     r_{lmi} =
>>          \int \int \int  drho(r,phi,theta) Y_{lm} R_i(r) dtheta dphi dr
>>
>>     where R_i(r) are the basis functions in radial direction.
>>
>> ​ Ah, but this is the beauty of the multipole expansion. As long as all
>> the
>> mass sources are completely external or completely internal to our
>> circumscribing sphere, then the radial functions are entirely
>> determi​ned, and
>> are just powers of r (where the power is related to the order of the
>> multipole
>> and whether it is external or internal).
>>
>
> Exactly, i.e.,
>   R_i(r) = r^i
> if I see it correctly, for some set of exponents i. Or do I misunderstand
> and you want to imply that it should be
>   R_l = r^{-l}
> or similar, and that we don't need another index 'i' at all?
>
>
> Best
>  W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth               email:            bangerth at math.tamu.edu
>                                 www: http://www.math.tamu.edu/~bangerth/
>
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