# [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 10:05:10 PDT 2015

But what I am suggesting is that we do not need to decompose it into radial
slices in the first place. We can just operate directly on the
volume-integral form of the multipole expansion.
>From Wikipedia:
[image: Inline image 2]
[image: Inline image 1]

If we take the formula for Q_lm and restrict it over a thin radial shell,
we can pull out the r^l and get the usual formula.  If we instead just do
the integral directly, over the existing finite element mesh, we can get
all the Q_lm and therefore evaluate \Phi

Ian

On Sun, Oct 25, 2015 at 9:59 AM, Wolfgang Bangerth <bangerth at tamu.edu>
wrote:

> On 10/25/2015 11:56 AM, Ian Rose wrote:
>
>> 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).
>>
>
> Ah, I see -- yes, you don't need it if you've already decomposed the depth
> into radial slices. What I mean is that the index 'i' can either denote a
> slice/depth range, or some polynomial basis function. In the former case,
> the (radial-direction) basis you are using just happen to be piecewise
> constants.
>
>
> Best
>  W.
>
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth               email:            bangerth at math.tamu.edu
>                                 www: http://www.math.tamu.edu/~bangerth/
>
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