Ack, I realize the pasted screenshot of the relevant equation has 
disappeared! I've included it as an attachment to this reply.

- Lucas

On Saturday, April 22, 2023 at 2:49:07 PM UTC-5 Lucas Myers wrote:

> Hi folks,
>
> I'd like to coarse-grain a finite element field, where the coarse-graining 
> procedure is just convolving the field with a Gaussian function. More 
> concretely, I'd like to do the following:
>
>
> For a regular Triangulation, we can calculate <X> at every quadrature 
> point by iterating through the entire Triangulation and calculating the 
> integrand at all of the quadrature points. In fact, because there is a 
> Gaussian in distance in the integrand, we only have to look at cells a 
> distance ~3a_0 away.
>
> However, for a distributed triangulation it could be the case that cells 
> 3a_0 away may be on a different MPI process. My first question is: is there 
> a way to extend the number of ghost cells along the boundary such that they 
> are some total distance away from the locally-owned cells on the edge of 
> the domain? And if not, is there a nice utility to allow me to access 
> neighboring cells on other domains (albeit, at the cost of some MPI 
> messages)? 
>
> Otherwise, is there a good way to do this? My guess would be to do all of 
> the local integrations first, and make a vector of cells which end up 
> butting against the boundary. Then one could use the `ghost_owners` 
> function to send information about the edge cells to the adjacent 
> subdomains, which would then send information back. However that seems a 
> little in the weeds of using MPI and also would require some error-prone 
> bookkeeping, which I would like to avoid if possible.
>
> Thanks so much for any help!
> - Lucas
>

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