[petsc-users] implementing non-local scalar field

[Swenson, Jennifer]

Dear PETSc Users,

As a part of my problem, I need to be able to look up the value of a scalar field (let's call it xi) that is defined via a somewhat non-trivial integral over a second scalar field (let's call it rho).  Mathematically we have
 [cid:07284a17-07f8-426b-85da-461ebc1fe4b8]
What we're modeling here is the average energy loss of an energetic ion that is passing through a solid material.  Ions can arrive with a specified direction, so to calculate xi at each point, we have to perform line integrals back toward the ion source, and keep track of how much mass the ion has passed through.

In a serial algorithm, one can in principle generate xi by working from the top down, subtracting energy from each row of grid points given information on the density field.  However, it is not clear how one could develop a robust parallel algorithm, much less one that works within the PETSc framework.

I would very grateful for any help you can offer.

Sincerely,
Jennifer Swenson

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