[petsc-users] implementing non-local scalar field -- updated

[Jennifer Swenson]

Note: This has been updated from the original thread to contain the
equation. I apologize for the previous error.

 

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

 

xi(x,t) = max( 0.1 - 1/L int{ rho_1[r(s),t] + rho_2[r(s),t] } ds )

 

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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