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

[Jed Brown]

Jennifer Swenson <jswenson at smu.edu> writes:

> 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 )

Is the RHS of this expression intended to depend on x?

> 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.

Are the ions tracked or do they just appear?

> 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.

It would help to know more about the integral that needs to be done and
the relative data sizes.
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