I have a complex problem I've been working on for years. It's essentially
stochastic optimization with PDE constraints. I know. So, I've brought it up to
the MPI+EC2 CPU cluster level with good results. Now I'd really love to push
this one just a level further. In a nutshell, one wants to approximate solving
[P] min f(q) + Exp[SUM{max(c(T,q)-cmin,0)}]
subject to dc/dt = Transport(c,v,q)
where "Transport" is simplifying the relationship between pumping rates q,
Darcy velocities v (gradients of a flow-type equation with q as RHS) and a
diffusion-advection process at the contamination level (essentially a heat eqn).
The optimization is stochastic because we don't know soil coefficients at the
cell level so we approximate by an "educated sampled guess" which becomes a
scenario. Hence the Expectation is discretized as a sum. And the domain is
fully
rectangular in every possible sense. 2D or 3D space domains are equally
relevant.
My first approach (I've thought of a funkier one I can discuss later) has been
to discretize Flow+Transport as finite-differenced-PDEs and just throw it at
clusters (one core per soil-scenario). My heavy question for the forum is: can
anyone see how to best shape this beast to keep cores fed?
Thanks!
Sergio
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