On Wed, 7 Dec 2011 02:54:35 +0000 (UTC), Sergio Lucero <[email protected]> wrote: > 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?
I assume you know about Paulius's 3D FD trick? 2D FD is rather straightforward. See http://dl.acm.org/citation.cfm?id=1513905&bnc=1 for both. HTH, Andreas
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