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A stochastic method is described for estimating Green's functions (GF's),appropriate to linear advection-diffusion-reaction transport problems, evolvingin arbitrary geometries. By allowing straightforward construction ofapproximate, though high-accuracy GF's, within any geometry, the techniquesolves the central challenge in obtaining Green's function solutions. Incontrast to Monte Carlo solutions of individual transport problems, subject tospecific sets of conditions and forcing, the proposed technique producesapproximate GF's that can be used: a) to obtain (infinite) sets of solutions,subject to any combination of (random and deterministic) boundary, initial, andinternal forcing, b) as high fidelity direct models in inverse problems, and c)as high quality process models in thermal and mass transport design,optimization, and process control problems.

Stochastic estimation of Green's functions with application to diffusion and advection-diffusion-reaction problems