  A stochastic method is described for estimating Green's functions (GF's),
appropriate to linear advection-diffusion-reaction transport problems, evolving
in arbitrary geometries. By allowing straightforward construction of
approximate, though high-accuracy GF's, within any geometry, the technique
solves the central challenge in obtaining Green's function solutions. In
contrast to Monte Carlo solutions of individual transport problems, subject to
specific sets of conditions and forcing, the proposed technique produces
approximate GF's that can be used: a) to obtain (infinite) sets of solutions,
subject to any combination of (random and deterministic) boundary, initial, and
internal 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.
