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Walk on Decomposed Subdomains
A research paper introducing 'Walk on Decomposed Subdomains', a hybrid Monte Carlo–deterministic solver for elliptic PDEs. The approach addresses the slow convergence and high variance of grid-free Monte Carlo methods (like Walk on Spheres) by decomposing the domain into smaller subdomains, precomputing Poisson kernel-based solution operators per tile, and coupling subdomains via an absorbing Markov chain solved deterministically. This combines the geometry-handling advantages of grid-free Monte Carlo with the fast convergence of grid-based solvers. The method is trivially parallelizable per tile and exposes a tunable trade-off between Monte Carlo estimation cost and deterministic global solve cost.
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