Abstract. Elliptic partial differential equations are ubiquitous in graphics and engineering, but remain challenging to solve on complex or evolving geometries. Traditional discretization schemes (e.g., FEM/FDM) provide stable, globally coupled solutions but require heavy meshing or extreme refinement to accurately resolve geometric detail. In contrast, grid-free Monte Carlo methods (e.g., Walk on Spheres/Stars) adapt naturally to arbitrary geometry and offer massive parallelism, but rely on...