Off-centered “Walk-on-Spheres” (WOS) algorithm

The “Walk-on-Spheres” (WOS) algorithm has played the central role in simulating the diffusion process in Diffusion Monte Carlo methods. In this paper, based on the isomorphism between the electrostatic Poisson problem and the corresponding diffusion motion expectation of the first-passage, we develop an off-centered WOS algorithm to replace the old WOS one. We find that the new off-centered WOS algorithm is much more efficient than the old one.