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Recent research shows that Monte Carlo diffusion methods are often the most efficient algorithms for solving certain elliptic boundary value problems. In this paper, we extend this research by providing two efficient algorithms based on the concept of "last-passage diffusion." These algorithms are qualitatively compared with each other (and with the best(More)
Computing the capacitance of the unit cube analytically is considered to be " one of the major unsolved problems of electrostatic theory. " However, due to improvements in computer performance and error analysis for " Walk on Spheres " (WOS) Monte Carlo algorithms, we can now calculate the capacitance of the unit cube to many more significant digits than(More)
Many important classes of problems in materials science and biotechnology require the solution of the Laplace or Poisson equation in disordered two-phase domains in which the phase interface is extensive and convoluted. Green's function first-passage (GFFP) methods solve such problems efficiently by generalizing the " walk on spheres " (WOS) method to allow(More)
This study presents a Feynman–Kac path-integral implementation for solving the Dirichlet problem for Poisson's equation. The algorithm is a modified " walk on spheres " (WOS) that includes the Feynman–Kac path-integral contribution for the source term. In our approach, we use an h-conditioned Green's function instead of simulating Brownian trajectories in(More)
The " Walk On Spheres " (WOS) algorithm and its relatives have long been used to solve a wide variety of boundary value problems [Ann. All WOS algorithms that require the construction of random walks that terminate, employ an-shell to ensure their termination in a finite number of steps. To remove the error related to this-shell, Green's function(More)
We describe two efficient methods of estimating the fluid permeability of standard models of porous media by using the statistics of continuous Brownian motion paths that initiate outside a sample and terminate on contacting the porous sample. The first method associates the ''penetration depth'' with a specific property of the Brownian paths, then uses the(More)
We develop and test the last-passage diffusion algorithm, a charge-based Monte Carlo algorithm, for the mutual capacitance of a system of conductors. The first-passage algorithm is highly efficient because it is charge based and incorporates importance sampling; it averages over the properties of Brownian paths that initiate outside the conductor and(More)