Chi-Ok Hwang

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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)
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)
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)
A discrete random walk method on grids was proposed and used to solve the linearized Poisson– Boltzmann equation ~LPBE! @R. Ettelaie, J. Chem. Phys. 103, 3657 ~1995!#. Here, we present an efficient grid-free random walk method. Based on a modified ‘‘walk on spheres’’ algorithm @B. S. Elepov and G. A. Mihailov, Sov. Math. Dokl. 14, 1276 ~1973!# for the LPBE,(More)
The “Walk On Spheres” (WOS) algorithm and its relatives have long been used to solve a wide variety of boundary value problems [Ann. Math. Stat. 27 (1956) 569; J. Heat Transfer 89 (1967) 121; J. Chem. Phys. 100 (1994) 3821; J. Appl. Phys. 71 (1992) 2727]. All WOS algorithms that require the construction of random walks that terminate, employ an -shell to(More)
This paper provides a review of a new method of addressing problems in diffusion Monte Carlo: the Green’s function first-passage method (GFFP). In particular, we address three new strands of thought and their interaction with the GFFP method: the use of angle-averaging methods to reduce vector or tensor Laplace equations to scalar Laplace equations; the use(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)