TY - JOUR

T1 - A global random walk on grid algorithm for second order elliptic equations

AU - Sabelfeld, Karl K.

AU - Smirnov, Dmitrii

N1 - Publisher Copyright: © 2021 Walter de Gruyter GmbH, Berlin/Boston.

PY - 2021/9/1

Y1 - 2021/9/1

N2 - We suggest in this paper a global random walk on grid (GRWG) method for solving second order elliptic equations. The equation may have constant or variable coefficients. The GRWS method calculates the solution in any desired family of m prescribed points of the gird in contrast to the classical stochastic differential equation based Feynman-Kac formula, and the conventional random walk on spheres (RWS) algorithm as well. The method uses only N trajectories instead of mN trajectories in the RWS algorithm and the Feynman-Kac formula. The idea is based on the symmetry property of the Green function and a double randomization approach.

AB - We suggest in this paper a global random walk on grid (GRWG) method for solving second order elliptic equations. The equation may have constant or variable coefficients. The GRWS method calculates the solution in any desired family of m prescribed points of the gird in contrast to the classical stochastic differential equation based Feynman-Kac formula, and the conventional random walk on spheres (RWS) algorithm as well. The method uses only N trajectories instead of mN trajectories in the RWS algorithm and the Feynman-Kac formula. The idea is based on the symmetry property of the Green function and a double randomization approach.

KW - elliptic equations

KW - fundamental solution

KW - Green's function

KW - random walks on grids, double randomization

UR - http://www.scopus.com/inward/record.url?scp=85113327156&partnerID=8YFLogxK

U2 - 10.1515/mcma-2021-2092

DO - 10.1515/mcma-2021-2092

M3 - Article

AN - SCOPUS:85113327156

VL - 27

SP - 211

EP - 225

JO - Monte Carlo Methods and Applications

JF - Monte Carlo Methods and Applications

SN - 0929-9629

IS - 3

M1 - 20212092

ER -