Walk On Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence

TY - JOUR

T1 - Walk On Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence

AU - Yang, Xuxin

AU - Rasila, Antti

AU - Sottinen, Tommi

N1 - Publisher Copyright: © 2016, Springer Science+Business Media New York.

PY - 2017/6/1

Y1 - 2017/6/1

N2 - We show that a constant-potential time-independent Schrödinger equation with Dirichlet boundary data can be reformulated as a Laplace equation with Dirichlet boundary data. With this reformulation, which we call the Duffin correspondence, we provide a classical Walk On Spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the boundary value problem. We compare the obtained Duffin WOS algorithm with existing modified WOS algorithms.

AB - We show that a constant-potential time-independent Schrödinger equation with Dirichlet boundary data can be reformulated as a Laplace equation with Dirichlet boundary data. With this reformulation, which we call the Duffin correspondence, we provide a classical Walk On Spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the boundary value problem. We compare the obtained Duffin WOS algorithm with existing modified WOS algorithms.

KW - Brownian motion

KW - Helmholtz equation

KW - Linearized Poisson–Boltzmann equation

KW - Monte Carlo simulation

KW - Numerical algorithm

KW - Walk On Spheres algorithm

KW - Yukawa equation

UR - http://www.scopus.com/inward/record.url?scp=85019253309&partnerID=8YFLogxK

U2 - 10.1007/s11009-016-9504-9

DO - 10.1007/s11009-016-9504-9

M3 - 文章

AN - SCOPUS:85019253309

SN - 1387-5841

VL - 19

SP - 589

EP - 602

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

IS - 2

ER -