Efficient simulation of the Schrödinger equation with a piecewise constant positive potential

TY - JOUR

T1 - Efficient simulation of the Schrödinger equation with a piecewise constant positive potential

AU - Yang, Xuxin

AU - Rasila, Antti

AU - Sottinen, Tommi

N1 - Publisher Copyright: © 2019 International Association for Mathematics and Computers in Simulation (IMACS)

PY - 2019/12

Y1 - 2019/12

N2 - We introduce a new method for the Monte Carlo simulation of a weak solution of the Schrödinger-type equation where the potential is piecewise constant and positive. The method, called the killing walk-on-spheres algorithm, combines the classical walk-on-spheres algorithm with killing that can be determined by using panharmonic measures. This paper continues our earlier work in which simulation of the solutions of the Yukawa and the Helmholtz partial differential equations were developed.

AB - We introduce a new method for the Monte Carlo simulation of a weak solution of the Schrödinger-type equation where the potential is piecewise constant and positive. The method, called the killing walk-on-spheres algorithm, combines the classical walk-on-spheres algorithm with killing that can be determined by using panharmonic measures. This paper continues our earlier work in which simulation of the solutions of the Yukawa and the Helmholtz partial differential equations were developed.

KW - Brownian motion

KW - Harmonic measure

KW - Killing walk-on-spheres

KW - Numerical algorithm

KW - Schrödinger equation

KW - Yukawa equation

UR - http://www.scopus.com/inward/record.url?scp=85067340902&partnerID=8YFLogxK

U2 - 10.1016/j.matcom.2019.05.012

DO - 10.1016/j.matcom.2019.05.012

M3 - 文章

AN - SCOPUS:85067340902

SN - 0378-4754

VL - 166

SP - 315

EP - 323

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

ER -