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

Xuxin Yang, Antti Rasila*, Tommi Sottinen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)315-323
Number of pages9
JournalMathematics and Computers in Simulation
Volume166
DOIs
StatePublished - Dec 2019

Keywords

  • Brownian motion
  • Harmonic measure
  • Killing walk-on-spheres
  • Numerical algorithm
  • Schrödinger equation
  • Yukawa equation

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