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

Xuxin Yang, Antti Rasila, Tommi Sottinen

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)589-602
Number of pages14
JournalMethodology and Computing in Applied Probability
Volume19
Issue number2
DOIs
Publication statusPublished - Jun 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • Brownian motion
  • Monte Carlo simulation
  • Numerical algorithm
  • Linearized Poisson–Boltzmann equation
  • Helmholtz equation
  • Walk On Spheres algorithm

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