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

Xuxin Yang, Antti Rasila*, Tommi Sottinen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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
StatePublished - 1 Jun 2017
Externally publishedYes

Keywords

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

Fingerprint Dive into the research topics of 'Walk On Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence'. Together they form a unique fingerprint.

Cite this