Walk on Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence
Numerical Analysis
2015-12-25 v1 Analysis of PDEs
Probability
Abstract
We show that a constant-potential time-independent Schr\"odinger 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.
Keywords
Cite
@article{arxiv.1512.07725,
title = {Walk on Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence},
author = {Xuxin Yang and Antti Rasila and Tommi Sottinen},
journal= {arXiv preprint arXiv:1512.07725},
year = {2015}
}
Comments
14 pages, 5 figures