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arXiv · 1512.07725

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

Xuxin Yang·Antti Rasila·Tommi Sottinen
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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.

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Xuxin Yang, Antti Rasila, Tommi Sottinen. 2015-12-24. Walk on Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence. https://arxiv.org/abs/1512.07725

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