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

Autor:	Yang, Xuxin, Rasila, Antti, Sottinen, Tommi
Rok vydání:	2015
Předmět:	Mathematics - Numerical Analysis Mathematics - Analysis of PDEs Mathematics - Probability 65C05 68U20 35Q40
Druh dokumentu:	Working Paper
Popis:	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. Comment: 14 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1512.07725 Zobrazit plný text záznamu View this record from Arxiv