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

Xuxin Yang; Antti Rasila; Tommi Sottinen

doi:10.1007/s11009-016-9504-9

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

Xuxin Yang, Antti Rasila, Tommi Sottinen

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-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 language	English
Pages (from-to)	589-602
Number of pages	14
Journal	Methodology and Computing in Applied Probability
Volume	19
Issue number	2
DOIs	https://doi.org/10.1007/s11009-016-9504-9
Publication status	Published - Jun 2017
MoE publication type	A1 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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10.1007/s11009-016-9504-9

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title = "Walk On Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence",

abstract = "We show that a constant-potential time-independent Schr{\"o}dinger 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 = "Brownian motion, Monte Carlo simulation, Numerical algorithm, Linearized Poisson–Boltzmann equation, Helmholtz equation, Walk On Spheres algorithm",

author = "Xuxin Yang and Antti Rasila and Tommi Sottinen",

year = "2017",

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journal = "Methodology and Computing in Applied Probability",

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T1 - Walk On Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence

AU - Yang, Xuxin

AU - Rasila, Antti

AU - Sottinen, Tommi

PY - 2017/6

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N2 - 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.

AB - 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.

KW - Brownian motion

KW - Monte Carlo simulation

KW - Numerical algorithm

KW - Linearized Poisson–Boltzmann equation

KW - Helmholtz equation

KW - Walk On Spheres algorithm

U2 - 10.1007/s11009-016-9504-9

DO - 10.1007/s11009-016-9504-9

M3 - Article

VL - 19

SP - 589

EP - 602

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

SN - 1387-5841

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ER -