Random walk methods for Monte Carlo simulations of Brownian diffusion on a sphere

Alexei Novikov, D. Kuzmin, O. Ahmadi

Research output: Contribution to journalArticle

Abstract

This paper is focused on efficient Monte Carlo simulations of Brownian diffusion effects in particle-based numerical methods for solving transport equations on a sphere (or a circle). Using the heat equation as a model problem, random walks are designed to emulate the action of the Laplace–Beltrami operator without evolving or reconstructing the probability density function. The intensity of perturbations is fitted to the value of the rotary diffusion coefficient in the deterministic model. Simplified forms of Brownian motion generators are derived for rotated reference frames, and several practical approaches to generating random walks on a sphere are discussed. The alternatives considered in this work include projections of Cartesian random walks, as well as polar random walks on the tangential plane. In addition, we explore the possibility of using look-up tables for the exact cumulative probability of perturbations. Numerical studies are performed to assess the practical utility of the methods under investigation.

Original languageEnglish (US)
Article number124670
JournalApplied Mathematics and Computation
Volume364
DOIs
StatePublished - Jan 1 2020

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Random walk
Monte Carlo Simulation
Brownian movement
Probability density function
Mathematical operators
Numerical methods
Perturbation
Laplace-Beltrami Operator
Look-up Table
Deterministic Model
Cartesian
Transport Equation
Heat Equation
Diffusion Coefficient
Brownian motion
Numerical Study
Circle
Numerical Methods
Projection
Generator

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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Random walk methods for Monte Carlo simulations of Brownian diffusion on a sphere. / Novikov, Alexei; Kuzmin, D.; Ahmadi, O.

In: Applied Mathematics and Computation, Vol. 364, 124670, 01.01.2020.

Research output: Contribution to journalArticle

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