Unconditionally stable monte carlo simulation for solving the multi-dimensional Allen–Cahn equation

In this study, we present an efficient and novel unconditionally stable Monte Carlo simulation (MCS) for solving the multi-dimensional Allen–Cahn (AC) equation, which can model the motion by mean curvature flow of a hypersurface. We use an operator splitting method, where the diffusion and nonlinear...

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Bibliographic Details
Published inElectronic research archive Vol. 31; no. 8; pp. 5104 - 5123
Main Authors Hwang, Youngjin, Kim, Ildoo, Kwak, Soobin, Ham, Seokjun, Kim, Sangkwon, Kim, Junseok
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
monte carlo simulation
multi-dimensional allen–cahn equation
operator splitting method
unconditionally stable scheme
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Summary:In this study, we present an efficient and novel unconditionally stable Monte Carlo simulation (MCS) for solving the multi-dimensional Allen–Cahn (AC) equation, which can model the motion by mean curvature flow of a hypersurface. We use an operator splitting method, where the diffusion and nonlinear terms are solved separately. The diffusion term is calculated using MCS for the stochastic differential equation, while the nonlinear term is locally computed for each particle in a virtual grid. Several numerical experiments are presented to demonstrate the performance of the proposed algorithm. The computational results confirm that the proposed algorithm can solve the AC equation more efficiently as the dimension of space increases.
ISSN:2688-1594
2688-1594
DOI:10.3934/era.2023261