An unconditionally stable hybrid numerical method for solving the Allen-Cahn equation
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Li, Yibao | - |
dc.contributor.author | Lee, Hyun Geun | - |
dc.contributor.author | Jeong, Darae | - |
dc.contributor.author | Kim, Junseok | - |
dc.date.accessioned | 2021-09-08T00:32:44Z | - |
dc.date.available | 2021-09-08T00:32:44Z | - |
dc.date.created | 2021-06-14 | - |
dc.date.issued | 2010-09 | - |
dc.identifier.issn | 0898-1221 | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/115779 | - |
dc.description.abstract | We present an unconditionally stable second-order hybrid numerical method for solving the Allen-Cahn equation representing a model for antiphase domain coarsening in a binary mixture. The proposed method is based on operator splitting techniques. The Allen-Cahn equation was divided into a linear and a nonlinear equation. First, the linear equation was discretized using a Crank-Nicolson scheme and the resulting discrete system of equations was solved by a fast solver such as a multigrid method. The nonlinear equation was then solved analytically due to the availability of a closed-form solution. Various numerical experiments are presented to confirm the accuracy, efficiency, and stability of the proposed method. In particular, we show that the scheme is unconditionally stable and second-order accurate in both time and space. (C) 2010 Elsevier Ltd. All rights reserved. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | PERGAMON-ELSEVIER SCIENCE LTD | - |
dc.subject | MEAN-CURVATURE | - |
dc.subject | GENERALIZED MOTION | - |
dc.subject | PHASE-TRANSITIONS | - |
dc.subject | APPROXIMATION | - |
dc.subject | MODEL | - |
dc.title | An unconditionally stable hybrid numerical method for solving the Allen-Cahn equation | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Kim, Junseok | - |
dc.identifier.doi | 10.1016/j.camwa.2010.06.041 | - |
dc.identifier.scopusid | 2-s2.0-77956060042 | - |
dc.identifier.wosid | 000281979800007 | - |
dc.identifier.bibliographicCitation | COMPUTERS & MATHEMATICS WITH APPLICATIONS, v.60, no.6, pp.1591 - 1606 | - |
dc.relation.isPartOf | COMPUTERS & MATHEMATICS WITH APPLICATIONS | - |
dc.citation.title | COMPUTERS & MATHEMATICS WITH APPLICATIONS | - |
dc.citation.volume | 60 | - |
dc.citation.number | 6 | - |
dc.citation.startPage | 1591 | - |
dc.citation.endPage | 1606 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.subject.keywordPlus | MEAN-CURVATURE | - |
dc.subject.keywordPlus | GENERALIZED MOTION | - |
dc.subject.keywordPlus | PHASE-TRANSITIONS | - |
dc.subject.keywordPlus | APPROXIMATION | - |
dc.subject.keywordPlus | MODEL | - |
dc.subject.keywordAuthor | Allen-Cahn equation | - |
dc.subject.keywordAuthor | Finite difference | - |
dc.subject.keywordAuthor | Unconditionally stable | - |
dc.subject.keywordAuthor | Operator splitting | - |
dc.subject.keywordAuthor | Motion by mean curvature | - |
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