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- Publisher Website: 10.4208/csiam-am.SO-2021-0030
- Scopus: eid_2-s2.0-85149777876
- WOS: WOS:000804100400002
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Article: On Symmetry Breaking of Allen-Cahn
Title | On Symmetry Breaking of Allen-Cahn |
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Authors | |
Keywords | Allen-Cahn equation steady state symmetry breaking |
Issue Date | 2022 |
Citation | CSIAM Transactions on Applied Mathematics, 2022, v. 3, n. 2, p. 221-243 How to Cite? |
Abstract | This paper is concerned with numerical solutions for the Allen-Cahn equation with standard double well potential and periodic boundary conditions. Surprisingly it is found that using standard numerical discretizations with high precision computational solutions may converge to completely incorrect steady states. This happens for very smooth initial data and state-of-the-art algorithms. We analyze this phenomenon and showcase the resolution of this problem by a new symmetry-preserving filter technique. We develop a new theoretical framework and rigorously prove the convergence to steady states for the filtered solutions. |
Persistent Identifier | http://hdl.handle.net/10722/327536 |
ISSN | 2023 Impact Factor: 1.2 2023 SCImago Journal Rankings: 0.786 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Li, Dong | - |
dc.contributor.author | Quan, Chaoyu | - |
dc.contributor.author | Tang, Tao | - |
dc.contributor.author | Yang, Wen | - |
dc.date.accessioned | 2023-03-31T05:32:04Z | - |
dc.date.available | 2023-03-31T05:32:04Z | - |
dc.date.issued | 2022 | - |
dc.identifier.citation | CSIAM Transactions on Applied Mathematics, 2022, v. 3, n. 2, p. 221-243 | - |
dc.identifier.issn | 2708-0560 | - |
dc.identifier.uri | http://hdl.handle.net/10722/327536 | - |
dc.description.abstract | This paper is concerned with numerical solutions for the Allen-Cahn equation with standard double well potential and periodic boundary conditions. Surprisingly it is found that using standard numerical discretizations with high precision computational solutions may converge to completely incorrect steady states. This happens for very smooth initial data and state-of-the-art algorithms. We analyze this phenomenon and showcase the resolution of this problem by a new symmetry-preserving filter technique. We develop a new theoretical framework and rigorously prove the convergence to steady states for the filtered solutions. | - |
dc.language | eng | - |
dc.relation.ispartof | CSIAM Transactions on Applied Mathematics | - |
dc.subject | Allen-Cahn equation | - |
dc.subject | steady state | - |
dc.subject | symmetry breaking | - |
dc.title | On Symmetry Breaking of Allen-Cahn | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.4208/csiam-am.SO-2021-0030 | - |
dc.identifier.scopus | eid_2-s2.0-85149777876 | - |
dc.identifier.volume | 3 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 221 | - |
dc.identifier.epage | 243 | - |
dc.identifier.eissn | 2708-0579 | - |
dc.identifier.isi | WOS:000804100400002 | - |