{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T01:33:18Z","timestamp":1791509598873,"version":"4.3.4"},"reference-count":34,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["NSFC 11971407"],"award-info":[{"award-number":["NSFC 11971407"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1720442"],"award-info":[{"award-number":["DMS-1720442"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,4,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We develop in this paper two classes of length preserving schemes for the Landau\u2013Lifshitz equation based on two different Lagrange multiplier approaches. In the first approach, the Lagrange multiplier [Formula: see text] equals [Formula: see text] at the continuous level, while in the second approach, the Lagrange multiplier [Formula: see text] is introduced to enforce the length constraint at the discrete level and is identically zero at the continuous level. By using a predictor-corrector approach, we construct efficient and robust length preserving higher-order schemes for the Landau\u2013Lifshitz equation, with the computational cost dominated by the predictor step which is simply a semi-implicit scheme. Furthermore, by introducing another space-independent Lagrange multiplier, we construct energy dissipative, in addition to length preserving, schemes for the Landau\u2013Lifshitz equation, at the expense of solving one nonlinear algebraic equation. We present ample numerical experiments to validate the stability and accuracy for the proposed schemes, and also provide a performance comparison with some existing schemes.<\/jats:p>","DOI":"10.1137\/22m1501143","type":"journal-article","created":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T04:03:25Z","timestamp":1682481805000},"page":"A530-A553","source":"Crossref","is-referenced-by-count":25,"title":["Length Preserving Numerical Schemes for Landau\u2013Lifshitz Equation Based on Lagrange Multiplier Approaches"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5645-5256","authenticated-orcid":true,"given":"Qing","family":"Cheng","sequence":"first","affiliation":[{"name":"Department of Mathematics, Tongji University, Shanghai 200092, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4885-5732","authenticated-orcid":true,"given":"Jie","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen, Fujian 361005, People\u2019s Republic of China. Department of Mathematics, Purdue University, West Lafayette, IN 47907 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,4,26]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/140962619"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3597"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202506001169"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/20M1335431"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/drab038"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2010.11.033"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s11831-011-9061-x"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-07-02079-0"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-84108-8"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2021.05.027"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/18M1166961"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2022.114585"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1137\/21M144877X"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1968-0242392-2"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142999352199"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1137\/130936476"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2005.10.010"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1137\/21M1402212"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1007\/BF01191298"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144504446187"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.53.2497"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-08-036364-6.50008-9"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.109046"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1142\/6679"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997327282"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2002010"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2426(199909)15:5<544::AID-NUM2>3.0.CO;2-Q"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-663-09498-2"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1080\/00036819008839963"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-71041-7"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2010.28.1669"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.24033\/bsmf.1662"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2001.6793"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.109104"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/22M1501143","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:25:44Z","timestamp":1787333144000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1501143"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,26]]},"references-count":34,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,4,30]]}},"alternative-id":["10.1137\/22M1501143"],"URL":"https:\/\/doi.org\/10.1137\/22m1501143","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,26]]}}}