{"id":"https://openalex.org/W4283736565","doi":"https://doi.org/10.1137/21m1438177","title":"On the Multiscale Landau\u2013Lifshitz\u2013Gilbert Equation: Two-Scale Convergence and Stability Analysis","display_name":"On the Multiscale Landau\u2013Lifshitz\u2013Gilbert Equation: Two-Scale Convergence and Stability Analysis","publication_year":2022,"publication_date":"2022-06-30","ids":{"openalex":"https://openalex.org/W4283736565","doi":"https://doi.org/10.1137/21m1438177"},"language":"en","primary_location":{"id":"doi:10.1137/21m1438177","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1438177","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025195102","display_name":"Jingrun Chen","orcid":"https://orcid.org/0000-0001-9977-2892"},"institutions":[{"id":"https://openalex.org/I308837","display_name":"Suzhou University of Science and Technology","ror":"https://ror.org/04en8wb91","country_code":"CN","type":"education","lineage":["https://openalex.org/I308837"]},{"id":"https://openalex.org/I3923682","display_name":"Soochow University","ror":"https://ror.org/05t8y2r12","country_code":"CN","type":"education","lineage":["https://openalex.org/I3923682"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jingrun Chen","raw_affiliation_strings":["School of Mathematical Sciences and Mathematical Center for Interdisciplinary Research, Soochow University, Suzhou, 215006, China, School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China, and Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou, Jiangsu 215123, China ()"],"raw_orcid":"https://orcid.org/0000-0001-9977-2892","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and Mathematical Center for Interdisciplinary Research, Soochow University, Suzhou, 215006, China, School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China, and Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou, Jiangsu 215123, China ()","institution_ids":["https://openalex.org/I3923682","https://openalex.org/I308837"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000360043","display_name":"Rui Du","orcid":"https://orcid.org/0000-0002-3811-7488"},"institutions":[{"id":"https://openalex.org/I3923682","display_name":"Soochow University","ror":"https://ror.org/05t8y2r12","country_code":"CN","type":"education","lineage":["https://openalex.org/I3923682"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rui Du","raw_affiliation_strings":["School of Mathematical Sciences and Mathematical Center for Interdisciplinary Research, Soochow University, Suzhou, 215006, China ()"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and Mathematical Center for Interdisciplinary Research, Soochow University, Suzhou, 215006, China ()","institution_ids":["https://openalex.org/I3923682"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043480738","display_name":"Zetao Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I3923682","display_name":"Soochow University","ror":"https://ror.org/05t8y2r12","country_code":"CN","type":"education","lineage":["https://openalex.org/I3923682"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zetao Ma","raw_affiliation_strings":["School of Mathematical Sciences, Soochow University, Suzhou, 215006, China (, )"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Soochow University, Suzhou, 215006, China (, )","institution_ids":["https://openalex.org/I3923682"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009821208","display_name":"Zhiwei Sun","orcid":"https://orcid.org/0000-0002-8932-3716"},"institutions":[{"id":"https://openalex.org/I3923682","display_name":"Soochow University","ror":"https://ror.org/05t8y2r12","country_code":"CN","type":"education","lineage":["https://openalex.org/I3923682"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiwei Sun","raw_affiliation_strings":["School of Mathematical Sciences, Soochow University, Suzhou, 215006, China (, )"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Soochow University, Suzhou, 215006, China (, )","institution_ids":["https://openalex.org/I3923682"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100699231","display_name":"Lei Zhang","orcid":"https://orcid.org/0000-0002-2917-9652"},"institutions":[{"id":"https://openalex.org/I4210158445","display_name":"Institute of Natural Science","ror":"https://ror.org/004tze884","country_code":"KP","type":"education","lineage":["https://openalex.org/I4210158445"]}],"countries":["KP"],"is_corresponding":false,"raw_author_name":"Lei Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Institute of Natural Sciences, and MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China ()"],"raw_orcid":"https://orcid.org/0000-0002-2917-9652","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Institute of Natural Sciences, and MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China ()","institution_ids":["https://openalex.org/I4210158445"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2874,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.56830324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"20","issue":"2","first_page":"835","last_page":"856"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.7454530596733093},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5355406403541565},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5264533162117004},{"id":"https://openalex.org/keywords/landau\u2013lifshitz\u2013gilbert-equation","display_name":"Landau\u2013Lifshitz\u2013Gilbert equation","score":0.44661256670951843},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3096837103366852},{"id":"https://openalex.org/keywords/magnetization","display_name":"Magnetization","score":0.21991810202598572},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"Magnetic field","score":0.12793046236038208}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.7454530596733093},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5355406403541565},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5264533162117004},{"id":"https://openalex.org/C196076714","wikidata":"https://www.wikidata.org/wiki/Q1071534","display_name":"Landau\u2013Lifshitz\u2013Gilbert equation","level":4,"score":0.44661256670951843},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3096837103366852},{"id":"https://openalex.org/C32546565","wikidata":"https://www.wikidata.org/wiki/Q856711","display_name":"Magnetization","level":3,"score":0.21991810202598572},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.12793046236038208},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1438177","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1438177","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4673460526","display_name":null,"funder_award_id":"11861131004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5501866456","display_name":null,"funder_award_id":"11501399","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5570764035","display_name":"\u5916\u52a0\u7535\u6d41\u4e0b\u78c1\u6027\u6750\u6599\u78c1\u5316\u5f3a\u5ea6\u52a8\u529b\u5b66\uff1a\u5efa\u6a21\u3001\u5206\u6790\u4e0e\u5e94\u7528","funder_award_id":"11971021","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6319611760","display_name":null,"funder_award_id":"11871339","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1538133328","https://openalex.org/W1553150814","https://openalex.org/W2027239222","https://openalex.org/W2041620563","https://openalex.org/W2043250494","https://openalex.org/W2095223686","https://openalex.org/W2095385436","https://openalex.org/W2116801612","https://openalex.org/W2142853269","https://openalex.org/W2149559046","https://openalex.org/W2752576738","https://openalex.org/W2768282495","https://openalex.org/W2782740643","https://openalex.org/W2965601763","https://openalex.org/W2979342693","https://openalex.org/W3022665889","https://openalex.org/W3212226042","https://openalex.org/W4220792498","https://openalex.org/W4231698935"],"related_works":["https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W3148032049","https://openalex.org/W2271181815"],"abstract_inverted_index":{".Permalloy":[0],"is":[1,23,100],"a":[2,9,80,95],"nickel-iron":[3],"magnetic":[4],"alloy,":[5],"which":[6],"typically":[7],"has":[8],"face-centered":[10],"cubic":[11],"phase":[12],"but":[13],"may":[14],"form":[15],"an":[16],"irregular":[17],"polycrystalline":[18],"structure.":[19],"Its":[20],"magnetization":[21],"dynamics":[22],"modeled":[24],"by":[25],"the":[26,40,48,57,62,68,72,84,104,107,114],"multiscale":[27,41,108],"Landau\u2013Lifshitz\u2013Gilbert":[28,117],"(LLG)":[29],"equation":[30,43,60,87],"with":[31],"locally":[32],"periodic":[33],"material":[34,92],"coefficients.":[35,93],"We":[36],"consider":[37],"homogenization":[38],"of":[39,74,83,91],"LLG":[42,59,86,111],"in":[44,51],"this":[45],"work,":[46],"and":[47,66,109,113],"novelty":[49],"lies":[50],"three":[52],"aspects.":[53],"First,":[54],"we":[55,78],"derive":[56],"homogenized":[58,85,110],"using":[61,71],"formal":[63],"asymptotic":[64],"expansion":[65],"prove":[67],"rigorous":[69],"convergence":[70,105],"notion":[73],"two-scale":[75],"convergence.":[76],"Second,":[77],"establish":[79],"stability":[81,115],"result":[82],"under":[88],"small":[89],"disturbances":[90],"Third,":[94],"modified":[96],"Gauss\u2013Seidel":[97],"projection":[98,121],"method":[99],"implemented":[101],"to":[102],"verify":[103],"between":[106],"equations":[112],"result.Keywordsmultiscale":[116],"equationtwo-scale":[118],"convergencestability":[119],"analysisGauss\u2013Seidel":[120],"methodMSC":[122],"codes35B2765N1278M4082D40":[123]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}