{"id":"https://openalex.org/W4405794776","doi":"https://doi.org/10.3390/a18010001","title":"An Efficient and Accurate Adaptive Time-Stepping Method for the Landau\u2013Lifshitz Equation","display_name":"An Efficient and Accurate Adaptive Time-Stepping Method for the Landau\u2013Lifshitz Equation","publication_year":2024,"publication_date":"2024-12-26","ids":{"openalex":"https://openalex.org/W4405794776","doi":"https://doi.org/10.3390/a18010001"},"language":"en","primary_location":{"id":"doi:10.3390/a18010001","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18010001","pdf_url":"https://www.mdpi.com/1999-4893/18/1/1/pdf?version=1735206042","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/18/1/1/pdf?version=1735206042","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048741165","display_name":"Hyundong Kim","orcid":null},"institutions":[{"id":"https://openalex.org/I133533813","display_name":"Gangneung\u2013Wonju National University","ror":"https://ror.org/0461cvh40","country_code":"KR","type":"education","lineage":["https://openalex.org/I133533813"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Hyundong Kim","raw_affiliation_strings":["Department of Mathematics and Physics, Gangneung-Wonju National University, Gangneung 25457, Republic of Korea"],"raw_orcid":"https://orcid.org/0009-0007-3986-3777","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, Gangneung-Wonju National University, Gangneung 25457, Republic of Korea","institution_ids":["https://openalex.org/I133533813"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083693585","display_name":"Soobin Kwak","orcid":"https://orcid.org/0000-0001-7693-8992"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Soobin Kwak","raw_affiliation_strings":["Department of Mathematics, Korea University, Seoul 02841, Republic of Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul 02841, Republic of Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090877053","display_name":"Moumni Mohammed","orcid":null},"institutions":[{"id":"https://openalex.org/I4210153608","display_name":"Universit\u00e9 Moulay Ismail de Meknes","ror":"https://ror.org/04cnscd67","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210153608"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Moumni Mohammed","raw_affiliation_strings":["MAMCS Group, FST Errachidia, Moulay Ismail University of Meknes, Boutalamine, P.O. Box 509, 52000 Errachidia, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MAMCS Group, FST Errachidia, Moulay Ismail University of Meknes, Boutalamine, P.O. Box 509, 52000 Errachidia, Morocco","institution_ids":["https://openalex.org/I4210153608"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101365829","display_name":"Seungyoon Kang","orcid":null},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Seungyoon Kang","raw_affiliation_strings":["Department of Mathematics, Korea University, Seoul 02841, Republic of Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul 02841, Republic of Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058565648","display_name":"Seokjun Ham","orcid":"https://orcid.org/0000-0002-2917-312X"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Seokjun Ham","raw_affiliation_strings":["Department of Mathematics, Korea University, Seoul 02841, Republic of Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul 02841, Republic of Korea","institution_ids":["https://openalex.org/I197347611"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100698865","display_name":"Junseok Kim","orcid":"https://orcid.org/0000-0002-0484-9189"},"institutions":[{"id":"https://openalex.org/I197347611","display_name":"Korea University","ror":"https://ror.org/047dqcg40","country_code":"KR","type":"education","lineage":["https://openalex.org/I197347611"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Junseok Kim","raw_affiliation_strings":["Department of Mathematics, Korea University, Seoul 02841, Republic of Korea"],"raw_orcid":"https://orcid.org/0000-0002-0484-9189","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Korea University, Seoul 02841, Republic of Korea","institution_ids":["https://openalex.org/I197347611"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5100698865"],"corresponding_institution_ids":["https://openalex.org/I197347611"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.0214,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.87531486,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"18","issue":"1","first_page":"1","last_page":"1"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/landau\u2013lifshitz\u2013gilbert-equation","display_name":"Landau\u2013Lifshitz\u2013Gilbert equation","score":0.7447638511657715},{"id":"https://openalex.org/keywords/time-stepping","display_name":"Time stepping","score":0.6274784803390503},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4607670307159424},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4232901930809021},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3967894911766052},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3936665654182434},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39020442962646484},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3727092146873474},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10406473278999329},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"Magnetic field","score":0.07148796319961548}],"concepts":[{"id":"https://openalex.org/C196076714","wikidata":"https://www.wikidata.org/wiki/Q1071534","display_name":"Landau\u2013Lifshitz\u2013Gilbert equation","level":4,"score":0.7447638511657715},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.6274784803390503},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4607670307159424},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4232901930809021},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3967894911766052},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3936665654182434},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39020442962646484},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3727092146873474},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10406473278999329},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.07148796319961548},{"id":"https://openalex.org/C32546565","wikidata":"https://www.wikidata.org/wiki/Q856711","display_name":"Magnetization","level":3,"score":0.0},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/a18010001","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18010001","pdf_url":"https://www.mdpi.com/1999-4893/18/1/1/pdf?version=1735206042","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ee0c6d72f5804b74a40fc3c94c1869a9","is_oa":false,"landing_page_url":"https://doaj.org/article/ee0c6d72f5804b74a40fc3c94c1869a9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 18, Iss 1, p 1 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a18010001","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18010001","pdf_url":"https://www.mdpi.com/1999-4893/18/1/1/pdf?version=1735206042","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G306706421","display_name":null,"funder_award_id":"2021R1A6A1A03044326","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G4933778068","display_name":null,"funder_award_id":"2021R1A6A1A03044326","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G5893839186","display_name":null,"funder_award_id":"BK 21","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405794776.pdf","grobid_xml":"https://content.openalex.org/works/W4405794776.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W1974982673","https://openalex.org/W2030905966","https://openalex.org/W2051028926","https://openalex.org/W2067049166","https://openalex.org/W2091885705","https://openalex.org/W2095223686","https://openalex.org/W2132232009","https://openalex.org/W2137262050","https://openalex.org/W2166539008","https://openalex.org/W2270740814","https://openalex.org/W2341275299","https://openalex.org/W2414506464","https://openalex.org/W2484574573","https://openalex.org/W2965601763","https://openalex.org/W2986587829","https://openalex.org/W3040694167","https://openalex.org/W3082846508","https://openalex.org/W3116082854","https://openalex.org/W3158008550","https://openalex.org/W3166541937","https://openalex.org/W3170720255","https://openalex.org/W3188819966","https://openalex.org/W3189583406","https://openalex.org/W3210301292","https://openalex.org/W4213061062","https://openalex.org/W4224437647","https://openalex.org/W4231698935","https://openalex.org/W4285587338","https://openalex.org/W4320525741","https://openalex.org/W4367052586","https://openalex.org/W4380924840","https://openalex.org/W4386410322","https://openalex.org/W4386468135","https://openalex.org/W4394819566","https://openalex.org/W4400977986","https://openalex.org/W4404594616","https://openalex.org/W6704284418","https://openalex.org/W6799501250","https://openalex.org/W6839995985"],"related_works":["https://openalex.org/W3209202329","https://openalex.org/W42498407","https://openalex.org/W2166091597","https://openalex.org/W2889044450","https://openalex.org/W3166541937","https://openalex.org/W2392533008","https://openalex.org/W4309777567","https://openalex.org/W4382721732","https://openalex.org/W105435840","https://openalex.org/W2019291954"],"abstract_inverted_index":{"This":[0],"article":[1],"presents":[2],"an":[3,21,36],"efficient":[4,131],"and":[5,29,65,132,145,151,158],"accurate":[6],"adaptive":[7,37,53,79,136],"time-stepping":[8,137],"finite":[9],"difference":[10],"method":[11],"(FDM)":[12],"for":[13,143],"solving":[14,147],"the":[15,42,56,78,109,127,148,156],"Landau\u2013Lifshitz":[16],"(LL)":[17],"equation,":[18],"which":[19],"is":[20,92,130],"important":[22],"mathematical":[23],"model":[24],"in":[25,67,155],"understanding":[26,157],"magnetic":[27,161],"materials":[28],"processes.":[30],"Our":[31],"proposed":[32,114,128],"algorithm":[33,129],"strategically":[34],"selects":[35],"time":[38,60,80,90,99],"step,":[39],"ensuring":[40],"that":[41,126],"maximum":[43],"displacement":[44],"falls":[45],"within":[46],"a":[47,74,88,95,140],"predefined":[48],"tolerance":[49],"threshold.":[50],"Furthermore,":[51],"this":[52],"approach":[54],"allows":[55],"utilization":[57],"of":[58,112,160],"larger":[59],"steps":[61],"near":[62],"equilibrium":[63],"states":[64],"results":[66,124],"faster":[68],"computations.":[69],"For":[70],"example,":[71],"we":[72,116],"introduce":[73],"numerical":[75],"test":[76],"where":[77],"step":[81,91,100],"decreases":[82],"from":[83],"3.05\u00d710\u22127":[84],"to":[85,153],"3.52\u00d710\u22129.":[86],"If":[87],"uniform":[89],"applied,":[93],"around":[94],"100":[96],"times":[97],"smaller":[98],"must":[101],"be":[102],"applied":[103],"at":[104],"unnecessary":[105],"cases.":[106],"To":[107],"demonstrate":[108],"high":[110],"performance":[111],"our":[113,135],"algorithm,":[115],"conduct":[117],"several":[118],"characteristic":[119],"benchmark":[120],"tests.":[121],"The":[122],"computational":[123],"confirm":[125],"accurate.":[133],"Overall,":[134],"FDM":[138],"offers":[139],"promising":[141],"solution":[142],"accurately":[144],"efficiently":[146],"LL":[149],"equation":[150],"contributes":[152],"advancements":[154],"analysis":[159],"phenomena.":[162]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
