{"id":"https://openalex.org/W7135181280","doi":"https://doi.org/10.48550/arxiv.2603.12134","title":"Global and local helicity-preservation in the finite element discretisation of magnetic relaxation","display_name":"Global and local helicity-preservation in the finite element discretisation of magnetic relaxation","publication_year":2026,"publication_date":"2026-03-12","ids":{"openalex":"https://openalex.org/W7135181280","doi":"https://doi.org/10.48550/arxiv.2603.12134"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.12134","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.12134","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.12134","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102855060","display_name":"Patrick E. Farrell","orcid":"https://orcid.org/0000-0002-1241-7060"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Farrell, Patrick E.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128925630","display_name":"Mingdong He","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"He, Mingdong","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128927648","display_name":"Kaibo Hu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hu, Kaibo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5010321711","display_name":"Ganghui Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Ganghui","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5102855060"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10251","display_name":"Solar and Space Plasma Dynamics","score":0.41519999504089355,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10251","display_name":"Solar and Space Plasma Dynamics","score":0.41519999504089355,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10346","display_name":"Magnetic confinement fusion research","score":0.3003999888896942,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10159","display_name":"Ionosphere and magnetosphere dynamics","score":0.10010000318288803,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/helicity","display_name":"Helicity","score":0.795799970626831},{"id":"https://openalex.org/keywords/magnetohydrodynamics","display_name":"Magnetohydrodynamics","score":0.6579999923706055},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6021000146865845},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.538100004196167},{"id":"https://openalex.org/keywords/magnetohydrodynamic-drive","display_name":"Magnetohydrodynamic drive","score":0.47909998893737793},{"id":"https://openalex.org/keywords/magnetic-helicity","display_name":"Magnetic helicity","score":0.4675999879837036},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.45080000162124634}],"concepts":[{"id":"https://openalex.org/C2775859700","wikidata":"https://www.wikidata.org/wiki/Q568855","display_name":"Helicity","level":2,"score":0.795799970626831},{"id":"https://openalex.org/C31532427","wikidata":"https://www.wikidata.org/wiki/Q2549249","display_name":"Magnetohydrodynamics","level":3,"score":0.6579999923706055},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6021000146865845},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5465999841690063},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.538100004196167},{"id":"https://openalex.org/C42471609","wikidata":"https://www.wikidata.org/wiki/Q1779048","display_name":"Magnetohydrodynamic drive","level":4,"score":0.47909998893737793},{"id":"https://openalex.org/C2781048686","wikidata":"https://www.wikidata.org/wiki/Q11587832","display_name":"Magnetic helicity","level":4,"score":0.4675999879837036},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.45080000162124634},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.43639999628067017},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.4316999912261963},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.40939998626708984},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.40209999680519104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37220001220703125},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.36550000309944153},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.35929998755455017},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3587999939918518},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.26579999923706055}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.12134","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.12134","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.12134","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.12134","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.5763574242591858}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Magnetic":[0],"relaxation":[1,24,109,134],"drives":[2],"plasma":[3],"toward":[4],"lower-energy":[5],"equilibria":[6],"under":[7],"helicity":[8,14,75,88,106,130],"constraints.":[9],"In":[10],"ideal":[11,98],"magnetohydrodynamics":[12],"(MHD),":[13],"is":[15],"locally":[16],"conserved,":[17],"while":[18],"resistive":[19],"theories":[20],"such":[21],"as":[22],"Taylor":[23],"preserve":[25],"only":[26,73,104],"global":[27,74,105],"helicity.":[28],"This":[29],"distinction":[30],"has":[31],"important":[32],"implications":[33],"for":[34],"structure-preserving":[35],"numerical":[36,139],"methods.":[37],"We":[38],"compare":[39],"three":[40],"finite":[41,57],"element":[42,58],"formulations:":[43],"an":[44],"unconstrained":[45],"scheme":[46],"that":[47,61,71,86],"does":[48],"not":[49],"conserve":[50],"helicity,":[51],"a":[52,67],"mixed":[53],"method":[54],"based":[55],"on":[56,79,115],"exterior":[59],"calculus":[60],"preserves":[62],"all":[63],"local":[64,87,111],"helicities,":[65],"and":[66,81,93,118,135],"Lagrange":[68],"multiplier":[69],"approach":[70],"enforces":[72],"conservation.":[76],"Numerical":[77,113],"experiments":[78],"braided":[80],"knotted":[82],"magnetic":[83,116,133],"fields":[84],"show":[85],"preservation":[89],"prevents":[90],"spurious":[91],"reconnection":[92],"maintains":[94],"nontrivial":[95],"topology":[96],"in":[97,138],"MHD":[99],"or":[100],"magneto-friction,":[101],"whereas":[102],"enforcing":[103],"allows":[107],"further":[108],"through":[110],"reconnection.":[112],"results":[114,123],"knots":[117],"braids":[119],"are":[120],"provided.":[121],"These":[122],"clarify":[124],"how":[125],"different":[126],"levels":[127],"of":[128],"discrete":[129],"constraints":[131],"influence":[132],"equilibrium":[136],"structure":[137],"computation.":[140]},"counts_by_year":[],"updated_date":"2026-03-14T06:46:50.379900","created_date":"2026-03-14T00:00:00"}
