{"id":"https://openalex.org/W4401709407","doi":"https://doi.org/10.1007/s10444-024-10181-0","title":"Arbitrary order spline representation of cohomology generators for isogeometric analysis of eddy current problems","display_name":"Arbitrary order spline representation of cohomology generators for isogeometric analysis of eddy current problems","publication_year":2024,"publication_date":"2024-08-19","ids":{"openalex":"https://openalex.org/W4401709407","doi":"https://doi.org/10.1007/s10444-024-10181-0"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-024-10181-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-024-10181-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-024-10181-0.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10444-024-10181-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089862616","display_name":"Bernard Kapidani","orcid":"https://orcid.org/0000-0001-7369-4400"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Bernard Kapidani","raw_affiliation_strings":["Chair of Numerical Modelling and Simulation, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chair of Numerical Modelling and Simulation, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057261665","display_name":"Melina Merkel","orcid":"https://orcid.org/0000-0002-2104-9167"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Melina Merkel","raw_affiliation_strings":["Computational Electromagnetics Group and Graduate School of Computational Engineering, Technische Universit\u00e4t Darmstadt, 64289, Darmstadt, Germany"],"raw_orcid":"https://orcid.org/0000-0002-2104-9167","affiliations":[{"raw_affiliation_string":"Computational Electromagnetics Group and Graduate School of Computational Engineering, Technische Universit\u00e4t Darmstadt, 64289, Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054323051","display_name":"Sebastian Sch\u00f6ps","orcid":"https://orcid.org/0000-0001-9150-0219"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sebastian Sch\u00f6ps","raw_affiliation_strings":["Computational Electromagnetics Group and Graduate School of Computational Engineering, Technische Universit\u00e4t Darmstadt, 64289, Darmstadt, Germany"],"raw_orcid":"https://orcid.org/0000-0001-9150-0219","affiliations":[{"raw_affiliation_string":"Computational Electromagnetics Group and Graduate School of Computational Engineering, Technische Universit\u00e4t Darmstadt, 64289, Darmstadt, Germany","institution_ids":["https://openalex.org/I31512782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071603624","display_name":"Rafael V\u00e1zquez","orcid":"https://orcid.org/0000-0001-6904-2055"},"institutions":[{"id":"https://openalex.org/I200284239","display_name":"Universidade de Santiago de Compostela","ror":"https://ror.org/030eybx10","country_code":"ES","type":"education","lineage":["https://openalex.org/I200284239"]},{"id":"https://openalex.org/I2802755756","display_name":"Centro de Supercomputaci\u00f3n de Galicia","ror":"https://ror.org/02z51cq88","country_code":"ES","type":"nonprofit","lineage":["https://openalex.org/I2802755756"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Rafael V\u00e1zquez","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain","Galician Centre for Mathematical Research and Technology (CITMAga), Campus Vida, E-15782, Santiago de Compostela, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain","institution_ids":["https://openalex.org/I200284239"]},{"raw_affiliation_string":"Galician Centre for Mathematical Research and Technology (CITMAga), Campus Vida, E-15782, Santiago de Compostela, Spain","institution_ids":["https://openalex.org/I2802755756"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5089862616"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.3412,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54124465,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"50","issue":"5","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"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/T10514","display_name":"Numerical methods in engineering","score":0.9866999983787537,"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"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9247999787330627,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7298713326454163},{"id":"https://openalex.org/keywords/isogeometric-analysis","display_name":"Isogeometric analysis","score":0.6987357139587402},{"id":"https://openalex.org/keywords/cohomology","display_name":"Cohomology","score":0.6259498000144958},{"id":"https://openalex.org/keywords/computational-science-and-engineering","display_name":"Computational Science and Engineering","score":0.6189507246017456},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.5961828827857971},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5556968450546265},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5340589284896851},{"id":"https://openalex.org/keywords/eddy-current","display_name":"Eddy current","score":0.5066207051277161},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4521780014038086},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.330373078584671},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.30664485692977905},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.13368558883666992},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.0935400128364563},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06785699725151062},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.06702399253845215}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7298713326454163},{"id":"https://openalex.org/C2780737243","wikidata":"https://www.wikidata.org/wiki/Q17082433","display_name":"Isogeometric analysis","level":3,"score":0.6987357139587402},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.6259498000144958},{"id":"https://openalex.org/C68597687","wikidata":"https://www.wikidata.org/wiki/Q362601","display_name":"Computational Science and Engineering","level":2,"score":0.6189507246017456},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.5961828827857971},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5556968450546265},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5340589284896851},{"id":"https://openalex.org/C131357438","wikidata":"https://www.wikidata.org/wiki/Q208598","display_name":"Eddy current","level":2,"score":0.5066207051277161},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4521780014038086},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.330373078584671},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30664485692977905},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.13368558883666992},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0935400128364563},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06785699725151062},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.06702399253845215},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10444-024-10181-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-024-10181-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-024-10181-0.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:tubiblio.ulb.tu-darmstadt.de:156495","is_oa":false,"landing_page_url":"http://tubiblio.ulb.tu-darmstadt.de/view/person/Kapidani=3ABernard=3A=3A.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4377196390","display_name":"TUbilio (Technical University of Darmstadt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31512782","host_organization_name":"Technische Universit\u00e4t Darmstadt","host_organization_lineage":["https://openalex.org/I31512782"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"NonPeerReviewed"},{"id":"pmh:oai:infoscience.epfl.ch:20.500.14299/243519","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/243519","pdf_url":"https://infoscience.epfl.ch/bitstreams/dd698166-b15a-4e4b-9214-cd3c17a1f956/download","source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"research article"}],"best_oa_location":{"id":"doi:10.1007/s10444-024-10181-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-024-10181-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-024-10181-0.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1358938806","display_name":null,"funder_award_id":"1562/6","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G215663931","display_name":null,"funder_award_id":"200021_188589","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G3586297670","display_name":null,"funder_award_id":"HOGAEMS n.200021_188589","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G3753187545","display_name":null,"funder_award_id":"SCHO 1562/6-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5205182052","display_name":null,"funder_award_id":"10.55776/F90","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5371310920","display_name":null,"funder_award_id":"492661287/TRR 361","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5477993868","display_name":null,"funder_award_id":"492661287","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5987873460","display_name":null,"funder_award_id":"CRC - TRR361/F90","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6773500248","display_name":null,"funder_award_id":"TRR 361","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320310430","display_name":"TU Graz, Internationale Beziehungen und Mobilit\u00e4tsprogramme","ror":"https://ror.org/00d7xrm67"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320323384","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4401709407.pdf","grobid_xml":"https://content.openalex.org/works/W4401709407.grobid-xml"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W1492013576","https://openalex.org/W1607663648","https://openalex.org/W1966250575","https://openalex.org/W1974325291","https://openalex.org/W1975069663","https://openalex.org/W1976715595","https://openalex.org/W1978521024","https://openalex.org/W1982343173","https://openalex.org/W2000425991","https://openalex.org/W2001440251","https://openalex.org/W2015256171","https://openalex.org/W2015580600","https://openalex.org/W2023300719","https://openalex.org/W2025459390","https://openalex.org/W2026522145","https://openalex.org/W2028246274","https://openalex.org/W2028407821","https://openalex.org/W2032132351","https://openalex.org/W2041177942","https://openalex.org/W2051799546","https://openalex.org/W2058641097","https://openalex.org/W2062618977","https://openalex.org/W2073916877","https://openalex.org/W2077127884","https://openalex.org/W2086016774","https://openalex.org/W2090805944","https://openalex.org/W2103302172","https://openalex.org/W2108542436","https://openalex.org/W2110458339","https://openalex.org/W2117127065","https://openalex.org/W2119340055","https://openalex.org/W2129633297","https://openalex.org/W2130970049","https://openalex.org/W2131341034","https://openalex.org/W2139356964","https://openalex.org/W2139687604","https://openalex.org/W2142139455","https://openalex.org/W2151161315","https://openalex.org/W2152410378","https://openalex.org/W2157746942","https://openalex.org/W2166927895","https://openalex.org/W2167100461","https://openalex.org/W2417343272","https://openalex.org/W2463453118","https://openalex.org/W2748771834","https://openalex.org/W2753058784","https://openalex.org/W2946260007","https://openalex.org/W2964172521","https://openalex.org/W2982431646","https://openalex.org/W3000193678","https://openalex.org/W3003648633","https://openalex.org/W3014564831","https://openalex.org/W3102241171","https://openalex.org/W3103476862","https://openalex.org/W3111356794","https://openalex.org/W3132743941","https://openalex.org/W3171921108","https://openalex.org/W3186119071","https://openalex.org/W3208036960","https://openalex.org/W3212665299","https://openalex.org/W3214606019","https://openalex.org/W4206477975","https://openalex.org/W4234555707"],"related_works":["https://openalex.org/W1940709639","https://openalex.org/W1924025565","https://openalex.org/W3025313650","https://openalex.org/W4297362898","https://openalex.org/W2352095914","https://openalex.org/W2989766329","https://openalex.org/W2129372062","https://openalex.org/W2981315515","https://openalex.org/W3166162663","https://openalex.org/W3119645684"],"abstract_inverted_index":{"Abstract":[0],"Common":[1],"formulations":[2,28],"of":[3,32,47,101],"the":[4,30,42,48],"eddy":[5],"current":[6],"problem":[7],"involve":[8],"either":[9],"vector":[10],"or":[11],"scalar":[12,26],"potentials,":[13],"each":[14],"with":[15,34,45,73],"its":[16],"own":[17],"advantages":[18],"and":[19,104],"disadvantages.":[20],"An":[21],"impasse":[22],"arises":[23],"when":[24],"using":[25],"potential-based":[27],"in":[29],"presence":[31],"conductors":[33],"non-trivial":[35],"topology.":[36],"A":[37],"remedy":[38],"is":[39],"to":[40,89],"augment":[41],"approximation":[43,72],"spaces":[44,100],"generators":[46],"first":[49],"cohomology":[50],"group.":[51],"Most":[52],"existing":[53],"algorithms":[54],"for":[55],"this":[56],"require":[57],"a":[58,92],"special,":[59],"e.g.,":[60],"hierarchical,":[61],"finite":[62],"element":[63],"basis":[64],"construction.":[65],"Using":[66],"insights":[67],"from":[68,96],"de":[69,105],"Rham":[70,106],"complex":[71],"splines,":[74],"we":[75],"show":[76],"that":[77],"additional":[78],"conditions":[79],"are":[80],"here":[81],"unnecessary.":[82],"Spanning":[83],"tree":[84],"techniques":[85],"can":[86],"be":[87],"adapted":[88],"operate":[90],"on":[91,108],"hexahedral":[93],"mesh":[94],"resulting":[95],"isomorphisms":[97],"between":[98],"spline":[99],"differential":[102],"forms":[103],"complexes":[107],"an":[109],"auxiliary":[110],"control":[111],"mesh.":[112]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
