{"id":"https://openalex.org/W6912609068","doi":"https://doi.org/10.5281/zenodo.7827802","title":"GMGPolar v1.0","display_name":"GMGPolar v1.0","publication_year":2023,"publication_date":"2023-04-14","ids":{"openalex":"https://openalex.org/W6912609068","doi":"https://doi.org/10.5281/zenodo.7827802"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.7827802","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.7827802","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"other","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.7827802","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Leleux, Philippe","orcid":"https://orcid.org/0000-0002-3760-4698"},"institutions":[{"id":"https://openalex.org/I154526488","display_name":"Inserm","ror":"https://ror.org/02vjkv261","country_code":"FR","type":"government","lineage":["https://openalex.org/I154526488"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Leleux, Philippe","raw_affiliation_strings":["INSERM"],"raw_orcid":"https://orcid.org/0000-0002-3760-4698","affiliations":[{"raw_affiliation_string":"INSERM","institution_ids":["https://openalex.org/I154526488"]}]},{"author_position":"middle","author":{"id":null,"display_name":"K\u00fchn, Martin J.","orcid":"https://orcid.org/0000-0002-0906-6984"},"institutions":[{"id":"https://openalex.org/I2898391981","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","ror":"https://ror.org/04bwf3e34","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2898391981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"K\u00fchn, Martin J.","raw_affiliation_strings":["German Aerospace Center"],"raw_orcid":"https://orcid.org/0000-0002-0906-6984","affiliations":[{"raw_affiliation_string":"German Aerospace Center","institution_ids":["https://openalex.org/I2898391981"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Schwarz, Christina","orcid":null},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Schwarz, Christina","raw_affiliation_strings":["Universit\u00e4t Bayreuth"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Bayreuth","institution_ids":["https://openalex.org/I54009628"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Kruse, Carola","orcid":"https://orcid.org/0000-0002-4142-7356"},"institutions":[{"id":"https://openalex.org/I4210106946","display_name":"Centre Europ\u00e9en de Recherche et de Formation Avanc\u00e9e en Calcul Scientifique","ror":"https://ror.org/02dzbc556","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210106946"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Kruse, Carola","raw_affiliation_strings":["CERFACS"],"raw_orcid":"https://orcid.org/0000-0002-4142-7356","affiliations":[{"raw_affiliation_string":"CERFACS","institution_ids":["https://openalex.org/I4210106946"]}]},{"author_position":"middle","author":{"id":null,"display_name":"R\u00fcde, Ulrich","orcid":"https://orcid.org/0000-0001-8796-8599"},"institutions":[{"id":"https://openalex.org/I4210146216","display_name":"Forschungsinstitut f\u00fcr Anwendungsorientierte Wissensverarbeitung","ror":"https://ror.org/04s7shc55","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I196349391","https://openalex.org/I4210146216"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"R\u00fcde, Ulrich","raw_affiliation_strings":["FAU Erlangen"],"raw_orcid":"https://orcid.org/0000-0001-8796-8599","affiliations":[{"raw_affiliation_string":"FAU Erlangen","institution_ids":["https://openalex.org/I4210146216"]}]},{"author_position":"last","author":{"id":null,"display_name":"Kuhn, Allan","orcid":null},"institutions":[{"id":"https://openalex.org/I2898391981","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","ror":"https://ror.org/04bwf3e34","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2898391981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Kuhn, Allan","raw_affiliation_strings":["German Aerospace Center"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"German Aerospace Center","institution_ids":["https://openalex.org/I2898391981"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I154526488"],"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":true,"primary_topic":null,"topics":[],"keywords":[{"id":"https://openalex.org/keywords/curvilinear-coordinates","display_name":"Curvilinear coordinates","score":0.9165999889373779},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.8145999908447266},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5652999877929688},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5633999705314636},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.44920000433921814},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.4083999991416931},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.3763999938964844},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.362199991941452}],"concepts":[{"id":"https://openalex.org/C98343798","wikidata":"https://www.wikidata.org/wiki/Q1790208","display_name":"Curvilinear coordinates","level":2,"score":0.9165999889373779},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.8145999908447266},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.61080002784729},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5652999877929688},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5633999705314636},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5579000115394592},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.44920000433921814},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.4083999991416931},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.3763999938964844},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3727000057697296},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.362199991941452},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.3603000044822693},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.34850001335144043},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.335099995136261},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.31779998540878296},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3140000104904175},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.29750001430511475},{"id":"https://openalex.org/C40069579","wikidata":"https://www.wikidata.org/wiki/Q62494","display_name":"Polar coordinate system","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2768000066280365},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.27390000224113464},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26589998602867126},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.25920000672340393},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.2558000087738037}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.5281/zenodo.7827802","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.7827802","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.5281/zenodo.7827802","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.7827802","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"GMGPolar":[0,20,87],"offers":[1,88],"a":[2,89],"taylored":[3],"Geometric":[4],"Multigrid":[5],"solver":[6],"for":[7,42,65,94,110],"geometries":[8,109],"described":[9,68],"by":[10,17,69],"curvilinear":[11,77],"coordinates":[12],"(in":[13],"its":[14,97],"simplest":[15],"case,":[16],"polar":[18],"coordinates).":[19],"uses":[21],"an":[22],"implicit":[23],"extrapolation":[24,59],"scheme":[25,60],"to":[26,50],"raise":[27],"the":[28],"convergence":[29,51],"order.":[30],"For":[31,76],"nonstandard":[32],"finite":[33,44],"elements,":[34],"this":[35],"result":[36],"has":[37],"been":[38,83],"shown":[39],"theoretically":[40],"and":[41,85,91],"nine-point":[43],"difference":[45],"stars,":[46],"we":[47],"observed":[48],"up":[49],"order":[52],"four":[53],"in":[54,74],"all":[55],"numerical":[56],"simulations.":[57,113],"This":[58],"can":[61],"be":[62],"used":[63],"likewise":[64],"other":[66],"domains":[67],"tensor-":[70],"or":[71],"product-format":[72],"meshes":[73],"2D.":[75],"domains,":[78],"suited":[79],"smoothing":[80],"schemes":[81],"have":[82],"developed":[84],"implemented.":[86],"matrix":[90],"matrix-free":[92],"version":[93],"most":[95],"of":[96,106],"operators.":[98],"Its":[99],"original":[100],"application":[101],"is":[102],"on":[103],"cross-sectional":[104],"views":[105],"realistic":[107],"Tokamak":[108],"fusion":[111],"plasma":[112]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}
