{"id":"https://openalex.org/W6912175178","doi":"https://doi.org/10.5281/zenodo.15732483","title":"GMGPolar v2.0.1","display_name":"GMGPolar v2.0.1","publication_year":2025,"publication_date":"2025-06-24","ids":{"openalex":"https://openalex.org/W6912175178","doi":"https://doi.org/10.5281/zenodo.15732483"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.15732483","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.15732483","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.15732483","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Litz, Julian","orcid":null},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]},{"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":true,"raw_author_name":"Litz, Julian","raw_affiliation_strings":["German Aerospace Center","Forschungszentrum J\u00fclich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"German Aerospace Center","institution_ids":["https://openalex.org/I2898391981"]},{"raw_affiliation_string":"Forschungszentrum J\u00fclich","institution_ids":["https://openalex.org/I171892758"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Leleux, Philippe","orcid":"https://orcid.org/0000-0002-3760-4698"},"institutions":[{"id":"https://openalex.org/I190497903","display_name":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes","ror":"https://ror.org/03vcm6439","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I190497903","https://openalex.org/I196454796","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210095849","https://openalex.org/I4210159245","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Leleux, Philippe","raw_affiliation_strings":["Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes"],"raw_orcid":"https://orcid.org/0000-0002-3760-4698","affiliations":[{"raw_affiliation_string":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes","institution_ids":["https://openalex.org/I190497903"]}]},{"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":"K\u00fchn, Martin J.","orcid":"https://orcid.org/0000-0002-0906-6984"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]},{"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","University of Bonn"],"raw_orcid":"https://orcid.org/0000-0002-0906-6984","affiliations":[{"raw_affiliation_string":"German Aerospace Center","institution_ids":["https://openalex.org/I2898391981"]},{"raw_affiliation_string":"University of Bonn","institution_ids":["https://openalex.org/I135140700"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I171892758","https://openalex.org/I2898391981"],"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":0.7781999707221985},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.6927000284194946},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6721000075340271},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.4796999990940094},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.4438000023365021},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.421999990940094},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4138999879360199},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.40549999475479126},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.4041999876499176}],"concepts":[{"id":"https://openalex.org/C98343798","wikidata":"https://www.wikidata.org/wiki/Q1790208","display_name":"Curvilinear coordinates","level":2,"score":0.7781999707221985},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.6927000284194946},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6721000075340271},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5440000295639038},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5389999747276306},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.4796999990940094},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4562999904155731},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.4438000023365021},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.421999990940094},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4138999879360199},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.40549999475479126},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4041999876499176},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3528999984264374},{"id":"https://openalex.org/C66963500","wikidata":"https://www.wikidata.org/wiki/Q3338735","display_name":"Neutron transport","level":3,"score":0.352400004863739},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.34700000286102295},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.3149999976158142},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3050000071525574},{"id":"https://openalex.org/C40069579","wikidata":"https://www.wikidata.org/wiki/Q62494","display_name":"Polar coordinate system","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.29649999737739563},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29159998893737793},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28850001096725464},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.2800000011920929},{"id":"https://openalex.org/C123213974","wikidata":"https://www.wikidata.org/wiki/Q833089","display_name":"LU decomposition","level":4,"score":0.2793999910354614},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2614000141620636},{"id":"https://openalex.org/C181145010","wikidata":"https://www.wikidata.org/wiki/Q4418033","display_name":"Mesh generation","level":3,"score":0.2596000134944916},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2563999891281128}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.5281/zenodo.15732483","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.15732483","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.15732483","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.15732483","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":[2,89,153,206,273,288,362],"taylored":[3],"Geometric":[4],"Multigrid":[5],"solver":[6,376],"for":[7,42,65,94,110,128,157,238,249,267,281,305,377],"geometries":[8,109],"described":[9,68],"by":[10,17,69,187,344,346],"curvilinear":[11,77],"coordinates":[12],"(in":[13],"its":[14,97],"simplest":[15],"case,":[16],"polar":[18],"coordinates).":[19],"uses":[21],"an":[22,292],"implicit":[23],"extrapolation":[24,59],"scheme":[25,60],"to":[26,50,117,136,196,217,257,339,369],"raise":[27],"the":[28,184,189,197,201,231,235,268,314,320,352,374],"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":[41,85,91,140,149,160,227,246,310,350,373,380],"nine-point":[43],"difference":[45],"stars,":[46],"we":[47],"observed":[48],"up":[49,338],"order":[52],"four":[53],"in":[54,74,291,295],"all":[55,306],"numerical":[56],"simulations.":[57,113],"This":[58],"can":[61],"be":[62,218],"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":[96,106,120,200,287,333,337,355],"operators.":[98],"Its":[99],"original":[100],"application":[101],"is":[102,175,279,285],"on":[103,178],"cross-sectional":[104],"views":[105],"realistic":[107],"Tokamak":[108],"fusion":[111],"plasma":[112],"Changes":[114,133],"from":[115,134],"v2.0.0":[116,137],"v2.0.1":[118],"Correction":[119],"broken":[121],"code":[122],"coverage":[123],"Improved":[124,183],"output":[125],"Changed":[126],"position":[127],"anisotropic":[129],"refinement":[130],"with":[131,234,328],"ZoniShifted":[132],"v1.0.3":[135],"1)":[138],"Enhancements":[139],"New":[141,242],"Class":[142],"Layout:":[143],"Linear":[144],"Algebra:":[145],"Introduced":[146,244],"custom":[147],"Vector":[148],"SparseMatrix":[150],"classes.":[151],"Added":[152,253,272,361],"(cyclic)":[154],"Tridiagonal":[155],"Solver":[156],"improved":[158,239,259],"performance":[159],"usability.":[161],"Input":[162],"Functions:":[163],"Separated":[164,224],"into":[165,225],"distinct":[166],"components:":[167],"DomainGeometry,":[168],"BoundaryConditions,":[169],"SourceTerm,":[170],"etc.":[171],"Polar":[172],"Grid:":[173],"Indexing":[174],"now":[176],"based":[177],"circle/radial":[179],"smoother.":[180],"Residual:":[181],"-":[182],"residual":[185],"calculation":[186],"addressing":[188],"unintuitive":[190],"behavior":[191,265],"that":[192],"previously":[193],"applied":[194],"only":[195],"interior":[198],"part":[199],"matrix.":[202],"Direct":[203],"Solver:":[204],"Fixed":[205],"bug":[207],"where":[208,283],"boundary":[209],"values":[210],"were":[211],"not":[212,325],"treated":[213],"correctly.":[214],"Built":[215],"matrices":[216,349],"symmetric,":[219],"reducing":[220],"factorization":[221],"time.":[222],"Smoother:":[223],"extrapolated":[226],"standard":[228],"smoothers.":[229],"Replaced":[230],"LU-Decomposition":[232],"algorithm":[233,237],"Thomas":[236],"efficiency":[240],"2)":[241],"Features":[243,360],"W-":[245],"F":[247],"cycles":[248],"enhanced":[250],"solving":[251],"capabilities.":[252],"FMG":[254],"(Full":[255],"Multigrid)":[256],"obtain":[258],"starting":[260],"solutions.":[261],"Implemented":[262],"advanced":[263],"caching":[264],"options":[266],"\"Give\"":[269],"implementation":[270],"strategy.":[271],"faster":[274],"strategy":[275],"named":[276],"'Take,'":[277],"which":[278,323],"appropriate":[280],"cases":[282],"memory":[284,296],"less":[286],"constraint,":[289],"resulting":[290],"80%":[293],"increase":[294],"usage.":[297],"Comprehensive":[298],"Unit":[299,303],"Tests:":[300],"Integrated":[301],"Google":[302],"Tests":[304],"classes,":[307],"ensuring":[308],"robust":[309],"reliable":[311],"functionality":[312],"across":[313],"codebase.":[315],"3)":[316],"Performance":[317],"Improvements":[318],"Removed":[319],"task-based":[321],"approach,":[322],"did":[324],"scale":[326],"well":[327],"increasing":[329],"parallelization.":[330],"Sequential":[331],"speed-up":[332,336],"2,":[334],"parallel":[335],"10":[340],"Reduced":[341],"maximum":[342],"usage":[343],"61.5%":[345],"constructing":[347],"symmetric":[348],"utilizing":[351],"tridiagonal":[353],"structure":[354],"smoother":[356],"matrices.":[357],"4)":[358],"Updated":[359],"new":[363],"LU":[364],"decomposition":[365],"solver,":[366],"allowing":[367],"users":[368],"choose":[370],"between":[371],"MUMPS":[372],"in-house":[375],"greater":[378],"flexibility":[379],"performance.":[381]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}