{"id":"https://openalex.org/W1968695821","doi":"https://doi.org/10.1177/109434209901300405","title":"PVODE, an ODE Solver for Parallel Computers","display_name":"PVODE, an ODE Solver for Parallel Computers","publication_year":1999,"publication_date":"1999-11-01","ids":{"openalex":"https://openalex.org/W1968695821","doi":"https://doi.org/10.1177/109434209901300405","mag":"1968695821"},"language":"en","primary_location":{"id":"doi:10.1177/109434209901300405","is_oa":false,"landing_page_url":"https://doi.org/10.1177/109434209901300405","pdf_url":null,"source":{"id":"https://openalex.org/S60606485","display_name":"The International Journal of High Performance Computing Applications","issn_l":"1094-3420","issn":["1094-3420","1741-2846"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The International Journal of High Performance Computing Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022259483","display_name":"George D. Byrne","orcid":null},"institutions":[{"id":"https://openalex.org/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"George D. Byrne","raw_affiliation_strings":["Applied Mathematics Department and Chemical & Environmental Engineering Department, Illinois Institute of Technology, Chicago, IL, U.S.A","Applied Mathematics Department and Chemical & Environmental Engineering Department, Illinois Institute of Technology, Chicago, IL, U.S.A.#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Mathematics Department and Chemical & Environmental Engineering Department, Illinois Institute of Technology, Chicago, IL, U.S.A","institution_ids":["https://openalex.org/I180949307"]},{"raw_affiliation_string":"Applied Mathematics Department and Chemical & Environmental Engineering Department, Illinois Institute of Technology, Chicago, IL, U.S.A.#TAB#","institution_ids":["https://openalex.org/I180949307"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023255650","display_name":"A.C. Hindmarsh","orcid":null},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alan C. Hindmarsh","raw_affiliation_strings":["Center for Applied Scientific Computing, Lawrence Livermore National\r                        Laboratory, Livermore, CA, U.S.A","Center for Applied Scientific Computing, Lawrence Livermore National#R# Laboratory, Livermore, CA, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Applied Scientific Computing, Lawrence Livermore National\r                        Laboratory, Livermore, CA, U.S.A","institution_ids":["https://openalex.org/I1282311441"]},{"raw_affiliation_string":"Center for Applied Scientific Computing, Lawrence Livermore National#R# Laboratory, Livermore, CA, U.S.A","institution_ids":["https://openalex.org/I1282311441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022259483"],"corresponding_institution_ids":["https://openalex.org/I180949307"],"apc_list":null,"apc_paid":null,"fwci":2.5269,"has_fulltext":false,"cited_by_count":90,"citation_normalized_percentile":{"value":0.87371744,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"13","issue":"4","first_page":"354","last_page":"365"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9997000098228455,"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":0.9997000098228455,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.8179018497467041},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.7191494703292847},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.712112307548523},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.6674169898033142},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.6173884868621826},{"id":"https://openalex.org/keywords/fortran","display_name":"Fortran","score":0.5793592929840088},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.5757671594619751},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.49151715636253357},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.478023886680603},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.45748013257980347},{"id":"https://openalex.org/keywords/message-passing","display_name":"Message passing","score":0.4366021156311035},{"id":"https://openalex.org/keywords/message-passing-interface","display_name":"Message Passing Interface","score":0.4318197965621948},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4121495485305786},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3368951976299286},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.32794445753097534},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.23571744561195374},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.21284815669059753},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.16671991348266602},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.16086873412132263}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8179018497467041},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7191494703292847},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.712112307548523},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6674169898033142},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.6173884868621826},{"id":"https://openalex.org/C2778241615","wikidata":"https://www.wikidata.org/wiki/Q83303","display_name":"Fortran","level":2,"score":0.5793592929840088},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.5757671594619751},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.49151715636253357},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.478023886680603},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.45748013257980347},{"id":"https://openalex.org/C854659","wikidata":"https://www.wikidata.org/wiki/Q1859284","display_name":"Message passing","level":2,"score":0.4366021156311035},{"id":"https://openalex.org/C166782233","wikidata":"https://www.wikidata.org/wiki/Q127879","display_name":"Message Passing Interface","level":3,"score":0.4318197965621948},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4121495485305786},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3368951976299286},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.32794445753097534},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.23571744561195374},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.21284815669059753},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.16671991348266602},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16086873412132263},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1177/109434209901300405","is_oa":false,"landing_page_url":"https://doi.org/10.1177/109434209901300405","pdf_url":null,"source":{"id":"https://openalex.org/S60606485","display_name":"The International Journal of High Performance Computing Applications","issn_l":"1094-3420","issn":["1094-3420","1741-2846"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The International Journal of High Performance Computing Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W193473568","https://openalex.org/W1500016939","https://openalex.org/W1510543252","https://openalex.org/W1968512837","https://openalex.org/W2044889656","https://openalex.org/W2064245996","https://openalex.org/W2284976701","https://openalex.org/W4241987383","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2113830538","https://openalex.org/W2385105452","https://openalex.org/W2137797529","https://openalex.org/W2034237012","https://openalex.org/W2118830201","https://openalex.org/W2109920203","https://openalex.org/W2091702533","https://openalex.org/W4320490673","https://openalex.org/W3000446122","https://openalex.org/W1575783825"],"abstract_inverted_index":{"PVODE":[0,56,137],"is":[1,22,29,69,138],"a":[2,36,58,82,94,98,111,122,130],"general-purpose":[3],"solver":[4],"for":[5,14,24,50,102],"ordinary":[6],"differential":[7],"equation":[8],"(ODE)":[9],"systems":[10],"that":[11,96],"implements":[12],"methods":[13],"both":[15],"stiff":[16,54,123],"and":[17,80,126],"nonstiff":[18],"systems.":[19,136],"The":[20,40,119],"code":[21],"designed":[23],"single-program":[25],"multiple-data":[26],"environments.":[27],"It":[28],"written":[30],"in":[31],"ANSI":[32],"standard":[33],"C,":[34],"with":[35,64,104,132],"highly":[37],"modular":[38],"structure.":[39],"version":[41],"being":[42],"distributed":[43],"uses":[44,57],"the":[45,53,73,105],"message-passing":[46,135],"interface":[47],"(MPI)":[48],"system":[49],"communication.":[51],"In":[52],"case,":[55],"backward":[59],"differentiation":[60],"formula":[61],"method":[62],"combined":[63],"preconditioned":[65],"GMRES":[66,106],"iteration.":[67,107],"Parallelism":[68],"achieved":[70],"by":[71],"distributing":[72],"ODE":[74,90],"solution":[75],"vector":[76,85],"into":[77],"user-specified":[78],"segments":[79],"parallelizing":[81],"set":[83,112],"of":[84,113],"kernels":[86],"accordingly.":[87],"For":[88],"PDE-based":[89],"systems,":[91],"we":[92],"provide":[93,110],"module":[95],"generates":[97],"band":[99],"block-diagonal":[100],"preconditioner":[101],"use":[103],"We":[108],"also":[109],"interfaces":[114],"to":[115],"accommodate":[116],"Fortran":[117],"applications.":[118],"paper":[120],"includes":[121],"example":[124],"problem":[125],"test":[127],"results":[128],"on":[129],"Cray-T3D":[131],"three":[133],"different":[134],"publicly":[139],"available.":[140]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":6}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
