{"id":"https://openalex.org/W2022396161","doi":"https://doi.org/10.1137/0916034","title":"An Algorithm with Polylog Parallel Complexity for Solving Parabolic Partial Differential Equations","display_name":"An Algorithm with Polylog Parallel Complexity for Solving Parabolic Partial Differential Equations","publication_year":1995,"publication_date":"1995-05-01","ids":{"openalex":"https://openalex.org/W2022396161","doi":"https://doi.org/10.1137/0916034","mag":"2022396161"},"language":"en","primary_location":{"id":"doi:10.1137/0916034","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0916034","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5063940298","display_name":"Graham Horton","orcid":"https://orcid.org/0000-0002-7757-4489"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. Horton","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062993526","display_name":"Stefan Vandewalle","orcid":"https://orcid.org/0000-0002-8988-2374"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Vandewalle","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5004248420","display_name":"Patrick H Worley","orcid":"https://orcid.org/0000-0003-1734-0821"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. Worley","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8136,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.92449522,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"16","issue":"3","first_page":"531","last_page":"541"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987000226974487,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987000226974487,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9944999814033508,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9944000244140625,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.8027005195617676},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7841968536376953},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6546193957328796},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.6031872034072876},{"id":"https://openalex.org/keywords/exponential-integrator","display_name":"Exponential integrator","score":0.5421420335769653},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.539532482624054},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5346668362617493},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.5126132369041443},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5000088214874268},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.4865052103996277},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.4673210680484772},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.4417564868927002},{"id":"https://openalex.org/keywords/massively-parallel","display_name":"Massively parallel","score":0.43732336163520813},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40527427196502686},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3550410270690918},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25644245743751526},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.19993454217910767},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18125897645950317},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.1545099914073944},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07994502782821655}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.8027005195617676},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7841968536376953},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6546193957328796},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.6031872034072876},{"id":"https://openalex.org/C122700484","wikidata":"https://www.wikidata.org/wiki/Q16148845","display_name":"Exponential integrator","level":5,"score":0.5421420335769653},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.539532482624054},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5346668362617493},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.5126132369041443},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5000088214874268},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.4865052103996277},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.4673210680484772},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.4417564868927002},{"id":"https://openalex.org/C190475519","wikidata":"https://www.wikidata.org/wiki/Q544384","display_name":"Massively parallel","level":2,"score":0.43732336163520813},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40527427196502686},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3550410270690918},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25644245743751526},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.19993454217910767},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18125897645950317},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.1545099914073944},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07994502782821655},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0916034","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0916034","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/124764","is_oa":false,"landing_page_url":"http://gateway.newisiknowledge.com/gateway/Gateway.cgi?&GWVersion=2&SrcAuth=INSPEC&SrcApp=PRODUCT_NAME&CKEY=HORT0531950016SG&SrcURL=WOS_RETURN_URL&DestLinkType=FullRecord&DestApp=INSPEC&SrcDesc=RETURN_ALT_TEXT&SrcAppSID=APP_SID","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, vol. 16 (3), Art.No. 3, (531-541)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W625917541","https://openalex.org/W1629601946","https://openalex.org/W1963965124","https://openalex.org/W1964922990","https://openalex.org/W1978291714","https://openalex.org/W1983240191","https://openalex.org/W1986125951","https://openalex.org/W1987455271","https://openalex.org/W1989707864","https://openalex.org/W1995664184","https://openalex.org/W1998620991","https://openalex.org/W2002236043","https://openalex.org/W2003236963","https://openalex.org/W2006850990","https://openalex.org/W2017380323","https://openalex.org/W2023635718","https://openalex.org/W2026064960","https://openalex.org/W2036597275","https://openalex.org/W2040491331","https://openalex.org/W2066308409","https://openalex.org/W2072295790","https://openalex.org/W2074559083","https://openalex.org/W2114279700","https://openalex.org/W2135913665","https://openalex.org/W2140779530","https://openalex.org/W2146398437","https://openalex.org/W2153118166","https://openalex.org/W2155072081"],"related_works":["https://openalex.org/W322277319","https://openalex.org/W1984227015","https://openalex.org/W3022010538","https://openalex.org/W2400926413","https://openalex.org/W1990866326","https://openalex.org/W2582405793","https://openalex.org/W1590810315","https://openalex.org/W4312705771","https://openalex.org/W4289812957","https://openalex.org/W3127383398"],"abstract_inverted_index":{"The":[0,59],"standard":[1],"numerical":[2],"algorithms":[3],"for":[4,22],"solving":[5],"parabolic":[6,30],"partial":[7,31],"differential":[8,32,74],"equations":[9,33,75],"are":[10,83,98],"inherently":[11],"sequential":[12],"in":[13,38],"the":[14,23,52,56,65,71,79],"time":[15,40],"direction.":[16],"This":[17],"paper":[18],"describes":[19],"an":[20],"algorithm":[21,60],"time-accurate":[24],"solution":[25],"of":[26,29,55,64,81],"certain":[27],"classes":[28],"that":[34,48,76],"can":[35],"be":[36],"parallelized":[37],"both":[39],"and":[41],"space.":[42],"It":[43],"has":[44],"a":[45,62,86,94],"serial":[46,53],"complexity":[47],"is":[49,61],"proportional":[50],"to":[51],"complexities":[54],"best-known":[57],"algorithms.":[58],"variant":[63],"multigrid":[66],"waveform":[67],"relaxation":[68],"method":[69],"where":[70],"scalar":[72],"ordinary":[73],"make":[77],"up":[78],"kernel":[80],"computation":[82],"solved":[84],"using":[85],"cyclic":[87],"reduction-type":[88],"algorithm.":[89],"Experimental":[90],"results":[91],"obtained":[92],"on":[93],"massively":[95],"parallel":[96],"multiprocessor":[97],"presented.":[99]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}