{"id":"https://openalex.org/W2076926241","doi":"https://doi.org/10.1137/0915030","title":"A Comparison of Preconditioned Nonsymmetric Krylov Methods on a Large-Scale MIMD Machine","display_name":"A Comparison of Preconditioned Nonsymmetric Krylov Methods on a Large-Scale MIMD Machine","publication_year":1994,"publication_date":"1994-03-01","ids":{"openalex":"https://openalex.org/W2076926241","doi":"https://doi.org/10.1137/0915030","mag":"2076926241"},"language":"en","primary_location":{"id":"doi:10.1137/0915030","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0915030","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":true,"oa_status":"green","oa_url":"https://www.osti.gov/servlets/purl/6014096","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018004800","display_name":"John N. Shadid","orcid":"https://orcid.org/0009-0001-9804-1649"},"institutions":[{"id":"https://openalex.org/I4210104735","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John N. Shadid","raw_affiliation_strings":["Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)","institution_ids":["https://openalex.org/I4210104735"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5106787959","display_name":"Ray Tuminaro","orcid":null},"institutions":[{"id":"https://openalex.org/I4210104735","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ray S. Tuminaro","raw_affiliation_strings":["Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)","institution_ids":["https://openalex.org/I4210104735"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210104735"],"apc_list":null,"apc_paid":null,"fwci":8.2448,"has_fulltext":true,"cited_by_count":43,"citation_normalized_percentile":{"value":0.98553743,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"15","issue":"2","first_page":"440","last_page":"459"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.9972000122070312,"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/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.9018718004226685},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.8574687242507935},{"id":"https://openalex.org/keywords/mimd","display_name":"MIMD","score":0.8210968971252441},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.7860844731330872},{"id":"https://openalex.org/keywords/biconjugate-gradient-stabilized-method","display_name":"Biconjugate gradient stabilized method","score":0.7409548759460449},{"id":"https://openalex.org/keywords/conjugate-residual-method","display_name":"Conjugate residual method","score":0.5839044451713562},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.569097638130188},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5345242619514465},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.48800745606422424},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48388800024986267},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.46077674627304077},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.45840954780578613},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.43686437606811523},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.42654529213905334},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.411962628364563},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36637765169143677},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35370874404907227},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.30510640144348145},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11351123452186584},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.06555292010307312}],"concepts":[{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.9018718004226685},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.8574687242507935},{"id":"https://openalex.org/C21032095","wikidata":"https://www.wikidata.org/wiki/Q1149237","display_name":"MIMD","level":2,"score":0.8210968971252441},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.7860844731330872},{"id":"https://openalex.org/C120553275","wikidata":"https://www.wikidata.org/wiki/Q4903720","display_name":"Biconjugate gradient stabilized method","level":3,"score":0.7409548759460449},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.5839044451713562},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.569097638130188},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5345242619514465},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.48800745606422424},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48388800024986267},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.46077674627304077},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.45840954780578613},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.43686437606811523},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.42654529213905334},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.411962628364563},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36637765169143677},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35370874404907227},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.30510640144348145},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11351123452186584},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.06555292010307312},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0915030","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0915030","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:osti.gov:6014096","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/6014096","pdf_url":"https://www.osti.gov/servlets/purl/6014096","source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:osti.gov:6014096","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/6014096","pdf_url":"https://www.osti.gov/servlets/purl/6014096","source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1275238458","display_name":null,"funder_award_id":"DE-AC04-76DP00789","funder_id":"https://openalex.org/F4320338291","funder_display_name":"Sandia National Laboratories"},{"id":"https://openalex.org/G1316987985","display_name":null,"funder_award_id":"DE\u2010AC04\u201076DP00789","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320338291","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2076926241.pdf","grobid_xml":"https://content.openalex.org/works/W2076926241.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1594290493","https://openalex.org/W1815303420","https://openalex.org/W1854226152","https://openalex.org/W1986125951","https://openalex.org/W1992208469","https://openalex.org/W1997831216","https://openalex.org/W2015105467","https://openalex.org/W2021810545","https://openalex.org/W2027062522","https://openalex.org/W2028192944","https://openalex.org/W2029830594","https://openalex.org/W2040298674","https://openalex.org/W2047344035","https://openalex.org/W2059167872","https://openalex.org/W2071649025","https://openalex.org/W2076485756","https://openalex.org/W2140153041","https://openalex.org/W2148028096","https://openalex.org/W2151317657","https://openalex.org/W2154590891","https://openalex.org/W2155216327","https://openalex.org/W2155505608","https://openalex.org/W2416227595","https://openalex.org/W2588081979","https://openalex.org/W3013046677","https://openalex.org/W4299343067"],"related_works":["https://openalex.org/W2371875888","https://openalex.org/W1620763245","https://openalex.org/W2486238093","https://openalex.org/W1510662217","https://openalex.org/W2130308425","https://openalex.org/W2592349247","https://openalex.org/W2896577559","https://openalex.org/W4283656204","https://openalex.org/W2120159737","https://openalex.org/W1976157534"],"abstract_inverted_index":{"Many":[0],"complex":[1],"physical":[2],"processes":[3],"are":[4,59,109],"modeled":[5],"by":[6],"coupled":[7],"systems":[8,28],"of":[9,18,24,29,40,43,71,114],"partial":[10],"differential":[11],"equations":[12],"(PDEs).":[13],"Often,":[14],"the":[15,22,34,37,61,69,79,89,112,115],"numerical":[16],"approximation":[17],"these":[19],"PDEs":[20],"requires":[21],"solution":[23,70],"large":[25,72],"sparse":[26,73],"nonsymmetric":[27],"equations.":[30],"In":[31,76],"this":[32,77],"paper":[33],"authors":[35],"compare":[36],"parallel":[38,83],"performance":[39],"a":[41,49,123],"number":[42],"preconditioned":[44],"Krylov":[45],"subspace":[46],"methods":[47,58],"on":[48,82,111,119],"large-scale":[50],"multiple":[51,53],"instruction":[52],"data":[54],"(MIMD)":[55],"machine.":[56],"These":[57],"among":[60],"most":[62],"robust":[63],"and":[64,102],"efficient":[65],"iterative":[66],"algorithms":[67],"for":[68],"linear":[74],"systems.":[75],"comparison,":[78],"focus":[80],"is":[81],"issues":[84],"associated":[85],"with":[86],"preconditioners":[87],"within":[88],"generalized":[90],"minimum":[91],"residual":[92,104],"(GMRES),":[93],"conjugate":[94],"gradient":[95,99],"squared":[96],"(CGS),":[97],"biconjugate":[98],"stabilized":[100],"(Bi-CGSTAB),":[101],"quasi-minimal":[103],"CGS":[105],"(QMRCGS)":[106],"methods.":[107],"Conclusions":[108],"drawn":[110],"effectiveness":[113],"different":[116],"schemes":[117],"based":[118],"results":[120],"obtained":[121],"from":[122],"1024":[124],"processor":[125],"nCUBE":[126],"2":[127],"hypercube.":[128]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
