{"id":"https://openalex.org/W2155505608","doi":"https://doi.org/10.1002/cpe.4330040605","title":"Sparse iterative algorithm software for large\u2010scale MIMD machines: An initial discussion and implementation","display_name":"Sparse iterative algorithm software for large\u2010scale MIMD machines: An initial discussion and implementation","publication_year":1992,"publication_date":"1992-09-01","ids":{"openalex":"https://openalex.org/W2155505608","doi":"https://doi.org/10.1002/cpe.4330040605","mag":"2155505608"},"language":"en","primary_location":{"id":"doi:10.1002/cpe.4330040605","is_oa":false,"landing_page_url":"https://doi.org/10.1002/cpe.4330040605","pdf_url":null,"source":{"id":"https://openalex.org/S4210209928","display_name":"Concurrency Practice and Experience","issn_l":"1040-3108","issn":["1040-3108","1096-9128"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Concurrency: Practice and Experience","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/A5018004800","display_name":"John N. Shadid","orcid":"https://orcid.org/0009-0001-9804-1649"},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John N. Shadid","raw_affiliation_strings":["Parallel Computational Sciences Department Sandia National Laboratories Albuquerque, NM, USA"],"affiliations":[{"raw_affiliation_string":"Parallel Computational Sciences Department Sandia National Laboratories Albuquerque, NM, USA","institution_ids":["https://openalex.org/I192454743"]}]},{"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":["Applied and Numerical Mathematics Department Sandia National Laboratories Albuquerque, NM, USA"],"affiliations":[{"raw_affiliation_string":"Applied and Numerical Mathematics Department Sandia National Laboratories Albuquerque, NM, USA","institution_ids":["https://openalex.org/I4210104735"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018004800"],"corresponding_institution_ids":["https://openalex.org/I192454743"],"apc_list":null,"apc_paid":null,"fwci":3.7154,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.94166249,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"4","issue":"6","first_page":"481","last_page":"497"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mimd","display_name":"MIMD","score":0.8183209896087646},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7705823183059692},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.7593421936035156},{"id":"https://openalex.org/keywords/matrix-free-methods","display_name":"Matrix-free methods","score":0.7285625338554382},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.6585161685943604},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.633517861366272},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.6164506673812866},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.529276430606842},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4575381278991699},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.45074301958084106},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.44354745745658875},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.43379220366477966},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42624953389167786},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37333863973617554},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3226724863052368},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.17327988147735596}],"concepts":[{"id":"https://openalex.org/C21032095","wikidata":"https://www.wikidata.org/wiki/Q1149237","display_name":"MIMD","level":2,"score":0.8183209896087646},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7705823183059692},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.7593421936035156},{"id":"https://openalex.org/C54219892","wikidata":"https://www.wikidata.org/wiki/Q4080929","display_name":"Matrix-free methods","level":4,"score":0.7285625338554382},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.6585161685943604},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.633517861366272},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.6164506673812866},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.529276430606842},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4575381278991699},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.45074301958084106},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.44354745745658875},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.43379220366477966},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42624953389167786},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37333863973617554},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3226724863052368},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.17327988147735596},{"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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/cpe.4330040605","is_oa":false,"landing_page_url":"https://doi.org/10.1002/cpe.4330040605","pdf_url":null,"source":{"id":"https://openalex.org/S4210209928","display_name":"Concurrency Practice and Experience","issn_l":"1040-3108","issn":["1040-3108","1096-9128"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Concurrency: Practice and Experience","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W89281171","https://openalex.org/W1489844249","https://openalex.org/W1497437240","https://openalex.org/W1559533846","https://openalex.org/W1815303420","https://openalex.org/W2021810545","https://openalex.org/W2058901976","https://openalex.org/W2059167872","https://openalex.org/W2071649025","https://openalex.org/W2092509590","https://openalex.org/W2111516947","https://openalex.org/W2114030927","https://openalex.org/W2140153041","https://openalex.org/W2154590891","https://openalex.org/W2155216327","https://openalex.org/W2161455936","https://openalex.org/W2316564661","https://openalex.org/W4237643032","https://openalex.org/W4245070659","https://openalex.org/W7070139461"],"related_works":["https://openalex.org/W2513846324","https://openalex.org/W1538056909","https://openalex.org/W1984807396","https://openalex.org/W1550904902","https://openalex.org/W2143594203","https://openalex.org/W2018388178","https://openalex.org/W1666350077","https://openalex.org/W1437491809","https://openalex.org/W266923872","https://openalex.org/W2963709814"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"parallelization":[2],"of":[3,26,32,40,68,89,105,127],"sophisticated":[4],"applications":[5,28,85],"has":[6],"dramatically":[7],"increased":[8],"in":[9],"recent":[10],"years.":[11],"As":[12],"machine":[13],"capabilities":[14],"rise,":[15],"greater":[16],"emphasis":[17],"on":[18,111],"modeling":[19],"complex":[20],"phenomena":[21],"can":[22,134],"be":[23,135],"expected.":[24],"Many":[25],"these":[27,128],"require":[29],"the":[30,81],"solution":[31],"large":[33,52],"sparse":[34,53,61,76,140],"matrix":[35,62,77,141],"equations":[36,43],"which":[37,72],"approximate":[38],"systems":[39,55],"partial":[41],"differential":[42],"(PDEs).":[44],"Therefore":[45],"we":[46],"consider":[47],"parallel":[48,60,69],"iterative":[49,70],"solvers":[50,71],"for":[51],"non\u2010symmetric":[54],"and":[56,86,93,107],"issues":[57],"related":[58],"to":[59,101],"software.":[63],"We":[64],"describe":[65],"a":[66,74,87,103,112],"collection":[67],"use":[73],"distributed":[75],"format":[78],"that":[79,131],"facilitates":[80],"interface":[82],"between":[83],"specific":[84],"variety":[88],"Krylov":[90],"subspace":[91],"techniques":[92],"multigrid":[94],"methods.":[95],"These":[96],"methods":[97],"have":[98],"been":[99],"used":[100],"solve":[102],"number":[104],"linear":[106],"non\u2010linear":[108],"PDE":[109],"problems":[110],"1024\u2010processor":[113],"NCUBE":[114],"2":[115],"hypercube.":[116],"Over":[117],"1":[118],"Gflop":[119],"sustained":[120],"computation":[121],"rates":[122],"are":[123],"achieved":[124],"with":[125],"many":[126],"solvers,":[129],"demonstrating":[130],"high":[132],"performance":[133],"attained":[136],"even":[137],"when":[138],"using":[139],"data":[142],"structures.":[143]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}