{"id":"https://openalex.org/W2066308409","doi":"https://doi.org/10.1137/0912001","title":"Limits on Parallelism in the Numerical Solution of Linear Partial Differential Equations","display_name":"Limits on Parallelism in the Numerical Solution of Linear Partial Differential Equations","publication_year":1991,"publication_date":"1991-01-01","ids":{"openalex":"https://openalex.org/W2066308409","doi":"https://doi.org/10.1137/0912001","mag":"2066308409"},"language":"en","primary_location":{"id":"doi:10.1137/0912001","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0912001","pdf_url":null,"source":{"id":"https://openalex.org/S4210181992","display_name":"SIAM Journal on Scientific and Statistical Computing","issn_l":"0196-5204","issn":["0196-5204","2168-3417"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 and Statistical 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/A5004248420","display_name":"Patrick H Worley","orcid":"https://orcid.org/0000-0003-1734-0821"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Patrick H. Worley","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004248420"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9867,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.86679842,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"12","issue":"1","first_page":"1","last_page":"35"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9983000159263611,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9977999925613403,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7040894031524658},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6078568696975708},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5684078335762024},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5085595846176147},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.47512155771255493},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.41570472717285156},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3313964903354645},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3171612322330475},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2945297658443451},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22149932384490967},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1103048026561737}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7040894031524658},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6078568696975708},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5684078335762024},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5085595846176147},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.47512155771255493},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.41570472717285156},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3313964903354645},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3171612322330475},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2945297658443451},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22149932384490967},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1103048026561737},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0912001","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0912001","pdf_url":null,"source":{"id":"https://openalex.org/S4210181992","display_name":"SIAM Journal on Scientific and Statistical Computing","issn_l":"0196-5204","issn":["0196-5204","2168-3417"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 and Statistical Computing","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/W1500590019","https://openalex.org/W1554451661","https://openalex.org/W1555673550","https://openalex.org/W1583497601","https://openalex.org/W1589943916","https://openalex.org/W1978564754","https://openalex.org/W2010069926","https://openalex.org/W2013761841","https://openalex.org/W2065015198","https://openalex.org/W2071649025","https://openalex.org/W2085319748","https://openalex.org/W2094969361","https://openalex.org/W2150871235","https://openalex.org/W2407497769","https://openalex.org/W2505936072","https://openalex.org/W2916392783","https://openalex.org/W2921847140","https://openalex.org/W3111685920","https://openalex.org/W4206566500","https://openalex.org/W4249044135"],"related_works":["https://openalex.org/W4255837520","https://openalex.org/W2387011115","https://openalex.org/W4234808182","https://openalex.org/W4255628145","https://openalex.org/W2382043075","https://openalex.org/W2809151339","https://openalex.org/W2216913934","https://openalex.org/W2360673138","https://openalex.org/W2809370583","https://openalex.org/W4301447905"],"abstract_inverted_index":{"The":[0,64],"problem":[1,193,210],"considered":[2],"is":[3,43,62,88,96,109,164,172,194,201],"that":[4,58,170,203,226],"of":[5,9,31,55,99,102,131,134,162,180,188,207,217,233,240,247],"approximating":[6],"the":[7,29,41,52,60,68,72,100,114,121,132,136,140,146,153,156,160,185,192,205,215,219,245],"solution":[8,61,187],"a":[10,36,48,87,89,97,177,189,209,241,248],"linear":[11],"scalar":[12],"partial":[13],"differential":[14],"equation":[15],"(PDE)":[16],"at":[17,214],"one":[18],"or":[19,159],"more":[20],"locations":[21],"in":[22,40],"its":[23],"domain.":[24],"A":[25],"lower":[26,49,65],"bound":[27,50,66,112],"on":[28,51,67,113,145],"amount":[30],"data":[32],"required":[33],"to":[34,175],"satisfy":[35],"given":[37,151],"error":[38],"tolerance":[39],"approximation":[42,246],"described.":[44],"Using":[45],"this":[46,198,228],"bound,":[47],"execution":[53,69,122,147,220],"time":[54,70,123,148],"parallel":[56],"algorithms":[57],"approximate":[59],"derived.":[63],"has":[71,168],"form":[73],"$\\alpha":[74,118],"\\cdot":[75,79],"f_{(":[76],"+":[77,93],")}":[78,94],"\\log":[80],"_2":[81],"\\epsilon^{":[82],"-":[83],"1}":[84],"$,":[85],"where":[86,155],"problem-dependent":[90],"constant,":[91],"$f_{(":[92],"$":[95,107,126,128],"measure":[98],"speed":[101],"floating":[103],"point":[104],"arithmetic,":[105],"and":[106,139,237],"\\epsilon$":[108],"an":[110,230,234,238],"upper":[111],"error.":[115],"Thus,":[116],"when":[117,183],">":[119],"0$,":[120],"increases":[124],"as":[125],"\\epsilon":[127],"decreases,":[129],"independent":[130],"number":[133,161,179],"processors,":[135],"interconnection":[137,157],"topology,":[138],"algorithm":[141,243],"used.":[142],"Lower":[143],"bounds":[144],"are":[149,224],"also":[150],"for":[152,244],"cases":[154],"network":[158],"processors":[163,181],"specified.":[165],"Recent":[166],"research":[167],"established":[169],"it":[171,200],"often":[173],"possible":[174],"use":[176],"large":[178],"efficiently":[182],"calculating":[184],"numerical":[186],"PDE":[190,236],"if":[191],"sufficiently":[195],"large.":[196],"In":[197],"paper,":[199],"shown":[202],"increasing":[204,218],"size":[206],"such":[208],"will":[211],"usually":[212],"come":[213],"cost":[216],"time.":[221],"Two":[222],"examples":[223],"described":[225],"verify":[227],"conclusion,":[229],"algorithm-independent":[231],"analysis":[232,239],"elliptic":[235],"specific":[242],"hyperbolic":[249],"PDE.":[250]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}