{"id":"https://openalex.org/W1989707864","doi":"https://doi.org/10.1137/0913075","title":"Efficient Parallel Algorithms for Solving Initial-Boundary Value and Time-Periodic Parabolic Partial Differential Equations","display_name":"Efficient Parallel Algorithms for Solving Initial-Boundary Value and Time-Periodic Parabolic Partial Differential Equations","publication_year":1992,"publication_date":"1992-11-01","ids":{"openalex":"https://openalex.org/W1989707864","doi":"https://doi.org/10.1137/0913075","mag":"1989707864"},"language":"en","primary_location":{"id":"doi:10.1137/0913075","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0913075","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/A5062993526","display_name":"Stefan Vandewalle","orcid":"https://orcid.org/0000-0002-8988-2374"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Stefan Vandewalle","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5070232245","display_name":"Robert Piessens","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert Piessens","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062993526"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.8842,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.97362978,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"13","issue":"6","first_page":"1330","last_page":"1346"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9990000128746033,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/intel-ipsc","display_name":"Intel iPSC","score":0.8048536777496338},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6808918714523315},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6519199013710022},{"id":"https://openalex.org/keywords/vectorization","display_name":"Vectorization (mathematics)","score":0.6366825103759766},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.6311401724815369},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.6222461462020874},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5500935912132263},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.5081231594085693},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.49575600028038025},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4865068793296814},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.47728171944618225},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47116121649742126},{"id":"https://openalex.org/keywords/method-of-lines","display_name":"Method of lines","score":0.45811739563941956},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.4305029511451721},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4227529466152191},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.39539816975593567},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3304286003112793},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3019012212753296},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.16445773839950562},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.15196168422698975},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.07686111330986023}],"concepts":[{"id":"https://openalex.org/C199115840","wikidata":"https://www.wikidata.org/wiki/Q108649754","display_name":"Intel iPSC","level":3,"score":0.8048536777496338},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6808918714523315},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6519199013710022},{"id":"https://openalex.org/C41681595","wikidata":"https://www.wikidata.org/wiki/Q7917855","display_name":"Vectorization (mathematics)","level":2,"score":0.6366825103759766},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6311401724815369},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.6222461462020874},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5500935912132263},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.5081231594085693},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.49575600028038025},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4865068793296814},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.47728171944618225},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47116121649742126},{"id":"https://openalex.org/C136798861","wikidata":"https://www.wikidata.org/wiki/Q1826712","display_name":"Method of lines","level":5,"score":0.45811739563941956},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.4305029511451721},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4227529466152191},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.39539816975593567},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3304286003112793},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3019012212753296},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.16445773839950562},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.15196168422698975},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.07686111330986023},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0913075","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0913075","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"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/124603","is_oa":false,"landing_page_url":"https://lirias.kuleuven.be/bitstream/123456789/124603/1/int3VdwPiesSISC.pdf","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 and statistical computing, vol. 13 (6), Art.No. 6, (1330-1346)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1964922990","https://openalex.org/W1970898340","https://openalex.org/W1987455271","https://openalex.org/W2025631352","https://openalex.org/W2026064960","https://openalex.org/W2027772856","https://openalex.org/W2062246004","https://openalex.org/W2062543345","https://openalex.org/W2075898997","https://openalex.org/W2140779530","https://openalex.org/W2154509600","https://openalex.org/W2163251884","https://openalex.org/W4230055019","https://openalex.org/W4239609295"],"related_works":["https://openalex.org/W4250003423","https://openalex.org/W2026686860","https://openalex.org/W2127111677","https://openalex.org/W1555339015","https://openalex.org/W2914457235","https://openalex.org/W2139778910","https://openalex.org/W2154509600","https://openalex.org/W2072900126","https://openalex.org/W1983768647","https://openalex.org/W2360271471"],"abstract_inverted_index":{"The":[0,65,101],"numerical":[1,102,111],"solution":[2],"of":[3,21,48,104,120],"a":[4,13],"parabolic":[5],"partial":[6],"differential":[7],"equation":[8],"is":[9,35,63,67,116],"usually":[10],"calculated":[11],"by":[12,53,109],"timestepping":[14],"method.":[15],"This":[16],"precludes":[17],"the":[18,26,46,49,55,59,94,105,121],"efficient":[19],"use":[20],"vectorization":[22],"and":[23,71,113],"parallelism":[24],"if":[25],"problem":[27,56],"to":[28,69,81,118],"be":[29,79],"solved":[30],"on":[31,74,96],"each":[32],"time":[33,60],"level":[34],"not":[36],"very":[37],"large.":[38],"In":[39],"this":[40],"paper":[41],"an":[42,97],"algorithm":[43],"that":[44,119],"overcomes":[45],"limitations":[47],"standard":[50,123],"marching":[51],"schemes":[52],"solving":[54],"at":[57],"all":[58],"levels":[61],"simultaneously":[62],"discussed.":[64],"method":[66,95,106],"applicable":[68],"linear":[70],"nonlinear":[72],"problems":[73,85],"arbitrary":[75],"domains.":[76],"It":[77],"can":[78],"used":[80],"solve":[82],"initial-boundary":[83],"value":[84],"as":[86,88],"well":[87],"time-periodic":[89],"equations.":[90],"We":[91],"have":[92],"implemented":[93],"Intel":[98],"iPSC/2-VX":[99],"hypercube.":[100],"properties":[103],"are":[107],"illustrated":[108],"two":[110],"examples":[112],"its":[114],"performance":[115],"compared":[117],"best":[122],"solvers.":[124]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
