{"id":"https://openalex.org/W2094411006","doi":"https://doi.org/10.1137/s1064827595288206","title":"Domain Decomposition Operator Splittings for the Solution of Parabolic Equations","display_name":"Domain Decomposition Operator Splittings for the Solution of Parabolic Equations","publication_year":1998,"publication_date":"1998-05-01","ids":{"openalex":"https://openalex.org/W2094411006","doi":"https://doi.org/10.1137/s1064827595288206","mag":"2094411006"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827595288206","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827595288206","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://figshare.com/articles/journal_contribution/Domain_Decomposition_Operator_Splittings_for_the_Solution_of_Parabolic_Equations/13677811","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060981469","display_name":"Tarek P. Mathew","orcid":null},"institutions":[{"id":"https://openalex.org/I12834331","display_name":"University of Wyoming","ror":"https://ror.org/01485tq96","country_code":"US","type":"education","lineage":["https://openalex.org/I12834331"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. P. Mathew","raw_affiliation_strings":["Department of Mathematics, University of Wyoming, Laramie, WY 82071-3036"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wyoming, Laramie, WY 82071-3036","institution_ids":["https://openalex.org/I12834331"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042595801","display_name":"Peter L. Polyakov","orcid":null},"institutions":[{"id":"https://openalex.org/I12834331","display_name":"University of Wyoming","ror":"https://ror.org/01485tq96","country_code":"US","type":"education","lineage":["https://openalex.org/I12834331"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. L. Polyakov","raw_affiliation_strings":["Department of Mathematics, University of Wyoming, Laramie, WY 82071-3036"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wyoming, Laramie, WY 82071-3036","institution_ids":["https://openalex.org/I12834331"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037976295","display_name":"Giovanni Russo","orcid":"https://orcid.org/0000-0003-4215-1926"},"institutions":[{"id":"https://openalex.org/I26415053","display_name":"University of L'Aquila","ror":"https://ror.org/01j9p1r26","country_code":"IT","type":"education","lineage":["https://openalex.org/I26415053"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. Russo","raw_affiliation_strings":["Dipartimento di Matematica, Universita dell'Aquila, Via Vetoio, Loc Coppito, 67010 L'Aquila, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universita dell'Aquila, Via Vetoio, Loc Coppito, 67010 L'Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031612753","display_name":"J. Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I12834331","display_name":"University of Wyoming","ror":"https://ror.org/01485tq96","country_code":"US","type":"education","lineage":["https://openalex.org/I12834331"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Wang","raw_affiliation_strings":["Department of Mathematics, University of Wyoming, Laramie, WY 82071-3036"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wyoming, Laramie, WY 82071-3036","institution_ids":["https://openalex.org/I12834331"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7312,"has_fulltext":false,"cited_by_count":59,"citation_normalized_percentile":{"value":0.93006161,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"19","issue":"3","first_page":"912","last_page":"932"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9993000030517578,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/mathematics","display_name":"Mathematics","score":0.8582050204277039},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.7325731515884399},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.5918015241622925},{"id":"https://openalex.org/keywords/alternating-direction-implicit-method","display_name":"Alternating direction implicit method","score":0.5671265125274658},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.5058498382568359},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5008759498596191},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.4892725646495819},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48213526606559753},{"id":"https://openalex.org/keywords/elliptic-operator","display_name":"Elliptic operator","score":0.4735890030860901},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.46188443899154663},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.448899507522583},{"id":"https://openalex.org/keywords/crank\u2013nicolson-method","display_name":"Crank\u2013Nicolson method","score":0.4342026114463806},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.42756545543670654},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.41435766220092773},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.410386323928833},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39011842012405396},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3470660448074341},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.21535786986351013},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.17306384444236755}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8582050204277039},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.7325731515884399},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.5918015241622925},{"id":"https://openalex.org/C142363948","wikidata":"https://www.wikidata.org/wiki/Q4736413","display_name":"Alternating direction implicit method","level":3,"score":0.5671265125274658},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.5058498382568359},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5008759498596191},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.4892725646495819},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48213526606559753},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.4735890030860901},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.46188443899154663},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.448899507522583},{"id":"https://openalex.org/C180931078","wikidata":"https://www.wikidata.org/wiki/Q588725","display_name":"Crank\u2013Nicolson method","level":3,"score":0.4342026114463806},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.42756545543670654},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.41435766220092773},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.410386323928833},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39011842012405396},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3470660448074341},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.21535786986351013},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.17306384444236755},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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":5,"locations":[{"id":"doi:10.1137/s1064827595288206","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827595288206","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:CiteSeerX.psu:10.1.1.938.6370","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.938.6370","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://repository.uwyo.edu/cgi/viewcontent.cgi?article%3D1012%26context%3Dmath_facpub","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/13677811","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Domain_Decomposition_Operator_Splittings_for_the_Solution_of_Parabolic_Equations/13677811","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:mountainscholar.org:20.500.11919/1581","is_oa":false,"landing_page_url":"https://hdl.handle.net/20.500.11919/1581","pdf_url":null,"source":{"id":"https://openalex.org/S4306402292","display_name":"Digital Collections of Colorado (Colorado State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I92446798","host_organization_name":"Colorado State University","host_organization_lineage":["https://openalex.org/I92446798"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Faculty Publications","raw_type":"Journal contribution"},{"id":"pmh:oai:repository.uwyo.edu:math_facpub-1012","is_oa":false,"landing_page_url":"https://repository.uwyo.edu/math_facpub/13","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Faculty Publications","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/13677811","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Domain_Decomposition_Operator_Splittings_for_the_Solution_of_Parabolic_Equations/13677811","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W70665148","https://openalex.org/W202241982","https://openalex.org/W1224802987","https://openalex.org/W1554725844","https://openalex.org/W1988975817","https://openalex.org/W1994206948","https://openalex.org/W1999453927","https://openalex.org/W1999630686","https://openalex.org/W2015347446","https://openalex.org/W2017085690","https://openalex.org/W2033736734","https://openalex.org/W2034298604","https://openalex.org/W2039706183","https://openalex.org/W2043857934","https://openalex.org/W2049161806","https://openalex.org/W2053788345","https://openalex.org/W2059654406","https://openalex.org/W2060777779","https://openalex.org/W2065330829","https://openalex.org/W2071037826","https://openalex.org/W2095036901","https://openalex.org/W2104126767","https://openalex.org/W2127981460","https://openalex.org/W2140323003","https://openalex.org/W3140595534","https://openalex.org/W3149580215","https://openalex.org/W4256161475","https://openalex.org/W4301283118"],"related_works":["https://openalex.org/W2123186262","https://openalex.org/W768539834","https://openalex.org/W2048336173","https://openalex.org/W2026628742","https://openalex.org/W1670331598","https://openalex.org/W2062472350","https://openalex.org/W2508526884","https://openalex.org/W1795839839","https://openalex.org/W2064745921","https://openalex.org/W2094411006"],"abstract_inverted_index":{"We":[0],"study":[1],"domain":[2,78],"decomposition":[3,79],"counterparts":[4],"of":[5,29,85,113],"the":[6,19,25,33,42,70,105,111,125,137,150,159,164],"classical":[7,34],"alternating":[8],"direction":[9],"implicit":[10,26],"(ADI)":[11],"and":[12,36,61,96,108],"fractional":[13],"step":[14,143],"(FS)":[15],"methods":[16,38],"for":[17,39,149],"solving":[18],"large":[20],"linear":[21,53],"systems":[22,54],"arising":[23],"from":[24],"time":[27,120,142],"stepping":[28],"parabolic":[30,40],"equations.":[31],"In":[32],"ADI":[35],"FS":[37],"equations,":[41],"elliptic":[43],"operator":[44],"is":[45,59,144],"split":[46],"along":[47,154],"coordinate":[48],"axes;":[49],"they":[50,109],"yield":[51],"tridiagonal":[52],"whenever":[55],"a":[56,83,140],"uniform":[57],"grid":[58],"used":[60],"when":[62,98],"mixed":[63,99],"derivative":[64,100],"terms":[65,101],"are":[66,89,102,147],"not":[67],"present":[68,103],"in":[69,104,128],"differential":[71,106],"equation.":[72],"Unlike":[73],"coordinate-axes-based":[74],"splittings,":[75],"we":[76],"employ":[77],"splittings":[80,88],"based":[81],"on":[82,93,116],"partition":[84],"unity.":[86],"Such":[87],"applicable":[90],"to":[91],"problems":[92],"nonuniform":[94],"meshes":[95],"even":[97],"equation":[107],"require":[110],"solution":[112],"one":[114],"problem":[115],"each":[117],"subdomain":[118],"per":[119],"step,":[121],"without":[122],"iteration.":[123],"However,":[124],"truncation":[126,152],"error":[127],"our":[129],"proposed":[130,165],"method":[131,162],"deteriorates":[132],"with":[133,155,163],"smaller":[134,141],"overlap":[135],"amongst":[136],"subdomains":[138],"unless":[139],"chosen.":[145],"Estimates":[146],"presented":[148],"asymptotic":[151],"error,":[153],"computational":[156],"results":[157],"comparing":[158],"standard":[160],"Crank--Nicolson":[161],"method.":[166]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}