{"id":"https://openalex.org/W1999230975","doi":"https://doi.org/10.1137/040609215","title":"Unconditional Stability of Corrected Explicit\u2010Implicit Domain Decomposition Algorithms for Parallel Approximation of Heat Equations","display_name":"Unconditional Stability of Corrected Explicit\u2010Implicit Domain Decomposition Algorithms for Parallel Approximation of Heat Equations","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1999230975","doi":"https://doi.org/10.1137/040609215","mag":"1999230975"},"language":"en","primary_location":{"id":"doi:10.1137/040609215","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040609215","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5078839627","display_name":"Hansheng Shi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Han\u2010Sheng Shi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5052651480","display_name":"Hong-lin Liao","orcid":"https://orcid.org/0000-0003-0777-6832"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hong-Lin Liao","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078839627"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4683,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.87671912,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"44","issue":"4","first_page":"1584","last_page":"1611"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991999864578247,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.7320601940155029},{"id":"https://openalex.org/keywords/zigzag","display_name":"Zigzag","score":0.7030196785926819},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6994727849960327},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.610314667224884},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5597965717315674},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5006923675537109},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.49440908432006836},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4939780831336975},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44965505599975586},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.44805052876472473},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.4287911057472229},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24712640047073364},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19344452023506165},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1430225670337677},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10872477293014526}],"concepts":[{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.7320601940155029},{"id":"https://openalex.org/C192271897","wikidata":"https://www.wikidata.org/wiki/Q198438","display_name":"Zigzag","level":2,"score":0.7030196785926819},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6994727849960327},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.610314667224884},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5597965717315674},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5006923675537109},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.49440908432006836},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4939780831336975},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44965505599975586},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.44805052876472473},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.4287911057472229},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24712640047073364},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19344452023506165},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1430225670337677},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10872477293014526},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040609215","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040609215","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.800000011920929,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1967011851","https://openalex.org/W1994206948","https://openalex.org/W1999453927","https://openalex.org/W1999630686","https://openalex.org/W2003887285","https://openalex.org/W2046980739","https://openalex.org/W2072030354","https://openalex.org/W2106377468","https://openalex.org/W2135799863","https://openalex.org/W2140323003"],"related_works":["https://openalex.org/W2808029097","https://openalex.org/W3035794677","https://openalex.org/W2032417936","https://openalex.org/W2588100896","https://openalex.org/W2152067480","https://openalex.org/W2326117044","https://openalex.org/W135216162","https://openalex.org/W4289782736","https://openalex.org/W2947454206","https://openalex.org/W1982759381"],"abstract_inverted_index":{"A":[0],"class":[1],"of":[2,15,63,73,103,115],"corrected":[3,132],"explicit\u2010implicit":[4],"domain":[5,20,82],"decomposition":[6,21],"(CEIDD)":[7],"methods":[8,23],"is":[9],"investigated":[10],"for":[11,29,84,112],"the":[12,51,60,64,71,74,79,94,106,119,125,138,148],"parallel":[13],"approximation":[14],"linear":[16],"heat":[17],"equations.":[18],"Explicit\u2010implicit":[19],"(EIDD)":[22],"are":[24,91,110],"computationally":[25],"and":[26,77,100,142],"communicationally":[27],"efficient":[28],"each":[30],"time":[31,38],"step":[32,39,47],"but":[33],"always":[34],"suffer":[35],"from":[36],"small":[37],"size":[40],"restrictions.":[41],"By":[42,118],"adding":[43],"an":[44],"interface":[45],"correction":[46],"to":[48,69],"Kuznetsov\u2019s":[49],"EIDD,":[50],"one\u2010dimensional":[52],"CEIDD":[53,75,95],"procedure":[54],"achieves":[55],"unconditional":[56],"stability":[57],"without":[58],"discarding":[59],"time\u2010stepwise":[61],"efficiency":[62],"EIDD":[65],"method.":[66,96],"In":[67],"order":[68],"maintain":[70],"virtues":[72],"method":[76],"improve":[78],"flexibility":[80],"in":[81,93,137,150],"partitioning,":[83],"solving":[85],"multidimensional":[86],"problems,":[87],"special":[88],"zigzag\u2010shaped":[89],"interfaces":[90],"suggested":[92],"Based":[97],"on":[98],"noncrossover":[99],"crossover":[101],"types":[102],"zigzag":[104],"interfaces,":[105],"resulting":[107],"CEIDD\u2010ZI":[108],"algorithms":[109],"studied":[111],"two":[113],"strategies":[114],"subdomain":[116],"partition.":[117],"energy":[120],"method,":[121],"it":[122],"shows":[123],"that":[124],"proposed":[126],"algorithms,":[127],"including":[128],"their":[129],"degenerate":[130],"cases\u2014the":[131],"explicit":[133],"hopscotch":[134],"schemes\u2014are":[135],"convergent":[136],"discrete":[139],"$H^1$":[140],"seminorm":[141],"$L^2$":[143],"norm.":[144],"Numerical":[145],"experiments":[146],"confirm":[147],"results":[149],"our":[151],"analysis.":[152]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}