{"id":"https://openalex.org/W2034646307","doi":"https://doi.org/10.1080/00207160701458252","title":"Splitting extrapolation method for solving second-order parabolic equations with curved boundaries by using domain decomposition and d-quadratic isoparametric finite elements","display_name":"Splitting extrapolation method for solving second-order parabolic equations with curved boundaries by using domain decomposition and d-quadratic isoparametric finite elements","publication_year":2007,"publication_date":"2007-06-01","ids":{"openalex":"https://openalex.org/W2034646307","doi":"https://doi.org/10.1080/00207160701458252","mag":"2034646307"},"language":"en","primary_location":{"id":"doi:10.1080/00207160701458252","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701458252","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5041708794","display_name":"Xiaoming He","orcid":"https://orcid.org/0000-0003-1270-4972"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xiaoming He","raw_affiliation_strings":["Department of Mathematics , Virginia Tech , Blacksburg, VA, 24061, U.S.A","Department of Mathematics, Virginia Tech, Blacksburg, VA, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Virginia Tech , Blacksburg, VA, 24061, U.S.A","institution_ids":["https://openalex.org/I859038795"]},{"raw_affiliation_string":"Department of Mathematics, Virginia Tech, Blacksburg, VA, U.S.A","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085245933","display_name":"Tao L\u00fc","orcid":"https://orcid.org/0000-0001-9144-6136"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao L\u00fc","raw_affiliation_strings":["Department of Mathematics , Sichuan University , Chengdu, Sichuan, 610064, P.R, China","Department of Mathematics , Sichuan University , Chengdu, Sichuan , P.R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Sichuan University , Chengdu, Sichuan, 610064, P.R, China","institution_ids":["https://openalex.org/I24185976"]},{"raw_affiliation_string":"Department of Mathematics , Sichuan University , Chengdu, Sichuan , P.R. China","institution_ids":["https://openalex.org/I24185976"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041708794"],"corresponding_institution_ids":["https://openalex.org/I859038795"],"apc_list":null,"apc_paid":null,"fwci":1.253,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.79087872,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"84","issue":"6","first_page":"767","last_page":"781"},"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":0.9994000196456909,"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":0.9994000196456909,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9988999962806702,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9976999759674072,"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/mathematics","display_name":"Mathematics","score":0.8373798727989197},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.7781955003738403},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5702633261680603},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.5605559349060059},{"id":"https://openalex.org/keywords/superconvergence","display_name":"Superconvergence","score":0.5312172174453735},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5239779353141785},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4438059329986572},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4383862316608429},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.43553411960601807},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.42130813002586365},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4207911193370819},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4119245409965515},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40966930985450745},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18665212392807007}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8373798727989197},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.7781955003738403},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5702633261680603},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.5605559349060059},{"id":"https://openalex.org/C83295009","wikidata":"https://www.wikidata.org/wiki/Q7643190","display_name":"Superconvergence","level":3,"score":0.5312172174453735},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5239779353141785},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4438059329986572},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4383862316608429},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43553411960601807},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42130813002586365},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4207911193370819},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4119245409965515},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40966930985450745},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18665212392807007},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160701458252","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701458252","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W586876262","https://openalex.org/W1993105366","https://openalex.org/W2041523977","https://openalex.org/W2058785380","https://openalex.org/W2093439303","https://openalex.org/W4205795514","https://openalex.org/W4210300254","https://openalex.org/W4236523868","https://openalex.org/W4249715296"],"related_works":["https://openalex.org/W2094577950","https://openalex.org/W2031157121","https://openalex.org/W1565666028","https://openalex.org/W2891538916","https://openalex.org/W2160252404","https://openalex.org/W4230524683","https://openalex.org/W3141012097","https://openalex.org/W185121461","https://openalex.org/W2148263540","https://openalex.org/W4236113016"],"abstract_inverted_index":{"This":[0,24],"article":[1],"discusses":[2],"a":[3,28,34,66,70,80,91,96,102,109,126],"splitting":[4,60],"extrapolation":[5,61],"method":[6,25,134],"for":[7,137,167],"solving":[8,78,138,168],"second-order":[9],"parabolic":[10,170],"equations":[11],"with":[12,74,95],"curved":[13,97],"boundaries":[14],"by":[15,77],"using":[16],"domain":[17,155],"decomposition":[18],"and":[19,33,119],"d-quadratic":[20,49],"isoparametric":[21,50],"finite":[22,51],"elements.":[23],"possesses":[26,125],"superconvergence,":[27],"high":[29,35,127],"order":[30],"of":[31,37,46,82,104,116,129,146,152],"accuracy":[32,76],"degree":[36,128],"parallelism.":[38,130],"First,":[39],"we":[40,58,142],"prove":[41],"the":[42,56,144,147,150,153,163],"multi-variable":[43],"asymptotic":[44],"expansion":[45],"fully":[47],"discrete":[48,84,106],"element":[52],"errors.":[53],"Based":[54],"on":[55,69,86,108],"expansion,":[57],"generate":[59,65],"formulas.":[62],"These":[63],"formulas":[64],"numerical":[67,158],"solution":[68],"globally":[71],"fine":[72],"grid":[73],"higher":[75],"only":[79],"set":[81,103],"smaller":[83,105],"subproblems":[85,107,113],"different":[87],"coarser":[88],"grids.":[89],"Therefore,":[90],"large-scale":[92],"multidimensional":[93],"problem":[94],"boundary":[98],"is":[99,135,165],"turned":[100],"into":[101],"polyhedron.":[110],"Because":[111],"these":[112],"are":[114],"independent":[115],"each":[117],"other":[118],"have":[120],"similar":[121],"scales,":[122],"our":[123],"algorithm":[124,164],"In":[131],"addition,":[132],"this":[133],"effective":[136,166],"discontinuous":[139],"problems":[140,148],"if":[141],"regard":[143],"interfaces":[145,151],"as":[149],"initial":[154],"decomposition.":[156],"Our":[157],"results":[159],"also":[160],"show":[161],"that":[162],"nonlinear":[169],"equations.":[171]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"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"}