{"id":"https://openalex.org/W2000188649","doi":"https://doi.org/10.1137/110836626","title":"An Efficient High Order Heterogeneous Multiscale Method for Elliptic Problems","display_name":"An Efficient High Order Heterogeneous Multiscale Method for Elliptic Problems","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2000188649","doi":"https://doi.org/10.1137/110836626","mag":"2000188649"},"language":"en","primary_location":{"id":"doi:10.1137/110836626","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110836626","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","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/A5054195099","display_name":"Ruo Li","orcid":"https://orcid.org/0000-0001-9919-835X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ruo Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111939462","display_name":"Pingbing Ming","orcid":"https://orcid.org/0000-0002-0779-1576"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pingbing Ming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5112660824","display_name":"Fengyang Tang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fengyang Tang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.68,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.70028757,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"10","issue":"1","first_page":"259","last_page":"283"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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/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/T11558","display_name":"Composite Material Mechanics","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/solver","display_name":"Solver","score":0.8019727468490601},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6910039782524109},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5897142887115479},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.547704815864563},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5085355043411255},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47228890657424927},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47034814953804016},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4420027434825897},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42989397048950195},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.41007137298583984},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3432198464870453},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1668931245803833},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0943061113357544}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.8019727468490601},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6910039782524109},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5897142887115479},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.547704815864563},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5085355043411255},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47228890657424927},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47034814953804016},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4420027434825897},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42989397048950195},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.41007137298583984},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3432198464870453},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1668931245803833},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0943061113357544},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110836626","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110836626","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1547249381","https://openalex.org/W1866311589","https://openalex.org/W1965745583","https://openalex.org/W1967001685","https://openalex.org/W1967345544","https://openalex.org/W1990157709","https://openalex.org/W1990495229","https://openalex.org/W2001477834","https://openalex.org/W2006154213","https://openalex.org/W2008584207","https://openalex.org/W2009934830","https://openalex.org/W2024881233","https://openalex.org/W2026058560","https://openalex.org/W2029450279","https://openalex.org/W2029918260","https://openalex.org/W2033331374","https://openalex.org/W2033855973","https://openalex.org/W2035358778","https://openalex.org/W2037707132","https://openalex.org/W2042199582","https://openalex.org/W2042892160","https://openalex.org/W2044892973","https://openalex.org/W2065451462","https://openalex.org/W2074772185","https://openalex.org/W2075711639","https://openalex.org/W2075912172","https://openalex.org/W2076483786","https://openalex.org/W2108845300","https://openalex.org/W2123893140","https://openalex.org/W2124939526","https://openalex.org/W2125839646","https://openalex.org/W2130711343","https://openalex.org/W2168728641","https://openalex.org/W3111685920","https://openalex.org/W3214098784"],"related_works":["https://openalex.org/W2257847510","https://openalex.org/W2012311345","https://openalex.org/W2351839991","https://openalex.org/W4232340806","https://openalex.org/W1996117993","https://openalex.org/W2050829265","https://openalex.org/W2030982372","https://openalex.org/W3010994357","https://openalex.org/W3027085067","https://openalex.org/W2029569614"],"abstract_inverted_index":{"We":[0],"propose":[1],"an":[2],"efficient":[3],"heterogeneous":[4],"multiscale":[5],"finite":[6],"element":[7],"method":[8,37,72],"based":[9],"on":[10,30],"a":[11],"local":[12],"least-squares":[13],"reconstruction":[14],"of":[15,26,33,79],"the":[16,20,24,31,34,49,53,63,70,75],"effective":[17],"matrix":[18],"using":[19],"data":[21],"retrieved":[22],"from":[23],"solution":[25],"cell":[27],"problems":[28],"posed":[29],"vertices":[32],"triangulation.":[35],"The":[36],"achieves":[38],"high":[39,43],"order":[40,44],"accuracy":[41],"for":[42,62],"macroscopic":[45,55],"solver":[46],"with":[47],"essentially":[48],"same":[50],"cost":[51,76],"as":[52],"linear":[54],"solver.":[56],"Optimal":[57],"error":[58],"bounds":[59],"are":[60],"proved":[61],"elliptic":[64],"problem.":[65],"Numerical":[66],"results":[67],"demonstrate":[68],"that":[69],"new":[71],"significantly":[73],"reduces":[74],"without":[77],"loss":[78],"accuracy.":[80]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}