{"id":"https://openalex.org/W4415930830","doi":"https://doi.org/10.3390/axioms14110820","title":"An Online Generalized Multiscale Method for Embedded Discrete Fracture Model","display_name":"An Online Generalized Multiscale Method for Embedded Discrete Fracture Model","publication_year":2025,"publication_date":"2025-11-05","ids":{"openalex":"https://openalex.org/W4415930830","doi":"https://doi.org/10.3390/axioms14110820"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14110820","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14110820","pdf_url":"https://www.mdpi.com/2075-1680/14/11/820/pdf?version=1762356447","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/11/820/pdf?version=1762356447","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059380196","display_name":"Zhengkang He","orcid":"https://orcid.org/0000-0003-4524-6867"},"institutions":[{"id":"https://openalex.org/I18452120","display_name":"Yantai University","ror":"https://ror.org/01rp41m56","country_code":"CN","type":"education","lineage":["https://openalex.org/I18452120"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengkang He","raw_affiliation_strings":["School of Mathematics and Information Sciences, Yantai University, Yantai 264005, China"],"raw_orcid":"https://orcid.org/0000-0003-4524-6867","affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Sciences, Yantai University, Yantai 264005, China","institution_ids":["https://openalex.org/I18452120"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040707822","display_name":"Bangmin Wu","orcid":"https://orcid.org/0009-0001-1798-5868"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bangmin Wu","raw_affiliation_strings":["College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China","institution_ids":["https://openalex.org/I96908189"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040707822"],"corresponding_institution_ids":["https://openalex.org/I96908189"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3223548,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"11","first_page":"820","last_page":"820"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9649999737739563,"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":0.9649999737739563,"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":0.017799999564886093,"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":0.0038999998942017555,"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/basis-function","display_name":"Basis function","score":0.5461999773979187},{"id":"https://openalex.org/keywords/snapshot","display_name":"Snapshot (computer storage)","score":0.5178999900817871},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5076000094413757},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4968999922275543},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.4564000070095062},{"id":"https://openalex.org/keywords/fracture","display_name":"Fracture (geology)","score":0.4009999930858612}],"concepts":[{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.5461999773979187},{"id":"https://openalex.org/C55282118","wikidata":"https://www.wikidata.org/wiki/Q252683","display_name":"Snapshot (computer storage)","level":2,"score":0.5178999900817871},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5076000094413757},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5005000233650208},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4968999922275543},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.4564000070095062},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4311999976634979},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4050000011920929},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40139999985694885},{"id":"https://openalex.org/C43369102","wikidata":"https://www.wikidata.org/wiki/Q2307625","display_name":"Fracture (geology)","level":2,"score":0.4009999930858612},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3855000138282776},{"id":"https://openalex.org/C141123601","wikidata":"https://www.wikidata.org/wiki/Q6935072","display_name":"Multiscale modeling","level":2,"score":0.3765999972820282},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.3553999960422516},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3407000005245209},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.27379998564720154},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2660999894142151},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26510000228881836},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.2574000060558319}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14110820","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14110820","pdf_url":"https://www.mdpi.com/2075-1680/14/11/820/pdf?version=1762356447","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c67a42d630b74d429641701fecdc6ffc","is_oa":true,"landing_page_url":"https://doaj.org/article/c67a42d630b74d429641701fecdc6ffc","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 11, p 820 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14110820","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14110820","pdf_url":"https://www.mdpi.com/2075-1680/14/11/820/pdf?version=1762356447","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G498616023","display_name":null,"funder_award_id":"12301528","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5779840617","display_name":null,"funder_award_id":"ZR2023QA069","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415930830.pdf","grobid_xml":"https://content.openalex.org/works/W4415930830.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W1977222265","https://openalex.org/W1994509203","https://openalex.org/W2008981917","https://openalex.org/W2018527710","https://openalex.org/W2083501255","https://openalex.org/W2083501502","https://openalex.org/W2094293004","https://openalex.org/W2095404433","https://openalex.org/W2114736792","https://openalex.org/W2126028850","https://openalex.org/W2131343962","https://openalex.org/W2158189140","https://openalex.org/W2344009215","https://openalex.org/W2346057040","https://openalex.org/W2411294711","https://openalex.org/W2415553453","https://openalex.org/W2522159446","https://openalex.org/W2560651211","https://openalex.org/W2605963356","https://openalex.org/W2628449416","https://openalex.org/W2731539268","https://openalex.org/W2962883966","https://openalex.org/W2963157298","https://openalex.org/W2963951078","https://openalex.org/W2978302777","https://openalex.org/W2990337424","https://openalex.org/W3001573531","https://openalex.org/W3128316752","https://openalex.org/W3159883664","https://openalex.org/W3169373166","https://openalex.org/W3185529939","https://openalex.org/W3193956177","https://openalex.org/W4205684207","https://openalex.org/W4220814313","https://openalex.org/W4285499386","https://openalex.org/W4379390277","https://openalex.org/W4379646220","https://openalex.org/W4385856740","https://openalex.org/W4396844158","https://openalex.org/W4399035293","https://openalex.org/W4408586723"],"related_works":[],"abstract_inverted_index":{"This":[0],"study":[1],"concerns":[2],"an":[3,18,31],"online":[4,90,139],"generalized":[5],"multiscale":[6,96,101,110],"method":[7],"for":[8,44],"flow":[9],"in":[10,38,81],"fractured":[11],"porous":[12],"media":[13],"that":[14,36,93],"is":[15],"based":[16],"on":[17,73],"embedded":[19],"discrete":[20,33],"fracture":[21,130],"model.":[22],"We":[23],"first":[24],"convert":[25],"a":[26,53,59,123],"two-point":[27],"flux-approximation":[28],"scheme":[29],"into":[30],"equivalent":[32],"weak":[34],"formulation":[35],"results":[37],"the":[39,45,50,76,100,109,119,136],"same":[40],"linear":[41],"algebraic":[42],"system":[43],"unknown":[46],"pressure.":[47],"Then,":[48],"by":[49],"use":[51],"of":[52,75,78,108,125,138],"suitable":[54],"local":[55,70],"snapshot":[56],"space":[57,102],"and":[58,103,122],"well-designed":[60],"spectral":[61],"decomposition,":[62],"we":[63,87],"compute":[64,88],"offline":[65],"basis":[66,91],"functions":[67,92],"to":[68,98,117,134],"capture":[69],"heterogeneity":[71],"information":[72,97],"account":[74],"presence":[77],"various":[79],"fractures":[80],"each":[82],"coarse":[83],"cell.":[84],"After":[85],"that,":[86],"residual-based":[89],"contain":[94],"global":[95],"enrich":[99],"thus":[104],"achieve":[105],"higher":[106],"accuracy":[107],"solution.":[111],"Meanwhile,":[112],"theoretical":[113],"analyses":[114],"are":[115,132],"conducted":[116],"show":[118],"convergence":[120],"behavior,":[121],"number":[124],"numerical":[126],"tests":[127],"with":[128],"different":[129],"configurations":[131],"performed":[133],"investigate":[135],"performance":[137],"enrichment.":[140]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-11-05T00:00:00"}
