{"id":"https://openalex.org/W2510971162","doi":"https://doi.org/10.1515/cmam-2022-0041","title":"Multiscale Sub-grid Correction Method for Time-Harmonic High-Frequency Elastodynamics with Wave Number Explicit Bounds","display_name":"Multiscale Sub-grid Correction Method for Time-Harmonic High-Frequency Elastodynamics with Wave Number Explicit Bounds","publication_year":2022,"publication_date":"2022-03-12","ids":{"openalex":"https://openalex.org/W2510971162","doi":"https://doi.org/10.1515/cmam-2022-0041","mag":"2510971162"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2022-0041","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2022-0041","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied 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/A5086318716","display_name":"Donald L. Brown","orcid":"https://orcid.org/0000-0002-3421-1063"},"institutions":[{"id":"https://openalex.org/I4210117756","display_name":"Shaker Heights Public Library","ror":"https://ror.org/02cjv3666","country_code":"US","type":"archive","lineage":["https://openalex.org/I4210117756"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Donald L. Brown","raw_affiliation_strings":["Applied Research and Development Division , The Equity Engineering Group , 20600 Chagrin Blvd #1200 , Shaker Heights , OH 44122 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Research and Development Division , The Equity Engineering Group , 20600 Chagrin Blvd #1200 , Shaker Heights , OH 44122 , USA","institution_ids":["https://openalex.org/I4210117756"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035829145","display_name":"Dietmar Gallistl","orcid":"https://orcid.org/0000-0001-8954-4175"},"institutions":[{"id":"https://openalex.org/I76198965","display_name":"Friedrich Schiller University Jena","ror":"https://ror.org/05qpz1x62","country_code":"DE","type":"education","lineage":["https://openalex.org/I76198965"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Dietmar Gallistl","raw_affiliation_strings":["Institut f\u00fcr Mathematik , Friedrich-Schiller-Universit\u00e4t Jena , Ernst-Abbe-Platz 2, 07743 Jena , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik , Friedrich-Schiller-Universit\u00e4t Jena , Ernst-Abbe-Platz 2, 07743 Jena , Germany","institution_ids":["https://openalex.org/I76198965"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035829145"],"corresponding_institution_ids":["https://openalex.org/I76198965"],"apc_list":null,"apc_paid":null,"fwci":0.3044,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.55304856,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"23","issue":"1","first_page":"65","last_page":"82"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9972000122070312,"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/context","display_name":"Context (archaeology)","score":0.621507465839386},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.553974986076355},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.507014274597168},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.47448256611824036},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4553540050983429},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4324128031730652},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4299895763397217},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3750861883163452},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1173878014087677}],"concepts":[{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.621507465839386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.553974986076355},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.507014274597168},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.47448256611824036},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4553540050983429},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4324128031730652},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4299895763397217},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3750861883163452},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1173878014087677},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2022-0041","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2022-0041","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1696918855","display_name":null,"funder_award_id":"891734","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G325672550","display_name":null,"funder_award_id":"SFB 1173","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W628726389","https://openalex.org/W1480707903","https://openalex.org/W1536676435","https://openalex.org/W1630083689","https://openalex.org/W1720292799","https://openalex.org/W1966793029","https://openalex.org/W1980404981","https://openalex.org/W1983122553","https://openalex.org/W1992325016","https://openalex.org/W2003803951","https://openalex.org/W2008747183","https://openalex.org/W2019072617","https://openalex.org/W2019517543","https://openalex.org/W2025124289","https://openalex.org/W2026718533","https://openalex.org/W2029342920","https://openalex.org/W2029966922","https://openalex.org/W2031621501","https://openalex.org/W2032941427","https://openalex.org/W2037475392","https://openalex.org/W2038870672","https://openalex.org/W2066812079","https://openalex.org/W2080212747","https://openalex.org/W2084991940","https://openalex.org/W2087828859","https://openalex.org/W2094438648","https://openalex.org/W2111021555","https://openalex.org/W2115850109","https://openalex.org/W2117866703","https://openalex.org/W2123996406","https://openalex.org/W2151177334","https://openalex.org/W2152583013","https://openalex.org/W2153532220","https://openalex.org/W2157935711","https://openalex.org/W2158928686","https://openalex.org/W2256669603","https://openalex.org/W2945655205","https://openalex.org/W2963691989","https://openalex.org/W2963942779","https://openalex.org/W2963961138","https://openalex.org/W3106381385"],"related_works":["https://openalex.org/W2980963558","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W4287664878","https://openalex.org/W3212023493","https://openalex.org/W1991411408","https://openalex.org/W4288278856","https://openalex.org/W2572370460"],"abstract_inverted_index":{"Abstract":[0],"The":[1,146],"simulation":[2],"of":[3,131,159],"the":[4,12,50,69,94,129,136,144,185,190],"elastodynamics":[5,95],"equations":[6],"at":[7],"high":[8],"frequency":[9],"suffers":[10],"from":[11,135],"well-known":[13],"pollution":[14,188],"effect.":[15],"We":[16,173],"present":[17],"a":[18,140],"Petrov\u2013Galerkin":[19],"multiscale":[20],"sub-grid":[21],"correction":[22],"method":[23,75,186],"that":[24],"remains":[25],"pollution-free":[26],"in":[27,98,106,148,178,189],"natural":[28,191],"resolution":[29,192],"and":[30,82,125,157,166,180,193],"oversampling":[31,46,194],"regimes.":[32],"This":[33],"is":[34],"accomplished":[35],"by":[36,45],"generating":[37],"corrections":[38],"to":[39,49,73,138,183,203],"coarse-grid":[40],"spaces":[41],"with":[42,102],"supports":[43],"determined":[44],"lengths":[47],"related":[48,83],"<m:math":[51,107],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[52,108],"<m:mrow>":[53,56],"<m:mi>log</m:mi>":[54],"<m:mo>\u2061</m:mo>":[55],"<m:mo":[57,60],"stretchy=\"false\">(</m:mo>":[58],"<m:mi>k</m:mi>":[59],"stretchy=\"false\">)</m:mo>":[61],"</m:mrow>":[62,63],"</m:math>":[64,114],"\\log(k)":[65],",":[66],"\ud835\udc58":[67,165],"being":[68],"wave":[70],"number.":[71],"Key":[72],"this":[74,87,149,170],"are":[76,151],"polynomial-in-\ud835\udc58":[77,91],"bounds":[78,92],"for":[79,93],"stability":[80,96],"constants":[81,97],"inf-sup":[84],"constants.":[85],"To":[86],"end,":[88],"we":[89],"establish":[90],"general":[99],"Lipschitz":[100],"domains":[101],"radiation":[103],"boundary":[104,154],"conditions":[105],"<m:msup>":[109],"<m:mi":[110],"mathvariant=\"double-struck\">R</m:mi>":[111],"<m:mn>3</m:mn>":[112],"</m:msup>":[113],"\\mathbb{R}^{3}":[115],".":[116],"Previous":[117],"methods":[118,147],"relied":[119],"on":[120,143,153,164],"variational":[121],"techniques,":[122],"Rellich":[123],"identities,":[124],"geometric":[126],"constraints.":[127],"In":[128],"context":[130],"elastodynamics,":[132],"these":[133],"suffer":[134],"need":[137],"hypothesize":[139],"Korn\u2019s":[141],"inequality":[142],"boundary.":[145],"work":[150],"based":[152],"integral":[155],"operators":[156],"estimation":[158],"Green\u2019s":[160],"function\u2019s":[161],"derivatives":[162],"dependence":[163],"do":[167],"not":[168],"require":[169],"extra":[171],"hypothesis.":[172],"also":[174],"implemented":[175],"numerical":[176],"examples":[177],"two":[179],"three":[181],"dimensions":[182],"show":[184],"eliminates":[187],"regimes,":[195],"as":[196,198],"well":[197,200],"performs":[199],"when":[201],"compared":[202],"standard":[204],"Lagrange":[205],"finite":[206],"elements.":[207]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
