{"id":"https://openalex.org/W1978631586","doi":"https://doi.org/10.1137/050625369","title":"A Matrix Analysis of Operator-Based Upscaling for the Wave Equation","display_name":"A Matrix Analysis of Operator-Based Upscaling for the Wave Equation","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1978631586","doi":"https://doi.org/10.1137/050625369","mag":"1978631586"},"language":"en","primary_location":{"id":"doi:10.1137/050625369","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050625369","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/A5030950920","display_name":"Oksana Korostyshevskaya","orcid":null},"institutions":[{"id":"https://openalex.org/I79272384","display_name":"University of Maryland, Baltimore County","ror":"https://ror.org/02qskvh78","country_code":"US","type":"education","lineage":["https://openalex.org/I79272384"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Oksana Korostyshevskaya","raw_affiliation_strings":["\u00a0 University of Maryland, Baltimore County"],"affiliations":[{"raw_affiliation_string":"\u00a0 University of Maryland, Baltimore County","institution_ids":["https://openalex.org/I79272384"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081942287","display_name":"Susan E. Minkoff","orcid":"https://orcid.org/0000-0003-0765-4755"},"institutions":[{"id":"https://openalex.org/I79272384","display_name":"University of Maryland, Baltimore County","ror":"https://ror.org/02qskvh78","country_code":"US","type":"education","lineage":["https://openalex.org/I79272384"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Susan E. Minkoff","raw_affiliation_strings":["\u00a0 University of Maryland, Baltimore County"],"affiliations":[{"raw_affiliation_string":"\u00a0 University of Maryland, Baltimore County","institution_ids":["https://openalex.org/I79272384"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030950920"],"corresponding_institution_ids":["https://openalex.org/I79272384"],"apc_list":null,"apc_paid":null,"fwci":0.6741,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.68963078,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"44","issue":"2","first_page":"586","last_page":"612"},"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":0.9995999932289124,"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":0.9995999932289124,"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/wave-equation","display_name":"Wave equation","score":0.6407642364501953},{"id":"https://openalex.org/keywords/microscale-chemistry","display_name":"Microscale chemistry","score":0.5795409679412842},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4826434254646301},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.48052653670310974},{"id":"https://openalex.org/keywords/acoustic-wave-equation","display_name":"Acoustic wave equation","score":0.47123607993125916},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.462968111038208},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4213279187679291},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3567908704280853},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3508804440498352},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3457571268081665},{"id":"https://openalex.org/keywords/wave-propagation","display_name":"Wave propagation","score":0.26847708225250244},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20103749632835388},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12407571077346802}],"concepts":[{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.6407642364501953},{"id":"https://openalex.org/C179428855","wikidata":"https://www.wikidata.org/wiki/Q1069216","display_name":"Microscale chemistry","level":2,"score":0.5795409679412842},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4826434254646301},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.48052653670310974},{"id":"https://openalex.org/C145589544","wikidata":"https://www.wikidata.org/wiki/Q4674723","display_name":"Acoustic wave equation","level":3,"score":0.47123607993125916},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.462968111038208},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4213279187679291},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3567908704280853},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3508804440498352},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3457571268081665},{"id":"https://openalex.org/C44886760","wikidata":"https://www.wikidata.org/wiki/Q1758425","display_name":"Wave propagation","level":2,"score":0.26847708225250244},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20103749632835388},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12407571077346802},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050625369","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050625369","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.552.9214","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.552.9214","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.umbc.edu/~sminkoff/save_papers/62536.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W190146808","https://openalex.org/W586529434","https://openalex.org/W1637323070","https://openalex.org/W1965130545","https://openalex.org/W1966480196","https://openalex.org/W1966922361","https://openalex.org/W1974210778","https://openalex.org/W1974462837","https://openalex.org/W2005788407","https://openalex.org/W2021669684","https://openalex.org/W2027239222","https://openalex.org/W2029918260","https://openalex.org/W2077597870","https://openalex.org/W2084543124","https://openalex.org/W2097842356","https://openalex.org/W2114051217","https://openalex.org/W2159094357","https://openalex.org/W4251896235"],"related_works":["https://openalex.org/W2897831310","https://openalex.org/W2367255960","https://openalex.org/W4291754597","https://openalex.org/W4285269578","https://openalex.org/W4387829386","https://openalex.org/W4283748940","https://openalex.org/W4378229727","https://openalex.org/W4206373024","https://openalex.org/W2120533002","https://openalex.org/W2331858031"],"abstract_inverted_index":{"Scientists":[0],"and":[1,88,103],"engineers":[2],"who":[3],"wish":[4],"to":[5,24,52,109,126,193,207,219,228],"understand":[6],"the":[7,21,25,69,74,98,110,157,166,169,176,180,188,195,198,220,236],"earth's":[8],"subsurface":[9],"are":[10],"faced":[11],"with":[12,202],"a":[13,79,136,184,240,246],"daunting":[14],"challenge.":[15],"Features":[16],"of":[17,28,41,44,139,149,168,179,197],"interest":[18],"range":[19],"from":[20],"microscale":[22],"(centimeters)":[23],"macroscale":[26],"(hundreds":[27],"kilometers).":[29],"It":[30],"is":[31,48,66,146,191],"unlikely":[32],"that":[33],"computational":[34,55],"power":[35],"limitations":[36],"will":[37],"ever":[38],"allow":[39],"modeling":[40],"this":[42,54,161],"level":[43],"detail.":[45],"Numerical":[46],"upscaling":[47,93,107,171],"one":[49,119],"technique":[50,94],"intended":[51],"reduce":[53],"burden.":[56],"The":[57,92,215],"operator-based":[58],"algorithm":[59,172],"(developed":[60],"originally":[61],"for":[62,68,86,122],"elliptic":[63],"flow":[64],"problems)":[65],"modified":[67,241],"acoustic":[70,111,222],"wave":[71,75,112,223,242],"equation.":[72],"With":[73],"equation":[76,113,201,217,224,243],"written":[77],"as":[78],"first-order":[80],"system":[81],"in":[82,115],"space,":[83],"we":[84,155],"solve":[85],"pressure":[87,216],"its":[89,150],"gradient":[90],"(acceleration).":[91],"relies":[95],"on":[96],"decomposing":[97],"solution":[99,196,238],"space":[100],"into":[101],"coarse":[102,127,144,212,229,233],"fine":[104],"components.":[105],"Operator-based":[106],"applied":[108],"proceeds":[114],"two":[116,154],"steps.":[117],"Step":[118],"involves":[120],"solving":[121],"fine-grid":[123],"features":[124],"internal":[125,162,227],"blocks.":[128,230],"This":[129],"stage":[130],"can":[131],"be":[132,194],"solved":[133,147],"quickly":[134],"via":[135,160],"well-chosen":[137],"set":[138],"coarse-grid":[140],"boundary":[141],"conditions.":[142],"Each":[143],"problem":[145,159],"independently":[148],"neighbors.":[151],"In":[152],"step":[153],"augment":[156],"coarse-scale":[158,189],"subgrid":[163],"information.":[164],"Unfortunately,":[165],"complexity":[167],"numerical":[170],"has":[173],"always":[174],"obscured":[175],"physical":[177],"meaning":[178],"resulting":[181],"solution.":[182],"Via":[183],"detailed":[185],"matrix":[186],"analysis,":[187],"acceleration":[190],"shown":[192],"original":[199],"constitutive":[200],"input":[203],"density":[204,210],"field":[205],"corresponding":[206],"an":[208],"averaged":[209],"along":[211,232],"block":[213],"edges.":[214],"corresponds":[218],"standard":[221],"at":[225],"nodes":[226],"However,":[231],"cell":[234],"boundaries,":[235],"upscaled":[237],"solves":[239],"which":[244],"includes":[245],"mixed":[247],"second-derivative":[248],"term.":[249]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}