{"id":"https://openalex.org/W1841946101","doi":"https://doi.org/10.1137/140958232","title":"An Efficient Numerical Method for Acoustic Wave Scattering in Random Media","display_name":"An Efficient Numerical Method for Acoustic Wave Scattering in Random Media","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1841946101","doi":"https://doi.org/10.1137/140958232","mag":"1841946101"},"language":"en","primary_location":{"id":"doi:10.1137/140958232","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140958232","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","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/A5011365911","display_name":"Xiaobing Feng","orcid":"https://orcid.org/0000-0002-9191-9092"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xiaobing Feng","raw_affiliation_strings":["#N##TAB##TAB##TAB##TAB# University of Tennessee#N##TAB##TAB##TAB#"],"affiliations":[{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# University of Tennessee#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110721594","display_name":"Junshan Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I82497590","display_name":"Auburn University","ror":"https://ror.org/02v80fc35","country_code":"US","type":"education","lineage":["https://openalex.org/I82497590"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Junshan Lin","raw_affiliation_strings":["Auburn.University"],"affiliations":[{"raw_affiliation_string":"Auburn.University","institution_ids":["https://openalex.org/I82497590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080079873","display_name":"Cody Lorton","orcid":"https://orcid.org/0000-0002-6617-8982"},"institutions":[{"id":"https://openalex.org/I83683471","display_name":"University of West Florida","ror":"https://ror.org/002w4zy91","country_code":"US","type":"education","lineage":["https://openalex.org/I83683471"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cody Lorton","raw_affiliation_strings":["University of West florida"],"affiliations":[{"raw_affiliation_string":"University of West florida","institution_ids":["https://openalex.org/I83683471"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5011365911"],"corresponding_institution_ids":["https://openalex.org/I75027704"],"apc_list":null,"apc_paid":null,"fwci":1.5254,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.87270658,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"3","issue":"1","first_page":"790","last_page":"822"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10822","display_name":"Acoustic Wave Phenomena Research","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","score":0.9980999827384949,"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/helmholtz-equation","display_name":"Helmholtz equation","score":0.7308181524276733},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6422922611236572},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.6196427941322327},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5020992755889893},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4975593388080597},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4604770243167877},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.4358431398868561},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3924205005168915},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3672148883342743},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2981638014316559},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2526668608188629},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16080814599990845},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.1600419282913208}],"concepts":[{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.7308181524276733},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6422922611236572},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.6196427941322327},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5020992755889893},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4975593388080597},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4604770243167877},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.4358431398868561},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3924205005168915},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3672148883342743},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2981638014316559},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2526668608188629},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16080814599990845},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.1600419282913208},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140958232","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140958232","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.761.541","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.761.541","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1402.5407.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W4509327","https://openalex.org/W595079961","https://openalex.org/W623361835","https://openalex.org/W1573293896","https://openalex.org/W1583622322","https://openalex.org/W1866311589","https://openalex.org/W2003803951","https://openalex.org/W2008111007","https://openalex.org/W2018159038","https://openalex.org/W2029342920","https://openalex.org/W2031027147","https://openalex.org/W2032941427","https://openalex.org/W2048752379","https://openalex.org/W2055460625","https://openalex.org/W2060528584","https://openalex.org/W2088117085","https://openalex.org/W2151084831"],"related_works":["https://openalex.org/W2186864281","https://openalex.org/W2092968426","https://openalex.org/W4255427455","https://openalex.org/W2540416959","https://openalex.org/W4365420316","https://openalex.org/W2735258363","https://openalex.org/W2369806658","https://openalex.org/W3193896743","https://openalex.org/W3176862315","https://openalex.org/W3120022531"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,107,114,126,136],"concerned":[3],"with":[4],"developing":[5],"efficient":[6,104],"numerical":[7,168],"methods":[8],"for":[9,78,99,117],"acoustic":[10],"wave":[11],"scattering":[12],"in":[13],"random":[14,21,30],"media":[15],"which":[16,83,106],"can":[17],"be":[18],"expressed":[19],"as":[20,48],"perturbations":[22],"of":[23,45,52,132,140,165],"homogeneous":[24],"media.":[25],"We":[26,39],"first":[27],"analyze":[28,57],"the":[29,46,53,80,100,110,120,129,133,147,157,163,166],"Helmholtz":[31,91,144],"problem":[32,145],"by":[33,86],"deriving":[34],"some":[35],"wavenumber-explicit":[36],"solution":[37,47],"estimates.":[38],"then":[40],"establish":[41],"a":[42,49,69],"multimodes":[43,65,122],"representation":[44],"power":[50],"series":[51],"perturbation":[54],"parameter":[55],"and":[56,102,160,170],"its":[58],"finite":[59],"modes":[60],"approximations.":[61],"Based":[62],"on":[63,109],"this":[64],"representation,":[66],"we":[67],"develop":[68],"Monte":[70],"Carlo":[71],"interior":[72],"penalty":[73],"discontinuous":[74],"Galerkin":[75],"(MCIP-DG)":[76],"method":[77,169],"approximating":[79],"mode":[81],"functions,":[82],"are":[84,97,153],"governed":[85],"recursively":[87],"defined":[88],"nearly":[89],"deterministic":[90,143],"equations.":[92],"Optimal":[93],"order":[94],"error":[95],"estimates":[96],"derived":[98],"method,":[101],"an":[103],"algorithm,":[105],"based":[108],"LU":[111,148],"direct":[112,149],"solver,":[113],"also":[115],"designed":[116],"efficiently":[118],"implementing":[119],"proposed":[121,167],"MCIP-DG":[123],"method.":[124],"It":[125],"proved":[127],"that":[128,139],"computational":[130],"complexity":[131],"whole":[134],"algorithm":[135],"comparable":[137],"to":[138,155,161],"solving":[141],"one":[142],"using":[146],"solver.":[150],"Numerical":[151],"experiments":[152],"provided":[154],"validate":[156],"theoretical":[158],"results":[159],"gauge":[162],"performance":[164],"algorithm.":[171]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
