{"id":"https://openalex.org/W3094697463","doi":"https://doi.org/10.1137/19m1294101","title":"A Novel Least Squares Method for Helmholtz Equations with Large Wave Numbers","display_name":"A Novel Least Squares Method for Helmholtz Equations with Large Wave Numbers","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3094697463","doi":"https://doi.org/10.1137/19m1294101","mag":"3094697463"},"language":"en","primary_location":{"id":"doi:10.1137/19m1294101","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1294101","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/A5034570816","display_name":"Qiya Hu","orcid":"https://orcid.org/0000-0003-3179-7115"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiya Hu","raw_affiliation_strings":[". LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sci-ences, Beijing 100190, China;",". School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"],"raw_orcid":"https://orcid.org/0000-0003-3179-7115","affiliations":[{"raw_affiliation_string":". LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sci-ences, Beijing 100190, China;","institution_ids":["https://openalex.org/I4210120485"]},{"raw_affiliation_string":". School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031942760","display_name":"Rongrong Song","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Rongrong Song","raw_affiliation_strings":[". LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sci-ences, Beijing 100190, China;",". School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":". LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sci-ences, Beijing 100190, China;","institution_ids":["https://openalex.org/I4210120485"]},{"raw_affiliation_string":". School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5031942760"],"corresponding_institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":0.7189,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.66953238,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"58","issue":"5","first_page":"3091","last_page":"3123"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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/T10514","display_name":"Numerical methods in engineering","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998000264167786,"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/mathematics","display_name":"Mathematics","score":0.8282569646835327},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.817703127861023},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5576604008674622},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5573580861091614},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.5375684499740601},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.5022861957550049},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.48741772770881653},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4432589113712311},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.4373834431171417},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38707655668258667},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.3320521116256714},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.2935975193977356},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.17171061038970947},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16076308488845825}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8282569646835327},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.817703127861023},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5576604008674622},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5573580861091614},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.5375684499740601},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.5022861957550049},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.48741772770881653},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4432589113712311},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.4373834431171417},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38707655668258667},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3320521116256714},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2935975193977356},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.17171061038970947},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16076308488845825},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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":1,"locations":[{"id":"doi:10.1137/19m1294101","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1294101","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2426982921","display_name":null,"funder_award_id":"G11571352","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1763512893","https://openalex.org/W1965599757","https://openalex.org/W1967469744","https://openalex.org/W1975804825","https://openalex.org/W1998739679","https://openalex.org/W2000867371","https://openalex.org/W2003803951","https://openalex.org/W2008051303","https://openalex.org/W2022599090","https://openalex.org/W2024381649","https://openalex.org/W2029660825","https://openalex.org/W2033922045","https://openalex.org/W2039459905","https://openalex.org/W2047719014","https://openalex.org/W2051710235","https://openalex.org/W2063463626","https://openalex.org/W2064309072","https://openalex.org/W2073370219","https://openalex.org/W2077458918","https://openalex.org/W2080212747","https://openalex.org/W2080631773","https://openalex.org/W2087828859","https://openalex.org/W2106567676","https://openalex.org/W2127600768","https://openalex.org/W2165091991","https://openalex.org/W2220250944","https://openalex.org/W2414531072","https://openalex.org/W2504776022","https://openalex.org/W2592456637","https://openalex.org/W2623900191","https://openalex.org/W2883136854","https://openalex.org/W2963187050"],"related_works":["https://openalex.org/W2159515580","https://openalex.org/W2081820376","https://openalex.org/W2091325992","https://openalex.org/W2059625160","https://openalex.org/W2006453807","https://openalex.org/W3194092090","https://openalex.org/W4365420316","https://openalex.org/W3193896743","https://openalex.org/W3176862315","https://openalex.org/W3120022531"],"abstract_inverted_index":{"In":[0,29],"this":[1,30],"paper":[2],"we":[3,132,159],"are":[4,76,81,179],"concerned":[5],"with":[6,12,94,193],"numerical":[7],"methods":[8,150,178],"for":[9,22,164,188],"Helmholtz":[10,27,64,74,191],"equations":[11,65,75,192],"large":[13,194],"wave":[14,149,156,195],"numbers.":[15,196],"We":[16],"design":[17],"a":[18,47,161],"least":[19],"squares":[20],"method":[21],"discretization":[23],"of":[24,41,56,59,62,109,154,168],"the":[25,38,54,57,60,68,72,88,95,102,110,124,135,141,147,152,165,169,176,189],"considered":[26],"equations.":[28],"method,":[31],"an":[32],"auxiliary":[33,89,103,111,170],"unknown":[34],"is":[35,51,98,113],"introduced":[36],"on":[37,78],"common":[39,69],"interface":[40],"any":[42],"two":[43],"neighboring":[44],"elements":[45,79],"and":[46,80,117,182],"quadratic":[48],"objective":[49,96],"functional":[50,97],"defined":[52,77],"by":[53,87,123],"jumps":[55],"traces":[58],"solutions":[61,138],"local":[63,73],"across":[66],"all":[67],"interfaces,":[70],"where":[71],"imposed":[82],"Robin-type":[83],"boundary":[84],"conditions":[85],"given":[86],"unknowns.":[90,104,171],"A":[91],"minimization":[92],"problem":[93],"proposed":[99,177],"to":[100],"determine":[101],"The":[105],"resulting":[106],"discrete":[107,166],"system":[108,167],"unknowns":[112],"Hermitian":[114],"positive":[115],"definite":[116],"so":[118],"it":[119],"can":[120],"be":[121],"solved":[122],"preconditioned":[125],"conjugate":[126],"gradient":[127],"method.":[128],"Under":[129],"some":[130],"assumptions":[131],"show":[133,174],"that":[134,175],"generated":[136],"approximate":[137],"possess":[139],"almost":[140],"same":[142],"$L^2$":[143],"convergence":[144],"order":[145],"as":[146],"plane":[148],"(for":[151],"case":[153],"constant":[155],"number).":[157],"Moreover,":[158],"construct":[160],"substructuring":[162],"preconditioner":[163],"Numerical":[172],"experiments":[173],"very":[180],"effective":[181],"have":[183],"little":[184],"\u201cwave":[185],"number":[186],"pollution\"":[187],"tested":[190]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
