{"id":"https://openalex.org/W1969309300","doi":"https://doi.org/10.1137/s1064827597325323","title":"A Domain Decomposition Method for the Helmholtz Equation in a Multilayer Domain","display_name":"A Domain Decomposition Method for the Helmholtz Equation in a Multilayer Domain","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W1969309300","doi":"https://doi.org/10.1137/s1064827597325323","mag":"1969309300"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827597325323","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827597325323","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5072928406","display_name":"Elisabeth Larsson","orcid":"https://orcid.org/0000-0003-1154-9587"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Elisabeth Larsson","raw_affiliation_strings":["Department of Scientific Computing, Information Technology, Uppsala University, Box 120, SE-751 04 Uppsala, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Scientific Computing, Information Technology, Uppsala University, Box 120, SE-751 04 Uppsala, Sweden","institution_ids":["https://openalex.org/I123387679"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5072928406"],"corresponding_institution_ids":["https://openalex.org/I123387679"],"apc_list":null,"apc_paid":null,"fwci":0.939,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.73205632,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"20","issue":"5","first_page":"1713","last_page":"1731"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.9994000196456909,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.9302561283111572},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7814317941665649},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.7734465599060059},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.6821342706680298},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.6726106405258179},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.6408417820930481},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5356782078742981},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5159257650375366},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4939635396003723},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4742357134819031},{"id":"https://openalex.org/keywords/incomplete-lu-factorization","display_name":"Incomplete LU factorization","score":0.45779305696487427},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.4496104419231415},{"id":"https://openalex.org/keywords/gaussian-elimination","display_name":"Gaussian elimination","score":0.44280874729156494},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4272440969944},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39562276005744934},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.3892873525619507},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3026915192604065},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.26489749550819397},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.24962010979652405},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.229765385389328}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9302561283111572},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7814317941665649},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.7734465599060059},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.6821342706680298},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.6726106405258179},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.6408417820930481},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5356782078742981},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5159257650375366},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4939635396003723},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4742357134819031},{"id":"https://openalex.org/C134978465","wikidata":"https://www.wikidata.org/wiki/Q1654069","display_name":"Incomplete LU factorization","level":4,"score":0.45779305696487427},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.4496104419231415},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.44280874729156494},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4272440969944},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39562276005744934},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3892873525619507},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3026915192604065},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.26489749550819397},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.24962010979652405},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.229765385389328},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1064827597325323","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827597325323","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.142.545","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.142.545","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.it.uu.se/research/reports/2000-006/2000-006-nc.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":22,"referenced_works":["https://openalex.org/W574635522","https://openalex.org/W584890378","https://openalex.org/W1500697756","https://openalex.org/W1546004968","https://openalex.org/W1570895503","https://openalex.org/W1982772190","https://openalex.org/W1986293636","https://openalex.org/W1990619251","https://openalex.org/W2004668340","https://openalex.org/W2026736496","https://openalex.org/W2036155965","https://openalex.org/W2037048184","https://openalex.org/W2037092148","https://openalex.org/W2056978740","https://openalex.org/W2070661544","https://openalex.org/W2071897054","https://openalex.org/W2085067463","https://openalex.org/W2090843874","https://openalex.org/W2100384730","https://openalex.org/W2140153041","https://openalex.org/W2496234105","https://openalex.org/W3111897257"],"related_works":["https://openalex.org/W2064419612","https://openalex.org/W4299944105","https://openalex.org/W4312478517","https://openalex.org/W2381203753","https://openalex.org/W2040165403","https://openalex.org/W2074304065","https://openalex.org/W2943897646","https://openalex.org/W3010195088","https://openalex.org/W2804034492","https://openalex.org/W2169593911"],"abstract_inverted_index":{"The":[0,30,56,98,112],"two-dimensional":[1],"Helmholtz":[2],"equation":[3],"for":[4,22,95,101,115],"problems":[5],"where":[6],"the":[7,26,41,44,82,87,96,102,108,121,124,166,180,185],"physical":[8],"domain":[9,75],"consists":[10],"of":[11,25,43,64,110,123],"layers":[12],"with":[13,34,70,91,156],"different":[14],"material":[15],"properties":[16],"is":[17,28,32,54,68,78,84,118,126,138,149,161],"studied.":[18],"An":[19],"efficient":[20],"preconditioner":[21,103,125],"iterative":[23,167],"solution":[24,164],"problem":[27,31,186],"constructed.":[29],"discretized":[33],"fourth-order":[35,49],"accurate":[36],"finite":[37,50],"difference":[38],"operators.":[39],"For":[40],"construction":[42,122],"radiation":[45],"boundary":[46],"conditions":[47],"a":[48,127,135,141,152,162],"element":[51],"method":[52,77,168],"also":[53],"used.":[55],"large,":[57],"sparse,":[58],"complex,":[59],"indefinite,":[60],"and":[61,176],"ill-conditioned":[62],"system":[63],"equations":[65],"that":[66,147],"arises":[67],"solved":[69],"preconditioned":[71],"restarted":[72],"GMRES.":[73],"A":[74],"decomposition":[76],"used,":[79],"in":[80,107,134,151,172],"which":[81,160],"preconditioning":[83],"based":[85],"on":[86],"Schur":[88],"complement":[89],"algorithm":[90],"\"fast":[92],"Poisson-type\"":[93],"preconditioners":[94],"subdomains.":[97],"memory":[99,174],"requirements":[100,175],"are":[104],"nearly":[105],"linear":[106],"number":[109],"unknowns.":[111],"arithmetic":[113,177],"complexity":[114],"each":[116],"iteration":[117],"low,":[119],"whereas":[120],"bit":[128],"more":[129],"expensive.":[130],"Electromagnetic":[131],"wave":[132],"propagation":[133],"three-layered":[136],"waveguide":[137],"used":[139],"as":[140],"model":[142],"problem.":[143],"Numerical":[144],"experiments":[145],"show":[146],"convergence":[148],"achieved":[150],"few":[153],"iterations.":[154],"Compared":[155],"banded":[157],"Gaussian":[158],"elimination,":[159],"standard":[163],"method,":[165],"shows":[169],"significant":[170],"gain":[171,182],"both":[173],"complexity.":[178],"Furthermore,":[179],"relative":[181],"grows":[183],"when":[184],"size":[187],"increases.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}