{"id":"https://openalex.org/W3167951494","doi":"https://doi.org/10.1007/s00211-022-01318-8","title":"Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation","display_name":"Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation","publication_year":2022,"publication_date":"2022-09-20","ids":{"openalex":"https://openalex.org/W3167951494","doi":"https://doi.org/10.1007/s00211-022-01318-8","mag":"3167951494"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-022-01318-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-022-01318-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-022-01318-8.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-022-01318-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076270422","display_name":"Shihua Gong","orcid":"https://orcid.org/0000-0003-3650-2283"},"institutions":[{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shihua Gong","raw_affiliation_strings":["School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, Guangdong, China","School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, 518172, Guangdong, China"],"affiliations":[{"raw_affiliation_string":"School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, Guangdong, China","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, 518172, Guangdong, China","institution_ids":["https://openalex.org/I4210116924"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089456729","display_name":"Martin J. Gander","orcid":"https://orcid.org/0000-0001-8450-9223"},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Martin J. Gander","raw_affiliation_strings":["Section de Mathmatiques, Universit de Genve, Geneva, Switzerland","Section de Math\u00e9matiques, Universit\u00e9 de Gen\u00e8ve, Geneva, Switzerland"],"affiliations":[{"raw_affiliation_string":"Section de Mathmatiques, Universit de Genve, Geneva, Switzerland","institution_ids":["https://openalex.org/I114457229"]},{"raw_affiliation_string":"Section de Math\u00e9matiques, Universit\u00e9 de Gen\u00e8ve, Geneva, Switzerland","institution_ids":["https://openalex.org/I114457229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064637859","display_name":"Ivan G. Graham","orcid":"https://orcid.org/0000-0002-5730-676X"},"institutions":[{"id":"https://openalex.org/I51601045","display_name":"University of Bath","ror":"https://ror.org/002h8g185","country_code":"GB","type":"education","lineage":["https://openalex.org/I51601045"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ivan G. Graham","raw_affiliation_strings":["Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK","Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK","institution_ids":["https://openalex.org/I51601045"]},{"raw_affiliation_string":"Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK","institution_ids":["https://openalex.org/I51601045"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054156966","display_name":"David Lafontaine","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I4210098964","display_name":"Toulouse Mathematics Institute","ror":null,"country_code":"FR","type":null,"lineage":["https://openalex.org/I4210098964"]},{"id":"https://openalex.org/I84500057","display_name":"Institut de Math\u00e9matiques de Toulouse","ror":"https://ror.org/014vp6c30","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I196454796","https://openalex.org/I4210141950","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405259414","https://openalex.org/I84500057"]},{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"David Lafontaine","raw_affiliation_strings":["CNRS and Institut de Mathmatiques de Toulouse, UMR5219, CNRS, UPS, Universit de Toulouse, 31062 Toulouse Cedex 9, France","CNRS and Institut de Math\u00e9matiques de Toulouse, UMR5219, CNRS, UPS, Universit\u00e9 de Toulouse, 31062, Toulouse Cedex 9, France"],"affiliations":[{"raw_affiliation_string":"CNRS and Institut de Mathmatiques de Toulouse, UMR5219, CNRS, UPS, Universit de Toulouse, 31062 Toulouse Cedex 9, France","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I4210098964","https://openalex.org/I17866349","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS and Institut de Math\u00e9matiques de Toulouse, UMR5219, CNRS, UPS, Universit\u00e9 de Toulouse, 31062, Toulouse Cedex 9, France","institution_ids":["https://openalex.org/I84500057","https://openalex.org/I134560555","https://openalex.org/I17866349","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083248653","display_name":"Euan A. Spence","orcid":"https://orcid.org/0000-0003-1236-4592"},"institutions":[{"id":"https://openalex.org/I51601045","display_name":"University of Bath","ror":"https://ror.org/002h8g185","country_code":"GB","type":"education","lineage":["https://openalex.org/I51601045"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Euan A. Spence","raw_affiliation_strings":["Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK","Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK","institution_ids":["https://openalex.org/I51601045"]},{"raw_affiliation_string":"Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK","institution_ids":["https://openalex.org/I51601045"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5076270422"],"corresponding_institution_ids":["https://openalex.org/I4210116924"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.9938,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.83502839,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"152","issue":"2","first_page":"259","last_page":"306"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9997000098228455,"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":0.9993000030517578,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6736895442008972},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.6207296252250671},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.6141576170921326},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5636498332023621},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.478193998336792},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4717472493648529},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38314688205718994},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.34273675084114075},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1271848976612091}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6736895442008972},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.6207296252250671},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.6141576170921326},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5636498332023621},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.478193998336792},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4717472493648529},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38314688205718994},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.34273675084114075},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1271848976612091},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00211-022-01318-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-022-01318-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-022-01318-8.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:unige.ch:aou:unige:168016","is_oa":true,"landing_page_url":"https://archive-ouverte.unige.ch/unige:168016","pdf_url":null,"source":{"id":"https://openalex.org/S4306402259","display_name":"Archive ouverte UNIGE (University of Geneva)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114457229","host_organization_name":"University of Geneva","host_organization_lineage":["https://openalex.org/I114457229"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISSN: 0029-599X","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arXiv.org:2106.05218","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.05218","pdf_url":"https://arxiv.org/pdf/2106.05218","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-04284755v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04284755","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Numerische Mathematik, 2022, 152 (2), pp.259-306. &#x27E8;10.1007/s00211-022-01318-8&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1007/s00211-022-01318-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-022-01318-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-022-01318-8.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2547005790","display_name":null,"funder_award_id":"EP/S003975/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8386841362","display_name":null,"funder_award_id":"EP/R005591/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320322","display_name":"University of Bath","ror":"https://ror.org/002h8g185"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3167951494.pdf","grobid_xml":"https://content.openalex.org/works/W3167951494.grobid-xml"},"referenced_works_count":70,"referenced_works":["https://openalex.org/W1482145699","https://openalex.org/W1586623601","https://openalex.org/W1602383637","https://openalex.org/W1604809219","https://openalex.org/W1720292799","https://openalex.org/W1780245888","https://openalex.org/W1798342062","https://openalex.org/W1965332272","https://openalex.org/W1986203219","https://openalex.org/W1987152170","https://openalex.org/W2008215882","https://openalex.org/W2024381649","https://openalex.org/W2029966922","https://openalex.org/W2035238652","https://openalex.org/W2037475392","https://openalex.org/W2037868571","https://openalex.org/W2049289952","https://openalex.org/W2060108637","https://openalex.org/W2074899029","https://openalex.org/W2084463157","https://openalex.org/W2092129801","https://openalex.org/W2096847169","https://openalex.org/W2107692173","https://openalex.org/W2108572708","https://openalex.org/W2138189258","https://openalex.org/W2161243591","https://openalex.org/W2171622994","https://openalex.org/W2282359489","https://openalex.org/W2285894756","https://openalex.org/W2592456637","https://openalex.org/W2741486118","https://openalex.org/W2767278683","https://openalex.org/W2806526478","https://openalex.org/W2843106559","https://openalex.org/W2898732677","https://openalex.org/W2935560966","https://openalex.org/W2949839419","https://openalex.org/W2963034542","https://openalex.org/W2963292939","https://openalex.org/W2964925612","https://openalex.org/W2970058161","https://openalex.org/W2989564749","https://openalex.org/W3010737952","https://openalex.org/W3029481163","https://openalex.org/W3035858788","https://openalex.org/W3041771677","https://openalex.org/W3087680391","https://openalex.org/W3091209979","https://openalex.org/W3101113552","https://openalex.org/W3102436487","https://openalex.org/W3104324886","https://openalex.org/W3107286782","https://openalex.org/W3111536438","https://openalex.org/W3112570415","https://openalex.org/W3121081131","https://openalex.org/W3126650022","https://openalex.org/W3137034750","https://openalex.org/W3137548732","https://openalex.org/W3145302568","https://openalex.org/W3160675600","https://openalex.org/W3183922141","https://openalex.org/W3208590247","https://openalex.org/W3209791911","https://openalex.org/W4231706539","https://openalex.org/W4235228724","https://openalex.org/W4238493769","https://openalex.org/W4281611113","https://openalex.org/W4287182243","https://openalex.org/W4310390511","https://openalex.org/W6824878655"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2115451617","https://openalex.org/W1541736886","https://openalex.org/W3216866263","https://openalex.org/W2053857640"],"abstract_inverted_index":{"Abstract":[0],"We":[1,34,86,226],"analyse":[2],"parallel":[3],"overlapping":[4,144],"Schwarz":[5],"domain":[6,138,208,258],"decomposition":[7],"methods":[8],"for":[9,133,152,188,201,256],"the":[10,14,43,51,92,95,102,124,154,157,165,181,198,213,216,232,238,253],"Helmholtz":[11],"equation,":[12],"where":[13],"exchange":[15],"of":[16,32,39,73,94,101,105,164,215],"information":[17],"between":[18,113],"subdomains":[19],"is":[20,67,128,171],"achieved":[21],"using":[22],"first-order":[23],"absorbing":[24],"(impedance)":[25],"transmission":[26],"conditions,":[27],"together":[28],"with":[29,79,192],"a":[30,36,54,70,89,129,189,245],"partition":[31],"unity.":[33],"provide":[35,117],"novel":[37],"analysis":[38],"this":[40],"method":[41,52,240],"at":[42],"PDE":[44],"level":[45],"(without":[46],"discretization).":[47],"First,":[48],"we":[49,148,210],"formulate":[50],"as":[53,180,261],"fixed":[55,96,125,166],"point":[56,97,126,167],"iteration,":[57],"and":[58,136],"show":[59,236],"(in":[60],"dimensions":[61],"1,":[62],"2,":[63],"3)":[64],"that":[65,160,230,237],"it":[66],"well-defined":[68],"in":[69,99,248],"tensor":[71],"product":[72],"appropriate":[74],"local":[75,103,111],"function":[76],"spaces,":[77],"each":[78,141],"$$L^2$$":[80],"<mml:math":[81],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>":[82],"impedance":[83],"boundary":[84],"data.":[85],"then":[87],"obtain":[88],"bound":[90],"on":[91,156],"norm":[93],"operator":[98,127],"terms":[100],"norms":[104,214],"certain":[106,221],"impedance-to-impedance":[107,158,217],"maps":[108,159,218],"arising":[109],"from":[110],"interactions":[112],"subdomains.":[114],"These":[115,234],"bounds":[116],"conditions":[118],"under":[119],"which":[120,175],"(some":[121],"power":[122,162],"of)":[123],"contraction.":[130],"In":[131],"2-d,":[132],"rectangular":[134],"domains":[135],"strip-wise":[137],"decompositions":[139],"(with":[140],"subdomain":[142],"only":[143],"its":[145],"immediate":[146],"neighbours),":[147],"present":[149],"two":[150,193],"techniques":[151],"verifying":[153],"assumptions":[155,200],"ensure":[161],"contractivity":[163],"operator.":[168],"The":[169],"first":[170],"through":[172],"semiclassical":[173],"analysis,":[174],"gives":[176],"rigorous":[177],"estimates":[178],"valid":[179],"frequency":[182],"tends":[183],"to":[184],"infinity.":[185],"At":[186],"least":[187],"model":[190],"case":[191],"subdomains,":[194],"these":[195],"results":[196],"verify":[197],"required":[199],"sufficiently":[202],"large":[203],"overlap.":[204],"For":[205],"more":[206],"realistic":[207],"decompositions,":[209,259],"directly":[211],"compute":[212],"by":[219,252],"solving":[220],"canonical":[222],"(local)":[223],"eigenvalue":[224],"problems.":[225],"give":[227],"numerical":[228],"experiments":[229],"illustrate":[231],"theory.":[233],"also":[235],"iterative":[239],"remains":[241],"convergent":[242],"and/or":[243],"provides":[244],"good":[246],"preconditioner":[247],"cases":[249],"not":[250],"covered":[251],"theory,":[254],"including":[255],"general":[257],"such":[260],"those":[262],"obtained":[263],"via":[264],"automatic":[265],"graph-partitioning":[266],"software.":[267]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}