{"id":"https://openalex.org/W2122956985","doi":"https://doi.org/10.1080/00207160701293006","title":"Additive Schwarz preconditioners for the<i>h</i>-<i>p</i>version boundary-element approximation to the hypersingular operator in three dimensions","display_name":"Additive Schwarz preconditioners for the<i>h</i>-<i>p</i>version boundary-element approximation to the hypersingular operator in three dimensions","publication_year":2007,"publication_date":"2007-09-25","ids":{"openalex":"https://openalex.org/W2122956985","doi":"https://doi.org/10.1080/00207160701293006","mag":"2122956985"},"language":"en","primary_location":{"id":"doi:10.1080/00207160701293006","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701293006","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5052916984","display_name":"Thanh Tran","orcid":"https://orcid.org/0000-0001-6117-4811"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Thanh Tran","raw_affiliation_strings":["School of Mathematics and Statistics, University of New South Wales , Sydney, 2052, Australia","School of Mathematics and Statistics, #R##N#University of New South Wales, Sydney, Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of New South Wales , Sydney, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"School of Mathematics and Statistics, #R##N#University of New South Wales, Sydney, Australia","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052916984"],"corresponding_institution_ids":["https://openalex.org/I31746571"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16512556,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"84","issue":"10","first_page":"1417","last_page":"1437"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9976000189781189,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.994700014591217,"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":0.9072655439376831},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.7918664813041687},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.5989595055580139},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5683799982070923},{"id":"https://openalex.org/keywords/boundary-element-method","display_name":"Boundary element method","score":0.5624313950538635},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5523751378059387},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5508546829223633},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5434039831161499},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5058576464653015},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.4922267496585846},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.4504186511039734},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4310997426509857},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4181895852088928},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4110180735588074},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4063355326652527},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.19819435477256775},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1853589415550232}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9072655439376831},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.7918664813041687},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.5989595055580139},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5683799982070923},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.5624313950538635},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5523751378059387},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5508546829223633},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5434039831161499},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5058576464653015},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.4922267496585846},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.4504186511039734},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4310997426509857},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4181895852088928},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4110180735588074},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4063355326652527},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.19819435477256775},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1853589415550232},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160701293006","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701293006","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7400000095367432,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W118285134","https://openalex.org/W560409768","https://openalex.org/W1597209545","https://openalex.org/W1972646935","https://openalex.org/W1976174856","https://openalex.org/W1978321922","https://openalex.org/W1987377268","https://openalex.org/W1997253006","https://openalex.org/W2004125666","https://openalex.org/W2015836100","https://openalex.org/W2041523977","https://openalex.org/W2043347951","https://openalex.org/W2048877125","https://openalex.org/W2060803111","https://openalex.org/W2069385753","https://openalex.org/W2071196586","https://openalex.org/W2075975893","https://openalex.org/W2088353152","https://openalex.org/W2126897161","https://openalex.org/W2199169705","https://openalex.org/W4253840677"],"related_works":["https://openalex.org/W2902154408","https://openalex.org/W2028890215","https://openalex.org/W2159100661","https://openalex.org/W2000290814","https://openalex.org/W3839471","https://openalex.org/W2339825459","https://openalex.org/W2138840323","https://openalex.org/W1994696552","https://openalex.org/W1515964003","https://openalex.org/W2367747968"],"abstract_inverted_index":{"We":[0],"study":[1],"different":[2],"preconditioners":[3,49],"for":[4,36],"the":[5,9,21,37,43,46,64,72],"h-p":[6],"version":[7],"of":[8,20,45,51,74],"Galerkin":[10],"boundary-element":[11],"method":[12],"when":[13],"used":[14],"to":[15],"solve":[16],"hypersingular":[17],"integral":[18,30],"equations":[19,31,41],"first":[22],"kind":[23],"on":[24],"a":[25],"surface":[26],"in":[27,42],"\u211d3.":[28],"These":[29],"result":[32],"from":[33],"Neumann":[34],"problems":[35],"Laplace":[38],"and":[39,56],"Lam\u00e9":[40],"exterior":[44],"surface.":[47],"The":[48],"are":[50],"additive":[52],"Schwarz":[53],"type":[54],"(non-overlapping":[55],"overlapping).":[57],"In":[58],"all":[59],"cases,":[60],"we":[61],"prove":[62],"that":[63],"condition":[65],"numbers":[66],"grow":[67],"at":[68],"most":[69],"logarithmically":[70],"with":[71],"degrees":[73],"freedom.":[75]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}