{"id":"https://openalex.org/W1978298401","doi":"https://doi.org/10.1090/s0025-5718-08-02150-9","title":"Overlapping additive Schwarz preconditioners for elliptic PDEs on the unit sphere","display_name":"Overlapping additive Schwarz preconditioners for elliptic PDEs on the unit sphere","publication_year":2008,"publication_date":"2008-10-14","ids":{"openalex":"https://openalex.org/W1978298401","doi":"https://doi.org/10.1090/s0025-5718-08-02150-9","mag":"1978298401"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-08-02150-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02150-9","pdf_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02150-9/S0025-5718-08-02150-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02150-9/S0025-5718-08-02150-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Q. T. Le Gia","orcid":null},"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":"Q. T. Le Gia","raw_affiliation_strings":["School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia","School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia,"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia,","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075686837","display_name":"Ian H. Sloan","orcid":"https://orcid.org/0000-0003-3769-0538"},"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":false,"raw_author_name":"I. H. Sloan","raw_affiliation_strings":["School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia","School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia,"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia,","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","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":false,"raw_author_name":"T. Tran","raw_affiliation_strings":["School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia","School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia,"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia,","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I31746571"],"apc_list":null,"apc_paid":null,"fwci":2.6741,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.89244265,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"78","issue":"265","first_page":"79","last_page":"79"},"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":0.9994000196456909,"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"}},"topics":[{"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9965999722480774,"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/mathematics","display_name":"Mathematics","score":0.8839253187179565},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.8475823998451233},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.7521489858627319},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.6845519542694092},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.6321040987968445},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6125629544258118},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.5033625960350037},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4990537166595459},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4727894961833954},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4702802002429962},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.4309282898902893},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34931856393814087},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28821486234664917},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.20732739567756653}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8839253187179565},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.8475823998451233},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.7521489858627319},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.6845519542694092},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.6321040987968445},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6125629544258118},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.5033625960350037},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4990537166595459},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4727894961833954},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4702802002429962},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.4309282898902893},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34931856393814087},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28821486234664917},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.20732739567756653},{"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":3,"locations":[{"id":"doi:10.1090/s0025-5718-08-02150-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02150-9","pdf_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02150-9/S0025-5718-08-02150-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.140.7113","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.7113","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2009-78-265/S0025-5718-08-02150-9/S0025-5718-08-02150-9.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.582.9433","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.582.9433","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.maths.unsw.edu.au/~qlegia/SloanTranLG_MathComp.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-08-02150-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02150-9","pdf_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02150-9/S0025-5718-08-02150-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1978298401.pdf","grobid_xml":"https://content.openalex.org/works/W1978298401.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W118285134","https://openalex.org/W1486164486","https://openalex.org/W1495010649","https://openalex.org/W1507506202","https://openalex.org/W1548589512","https://openalex.org/W1562641538","https://openalex.org/W1587996250","https://openalex.org/W1597209545","https://openalex.org/W1737033906","https://openalex.org/W1963785789","https://openalex.org/W1988473367","https://openalex.org/W1995274909","https://openalex.org/W1999882624","https://openalex.org/W2003789632","https://openalex.org/W2003971308","https://openalex.org/W2004125666","https://openalex.org/W2004308928","https://openalex.org/W2016969219","https://openalex.org/W2021969763","https://openalex.org/W2023638740","https://openalex.org/W2040314635","https://openalex.org/W2043347951","https://openalex.org/W2060803111","https://openalex.org/W2062360755","https://openalex.org/W2102596289","https://openalex.org/W2105776550","https://openalex.org/W2124471636","https://openalex.org/W2127689830","https://openalex.org/W2158127704","https://openalex.org/W2171073252","https://openalex.org/W3106701803","https://openalex.org/W4229514648","https://openalex.org/W4292166790","https://openalex.org/W4302819252","https://openalex.org/W6812997142"],"related_works":["https://openalex.org/W2902154408","https://openalex.org/W1515964003","https://openalex.org/W2504287632","https://openalex.org/W1994696552","https://openalex.org/W3046643187","https://openalex.org/W2286395548","https://openalex.org/W4241403127","https://openalex.org/W1423765865","https://openalex.org/W2493580937","https://openalex.org/W132556536"],"abstract_inverted_index":{"We":[0],"present":[1],"an":[2],"overlapping":[3],"domain":[4],"decomposition":[5],"technique":[6],"for":[7],"solving":[8],"elliptic":[9],"partial":[10],"differential":[11],"equations":[12],"on":[13,29,40,58],"the":[14,30,36,41,45],"sphere.":[15,31],"The":[16,32,51],"approximate":[17],"solution":[18],"is":[19,53],"constructed":[20],"using":[21],"shifts":[22],"of":[23,35],"a":[24],"strictly":[25],"positive":[26],"definite":[27],"kernel":[28],"condition":[33],"number":[34],"Schwarz":[37],"operator":[38],"depends":[39],"way":[42],"we":[43],"decompose":[44],"scattered":[46,61],"set":[47],"into":[48],"smaller":[49],"subsets.":[50],"method":[52],"illustrated":[54],"by":[55],"numerical":[56],"experiments":[57],"relatively":[59],"large":[60],"point":[62],"sets":[63],"taken":[64],"from":[65],"MAGSAT":[66],"satellite":[67],"data.":[68]},"counts_by_year":[{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}