{"id":"https://openalex.org/W2069887143","doi":"https://doi.org/10.1007/s00211-011-0428-6","title":"Multiscale RBF collocation for solving PDEs on spheres","display_name":"Multiscale RBF collocation for solving PDEs on spheres","publication_year":2011,"publication_date":"2011-11-08","ids":{"openalex":"https://openalex.org/W2069887143","doi":"https://doi.org/10.1007/s00211-011-0428-6","mag":"2069887143"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-011-0428-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-011-0428-6","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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":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, University of New South Wales, Sydney, NSW, 2052, Australia","University of New South Wales, School of Mathematics and Statistics, 2052, Sydney, NSW, Australia#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"University of New South Wales, School of Mathematics and Statistics, 2052, Sydney, NSW, Australia#TAB#","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, University of New South Wales, Sydney, NSW, 2052, Australia","University of New South Wales, School of Mathematics and Statistics, 2052, Sydney, NSW, Australia#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"University of New South Wales, School of Mathematics and Statistics, 2052, Sydney, NSW, Australia#TAB#","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066096555","display_name":"Holger Wendland","orcid":"https://orcid.org/0000-0002-9614-5321"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"H. Wendland","raw_affiliation_strings":["Mathematical Institute, University of Oxford, 24-29 St. Giles\u2019, Oxford, OX1 3LB, UK","University of Oxford, Mathematical Institute, 24-29 St Giles\u2019, OX1 3LB, Oxford, UK#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, 24-29 St. Giles\u2019, Oxford, OX1 3LB, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"University of Oxford, Mathematical Institute, 24-29 St Giles\u2019, OX1 3LB, Oxford, UK#TAB#","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I31746571"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":2.6694,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.90111643,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"121","issue":"1","first_page":"99","last_page":"125"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"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/T11558","display_name":"Composite Material Mechanics","score":0.9991999864578247,"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/radial-basis-function","display_name":"Radial basis function","score":0.9015400409698486},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6940159797668457},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.683420717716217},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.665908694267273},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.6464828848838806},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5304303169250488},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5168610215187073},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.4930398166179657},{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.4427404999732971},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.43869057297706604},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.42175647616386414},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.42099103331565857},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4039335250854492},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3011026978492737},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.2690070867538452},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2053995430469513},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1684720814228058},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06602570414543152}],"concepts":[{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.9015400409698486},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6940159797668457},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.683420717716217},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.665908694267273},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.6464828848838806},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5304303169250488},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5168610215187073},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.4930398166179657},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.4427404999732971},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.43869057297706604},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.42175647616386414},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.42099103331565857},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4039335250854492},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3011026978492737},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.2690070867538452},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2053995430469513},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1684720814228058},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06602570414543152},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00211-011-0428-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-011-0428-6","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:uuid:175371b0-4630-4b94-8675-18e01d8512bb","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/980","raw_type":"Technical Report"},{"id":"pmh:oai:eref.uni-bayreuth.de:38891","is_oa":false,"landing_page_url":"https://eref.uni-bayreuth.de/38891/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196442","display_name":"ERef Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel in einer Zeitschrift"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:175371b0-4630-4b94-8675-18e01d8512bb","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:175371b0-4630-4b94-8675-18e01d8512bb","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/980","raw_type":"Report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W112187595","https://openalex.org/W144669444","https://openalex.org/W1486164486","https://openalex.org/W1572940464","https://openalex.org/W1963785789","https://openalex.org/W1977027705","https://openalex.org/W1995274909","https://openalex.org/W2019180174","https://openalex.org/W2023638740","https://openalex.org/W2032523091","https://openalex.org/W2040314635","https://openalex.org/W2047877145","https://openalex.org/W2051169944","https://openalex.org/W2055528045","https://openalex.org/W2062360755","https://openalex.org/W2079929209","https://openalex.org/W2084196626","https://openalex.org/W2088822475","https://openalex.org/W2102596289","https://openalex.org/W2126928268","https://openalex.org/W2146589365","https://openalex.org/W2150612352","https://openalex.org/W2166050051","https://openalex.org/W2217261373","https://openalex.org/W2313689636","https://openalex.org/W3106701803","https://openalex.org/W4240240566"],"related_works":["https://openalex.org/W2791210196","https://openalex.org/W2078318892","https://openalex.org/W4255016916","https://openalex.org/W2111003632","https://openalex.org/W1987365920","https://openalex.org/W3097031132","https://openalex.org/W2889856026","https://openalex.org/W1989122168","https://openalex.org/W2150070385","https://openalex.org/W2000247808"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}