{"id":"https://openalex.org/W2945311161","doi":"https://doi.org/10.1080/00207160.2019.1619705","title":"On fast multipole methods for Fredholm integral equations of the second kind with singular and highly oscillatory kernels","display_name":"On fast multipole methods for Fredholm integral equations of the second kind with singular and highly oscillatory kernels","publication_year":2019,"publication_date":"2019-05-15","ids":{"openalex":"https://openalex.org/W2945311161","doi":"https://doi.org/10.1080/00207160.2019.1619705","mag":"2945311161"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2019.1619705","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2019.1619705","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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/A5100379770","display_name":"Bin Li","orcid":"https://orcid.org/0000-0002-0866-5141"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]},{"id":"https://openalex.org/I24407930","display_name":"Hunan University of Science and Engineering","ror":"https://ror.org/04ymz0q33","country_code":"CN","type":"education","lineage":["https://openalex.org/I24407930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bin Li","raw_affiliation_strings":["College of Science, Hunan University of Science and Engineering, Yongzhou, People's Republic of China","School of Mathematics and Statistics, Central South University, Changsha, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Hunan University of Science and Engineering, Yongzhou, People's Republic of China","institution_ids":["https://openalex.org/I24407930"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha, People's Republic of China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002179101","display_name":"Shuhuang Xiang","orcid":"https://orcid.org/0000-0002-6727-6170"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shuhuang Xiang","raw_affiliation_strings":["School of Mathematics and Statistics, Central South University, Changsha, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha, People's Republic of China","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002179101"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":null,"apc_paid":null,"fwci":0.1206,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.45093772,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"97","issue":"7","first_page":"1391","last_page":"1411"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":1.0,"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/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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8091586232185364},{"id":"https://openalex.org/keywords/fast-multipole-method","display_name":"Fast multipole method","score":0.7481115460395813},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.6341557502746582},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6271623373031616},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6089306473731995},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5911332964897156},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5588374733924866},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5268798470497131},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.5016367435455322},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4980325698852539},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4697228968143463},{"id":"https://openalex.org/keywords/multipole-expansion","display_name":"Multipole expansion","score":0.45086508989334106},{"id":"https://openalex.org/keywords/boundary-element-method","display_name":"Boundary element method","score":0.432149738073349},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43179500102996826},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3891785442829132},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.16691991686820984},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08048820495605469},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.07928171753883362}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8091586232185364},{"id":"https://openalex.org/C135115559","wikidata":"https://www.wikidata.org/wiki/Q5437040","display_name":"Fast multipole method","level":3,"score":0.7481115460395813},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.6341557502746582},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6271623373031616},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6089306473731995},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5911332964897156},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5588374733924866},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5268798470497131},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.5016367435455322},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4980325698852539},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4697228968143463},{"id":"https://openalex.org/C52765159","wikidata":"https://www.wikidata.org/wiki/Q1027847","display_name":"Multipole expansion","level":2,"score":0.45086508989334106},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.432149738073349},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43179500102996826},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3891785442829132},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.16691991686820984},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08048820495605469},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07928171753883362},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2019.1619705","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2019.1619705","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W599820626","https://openalex.org/W1573376668","https://openalex.org/W1584610719","https://openalex.org/W1963750172","https://openalex.org/W1971281392","https://openalex.org/W1971525833","https://openalex.org/W1982115588","https://openalex.org/W1987397719","https://openalex.org/W1987724179","https://openalex.org/W1988846634","https://openalex.org/W1991030360","https://openalex.org/W1996550962","https://openalex.org/W1996820786","https://openalex.org/W1998301011","https://openalex.org/W1998360055","https://openalex.org/W1998650240","https://openalex.org/W2002491408","https://openalex.org/W2005998530","https://openalex.org/W2012883034","https://openalex.org/W2013571568","https://openalex.org/W2032439996","https://openalex.org/W2038977052","https://openalex.org/W2040922434","https://openalex.org/W2042617956","https://openalex.org/W2044579590","https://openalex.org/W2044662130","https://openalex.org/W2045431810","https://openalex.org/W2049538131","https://openalex.org/W2051395078","https://openalex.org/W2053886231","https://openalex.org/W2054557822","https://openalex.org/W2059961698","https://openalex.org/W2061104034","https://openalex.org/W2061749829","https://openalex.org/W2069883496","https://openalex.org/W2070291256","https://openalex.org/W2070966814","https://openalex.org/W2077852080","https://openalex.org/W2083206954","https://openalex.org/W2089210221","https://openalex.org/W2095682995","https://openalex.org/W2113495404","https://openalex.org/W2117762537","https://openalex.org/W2124421983","https://openalex.org/W2128601600","https://openalex.org/W2130308425","https://openalex.org/W2147983461","https://openalex.org/W2158699284","https://openalex.org/W2159171280","https://openalex.org/W2160431995","https://openalex.org/W2238932318","https://openalex.org/W2517822255","https://openalex.org/W2586197211","https://openalex.org/W2986057930","https://openalex.org/W3101325927"],"related_works":["https://openalex.org/W1822333417","https://openalex.org/W2952819168","https://openalex.org/W2158582466","https://openalex.org/W599820626","https://openalex.org/W2008452721","https://openalex.org/W2383541900","https://openalex.org/W2351450261","https://openalex.org/W2004427012","https://openalex.org/W2058794676","https://openalex.org/W2363724863"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"a":[3],"special":[4],"boundary":[5],"element":[6],"method":[7,40],"for":[8],"Fredholm":[9],"integral":[10],"equations":[11],"of":[12,26,75,118,138],"the":[13,24,27,31,37,46,58,68,73,76,80,84,96,104,109,114,131,136,139],"second":[14],"kind":[15],"with":[16],"singular":[17],"and":[18,30,107,128,133],"highly":[19],"oscillatory":[20,53],"kernels.":[21],"To":[22],"accelerate":[23],"resolution":[25],"linear":[28],"system":[29,86],"matrix-vector":[32],"multiplication":[33],"in":[34,79,123],"each":[35],"iteration,":[36],"fast":[38],"multipole":[39],"(FMM)":[41],"is":[42,87,120],"applied,":[43],"which":[44],"reduces":[45],"complexity":[47],"from":[48,103],"O(N2)":[49],"to":[50],"O(N).":[51],"The":[52],"integrals":[54],"are":[55],"calculated":[56],"by":[57],"steepest":[59],"decent":[60],"method,":[61],"whose":[62],"accuracy":[63],"becomes":[64],"more":[65,88],"accurate":[66],"as":[67,91],"frequency":[69],"increases.":[70],"We":[71],"study":[72],"role":[74],"high-frequency":[77,92],"w":[78,93,98],"FMM,":[81],"showing":[82],"that":[83],"discretization":[85],"well":[89],"conditioned":[90],"increase.":[94],"Moreover,":[95],"larger":[97],"may":[99],"reduce":[100],"rank":[101],"expressions":[102],"kernel":[105],"function,":[106],"decrease":[108],"absolute":[110],"errors.":[111],"At":[112],"last,":[113],"optimal":[115],"convergence":[116],"rate":[117],"truncation":[119],"also":[121],"represented":[122],"this":[124],"paper.":[125],"Numerical":[126],"experiments":[127],"applications":[129],"support":[130],"claims":[132],"further":[134],"illustrate":[135],"performance":[137],"method.":[140]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
