{"id":"https://openalex.org/W2053427328","doi":"https://doi.org/10.1137/s0036142999362845","title":"A Method for Computing Nearly Singular Integrals","display_name":"A Method for Computing Nearly Singular Integrals","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2053427328","doi":"https://doi.org/10.1137/s0036142999362845","mag":"2053427328"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142999362845","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999362845","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5042633348","display_name":"J. Thomas Beale","orcid":"https://orcid.org/0000-0001-8354-0667"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J. Thomas Beale","raw_affiliation_strings":["Duke University"],"affiliations":[{"raw_affiliation_string":"Duke University","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108573446","display_name":"Ming\u2010Chih Lai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ming-Chih Lai","raw_affiliation_strings":["Department of Applied Mathematics"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042633348"],"corresponding_institution_ids":["https://openalex.org/I170897317"],"apc_list":null,"apc_paid":null,"fwci":4.152,"has_fulltext":false,"cited_by_count":108,"citation_normalized_percentile":{"value":0.92798842,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"38","issue":"6","first_page":"1902","last_page":"1925"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987999796867371,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8365474939346313},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6256248354911804},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.6070491075515747},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5727990865707397},{"id":"https://openalex.org/keywords/laplaces-equation","display_name":"Laplace's equation","score":0.5479190945625305},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.5349256992340088},{"id":"https://openalex.org/keywords/singular-integral","display_name":"Singular integral","score":0.47525593638420105},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4369983673095703},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3652658462524414},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.3572760224342346}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8365474939346313},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6256248354911804},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.6070491075515747},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5727990865707397},{"id":"https://openalex.org/C70615421","wikidata":"https://www.wikidata.org/wiki/Q339444","display_name":"Laplace's equation","level":3,"score":0.5479190945625305},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.5349256992340088},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.47525593638420105},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4369983673095703},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3652658462524414},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.3572760224342346}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142999362845","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999362845","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.36.5304","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.5304","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.duke.edu/faculty/beale/papers/nearsing.ps","raw_type":"text"}],"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/W166676326","https://openalex.org/W1517670975","https://openalex.org/W1576316925","https://openalex.org/W1968055746","https://openalex.org/W1984752534","https://openalex.org/W1987851352","https://openalex.org/W1992268304","https://openalex.org/W2001536020","https://openalex.org/W2014208709","https://openalex.org/W2028085547","https://openalex.org/W2030738345","https://openalex.org/W2038814712","https://openalex.org/W2039893955","https://openalex.org/W2047925487","https://openalex.org/W2067216123","https://openalex.org/W2070124653","https://openalex.org/W2080922987","https://openalex.org/W2083206954","https://openalex.org/W2088156497","https://openalex.org/W2091735404","https://openalex.org/W2094674140","https://openalex.org/W2095006601","https://openalex.org/W2157066783","https://openalex.org/W2317624970","https://openalex.org/W2801209324","https://openalex.org/W3008609509","https://openalex.org/W4245845296"],"related_works":["https://openalex.org/W2387536758","https://openalex.org/W2545824990","https://openalex.org/W3168586318","https://openalex.org/W2030896072","https://openalex.org/W3128284001","https://openalex.org/W2027204516","https://openalex.org/W2114064032","https://openalex.org/W2068059250","https://openalex.org/W2058127109","https://openalex.org/W5603432"],"abstract_inverted_index":{"We":[0,67],"develop":[1],"a":[2,6,12,20,27,41,45,86,98,137,140],"method":[3,88,111],"for":[4,53,72,89,94,151,157],"computing":[5],"nearly":[7],"singular":[8],"integral,":[9],"such":[10],"as":[11],"double":[13,153],"layer":[14,154],"potential":[15,155],"due":[16,56,135],"to":[17,35,57,79,108,130,136],"sources":[18],"on":[19,97,139],"curve":[21],"in":[22,104,143],"the":[23,30,37,54,73,91,105,132,152,158],"plane,":[24,106],"evaluated":[25],"at":[26],"point":[28],"near":[29],"curve.":[31],"The":[32],"approach":[33,125],"is":[34,85],"regularize":[36],"singularity":[38],"and":[39,59,156],"obtain":[40],"preliminary":[42],"value":[43],"from":[44],"standard":[46],"quadrature":[47],"rule.":[48],"Then":[49],"we":[50],"add":[51],"corrections":[52],"errors":[55],"smoothing":[58],"discretization,":[60],"which":[61],"are":[62,149],"found":[63],"by":[64],"asymptotic":[65],"analysis.":[66],"prove":[68],"an":[69,101,109,144],"error":[70],"estimate":[71],"corrected":[74],"value,":[75],"uniform":[76],"with":[77],"respect":[78],"thepoint":[80],"of":[81,112],"evaluation.":[82],"One":[83],"application":[84],"simple":[87],"solving":[90],"Dirichlet":[92,159],"problem":[93],"Laplace's":[95],"equation":[96],"grid":[99],"covering":[100],"irregular":[102],"region":[103],"similar":[107],"earlier":[110],"A.":[113],"Mayo":[114],"[SIAM":[115],"J.":[116],"Sci.":[117],"Statist.":[118],"Comput.,":[119],"6":[120],"(1985),":[121],"pp.":[122],"144--157].":[123],"This":[124],"could":[126],"also":[127],"be":[128],"used":[129],"compute":[131],"pressure":[133],"gradient":[134],"force":[138],"moving":[141],"boundary":[142],"incompressible":[145],"fluid.":[146],"Computational":[147],"examples":[148],"given":[150],"problem.":[160]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}