{"id":"https://openalex.org/W4390697222","doi":"https://doi.org/10.1137/23m1550803","title":"On Optimal Zero-Padding of Kernel Truncation Method","display_name":"On Optimal Zero-Padding of Kernel Truncation Method","publication_year":2024,"publication_date":"2024-01-10","ids":{"openalex":"https://openalex.org/W4390697222","doi":"https://doi.org/10.1137/23m1550803"},"language":"en","primary_location":{"id":"doi:10.1137/23m1550803","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1550803","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5100352359","display_name":"Xin Liu","orcid":"https://orcid.org/0009-0005-5174-9446"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xin Liu","raw_affiliation_strings":["Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114116798","display_name":"Qinglin Tang","orcid":null},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]},{"id":"https://openalex.org/I4210125143","display_name":"Chengdu University","ror":"https://ror.org/034z67559","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210125143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qinglin Tang","raw_affiliation_strings":["School of Mathematics, SiChuan University, ChengDu, 610065, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, SiChuan University, ChengDu, 610065, China","institution_ids":["https://openalex.org/I24185976","https://openalex.org/I4210125143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089525630","display_name":"S. D. Zhang","orcid":"https://orcid.org/0000-0001-6417-506X"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shaobo Zhang","raw_affiliation_strings":["Corresponding author. Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China"],"raw_orcid":"https://orcid.org/0000-0001-6417-506X","affiliations":[{"raw_affiliation_string":"Corresponding author. Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101607718","display_name":"Yong Zhang","orcid":"https://orcid.org/0000-0003-0397-7143"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong Zhang","raw_affiliation_strings":["Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China","institution_ids":["https://openalex.org/I162868743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100352359"],"corresponding_institution_ids":["https://openalex.org/I162868743"],"apc_list":null,"apc_paid":null,"fwci":3.6005,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.93353771,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"46","issue":"1","first_page":"A23","last_page":"A49"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"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/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"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/T11367","display_name":"Particle accelerators and beam dynamics","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T11965","display_name":"Quantum, superfluid, helium dynamics","score":0.9968000054359436,"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":0.67203688621521},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5936378240585327},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.5759269595146179},{"id":"https://openalex.org/keywords/fast-multipole-method","display_name":"Fast multipole method","score":0.5479804873466492},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5089576244354248},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.5086480379104614},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.4584353566169739},{"id":"https://openalex.org/keywords/padding","display_name":"Padding","score":0.4534894526004791},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.42699697613716125},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.42303481698036194},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.4201813340187073},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24668145179748535},{"id":"https://openalex.org/keywords/multipole-expansion","display_name":"Multipole expansion","score":0.2198815941810608},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.19718965888023376},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1519027054309845}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.67203688621521},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5936378240585327},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.5759269595146179},{"id":"https://openalex.org/C135115559","wikidata":"https://www.wikidata.org/wiki/Q5437040","display_name":"Fast multipole method","level":3,"score":0.5479804873466492},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5089576244354248},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.5086480379104614},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.4584353566169739},{"id":"https://openalex.org/C165435473","wikidata":"https://www.wikidata.org/wiki/Q1509884","display_name":"Padding","level":2,"score":0.4534894526004791},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.42699697613716125},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.42303481698036194},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.4201813340187073},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24668145179748535},{"id":"https://openalex.org/C52765159","wikidata":"https://www.wikidata.org/wiki/Q1027847","display_name":"Multipole expansion","level":2,"score":0.2198815941810608},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.19718965888023376},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1519027054309845},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m1550803","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1550803","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2487604691","display_name":null,"funder_award_id":"12271400","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2718444891","display_name":null,"funder_award_id":"11971335","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1490180844","https://openalex.org/W1494364037","https://openalex.org/W1910943476","https://openalex.org/W1989677470","https://openalex.org/W2032073723","https://openalex.org/W2040823523","https://openalex.org/W2050338742","https://openalex.org/W2051993838","https://openalex.org/W2057813447","https://openalex.org/W2061726996","https://openalex.org/W2069970911","https://openalex.org/W2075114155","https://openalex.org/W2120062331","https://openalex.org/W2154630483","https://openalex.org/W2274947949","https://openalex.org/W2325158909","https://openalex.org/W2336632864","https://openalex.org/W2804346888","https://openalex.org/W2899784371","https://openalex.org/W2906310599","https://openalex.org/W3099965099","https://openalex.org/W3101835573","https://openalex.org/W4253937035"],"related_works":["https://openalex.org/W1922056548","https://openalex.org/W2040666836","https://openalex.org/W2392438811","https://openalex.org/W2373419133","https://openalex.org/W2238041693","https://openalex.org/W2112774109","https://openalex.org/W125347959","https://openalex.org/W1990789772","https://openalex.org/W138907054","https://openalex.org/W2536422707"],"abstract_inverted_index":{".The":[0],"kernel":[1,28,65],"truncation":[2,242],"method":[3],"(KTM)":[4],"is":[5,45,194],"a":[6,72,79,85,144],"commonly":[7],"used":[8],"algorithm":[9],"to":[10,54,69,205,221],"compute":[11],"the":[12,26,35,40,56,64,75,89,105,139,158,162,169,207,214,226],"convolution-type":[13],"nonlocal":[14,153,223,240],"potential":[15,108],"\\(\\Phi":[16],"({\\textbf":[17,43],"x})=(U\\ast":[18],"\\rho":[19],")({\\textbf":[20],"x}),\\,{\\textbf":[21],"x}":[22],"\\in{\\mathbb":[23],"R^d},\\)":[24],"where":[25],"convolution":[27],"\\(U({\\textbf":[29],"x})\\)":[30,44],"might":[31],"be":[32],"singular":[33],"at":[34],"origin":[36],"and/or":[37],"far-field":[38],"and":[39,47,84,151,164,173,183,236],"density":[41,163,171],"\\(\\rho":[42],"smooth":[46],"fast":[48],"decaying.":[49],"In":[50,133],"KTM,":[51],"in":[52,88,109,143],"order":[53],"capture":[55],"Fourier":[57,90],"integrand's":[58],"oscillations":[59],"that":[60],"are":[61,203],"brought":[62],"by":[63,92],"truncation,":[66],"one":[67],"needs":[68],"carry":[70],"out":[71],"zero-padding":[73,95,141,211],"of":[74,161,176],"density,":[76,216],"which":[77,193],"means":[78],"larger":[80],"physical":[81],"computation":[82],"domain":[83],"finer":[86],"mesh":[87],"space":[91,149],"duality.":[93],"The":[94],"factor,":[96],"\\(\\sqrt{d}+1\\),":[97],"was":[98],"first":[99,137],"given":[100],"as":[101],"empirical":[102],"formula":[103],"for":[104,147,213],"2D/3D":[106],"Coulomb":[107],"[M.":[110],"R.":[111],"Jarvis":[112],"et":[113,125],"al.":[114,126],"Phys.":[115,127,188],"Rev.":[116,128],"B,":[117,129],"56":[118],"(1997),":[119],"pp.":[120,191],"14972\u201314978;":[121],"C.":[122],"A.":[123],"Rozzi":[124],"73":[130],"(2006),":[131],"205119].":[132],"this":[134],"article,":[135],"we":[136,156,167],"rederive":[138],"optimal":[140,210],"factor":[142,212],"rigorous":[145],"way":[146],"arbitrary":[148],"dimension":[150],"different":[152,222],"potentials.":[154],"Then,":[155],"present":[157],"error":[159],"estimates":[160],"potential.":[165],"Next,":[166],"investigate":[168],"anisotropic":[170,215],"case,":[172],"provide":[174],"details":[175],"tensor":[177],"acceleration":[178],"[F.":[179],"Vico,":[180],"L.":[181],"Greengard,":[182],"M.":[184],"Ferrando,":[185],"J.":[186],"Comput.":[187],"323":[189],"(2016),":[190],"191\u2013203],":[192],"an":[195],"important":[196],"performance":[197],"improvement.":[198],"Finally,":[199],"extensive":[200],"numerical":[201],"results":[202],"provided":[204],"confirm":[206],"accuracy,":[208],"efficiency,":[209],"together":[217],"with":[218],"some":[219],"applications":[220],"potentials,":[224],"including":[225],"one-dimensional/two-dimensional":[227],"(2D)/three-dimensional":[228],"(3D)":[229],"Poisson,":[230],"2D":[231],"Coulomb,":[232],"quasi-2D/3D":[233],"dipole-dipole":[234],"Interaction,":[235],"3D":[237],"quadrupolar":[238],"potential.Keywordsconvolution-type":[239],"potentialkernel":[241],"methodoptimal":[243],"zero-paddingerror":[244],"estimatesanisotropic":[245],"densityMSC":[246],"codes65D3268Q25":[247]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
