{"id":"https://openalex.org/W2889322495","doi":"https://doi.org/10.1137/18m1210460","title":"A Multigrid Method for Nonlocal Problems: Non--Diagonally Dominant or Toeplitz-Plus-Tridiagonal Systems","display_name":"A Multigrid Method for Nonlocal Problems: Non--Diagonally Dominant or Toeplitz-Plus-Tridiagonal Systems","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2889322495","doi":"https://doi.org/10.1137/18m1210460","mag":"2889322495"},"language":"en","primary_location":{"id":"doi:10.1137/18m1210460","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1210460","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1808.09595","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Minghua Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Minghua Chen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Sven-Erik Ekstr\u00f6m","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sven-Erik Ekstr\u00f6m","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Stefano Serra-Capizzano","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefano Serra-Capizzano","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4335,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.66676641,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"41","issue":"4","first_page":"1546","last_page":"1570"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.2639000117778778,"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":0.2639000117778778,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.18780000507831573,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.17509999871253967,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.7203999757766724},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.48820000886917114},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.4797999858856201},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4684999883174896},{"id":"https://openalex.org/keywords/diagonally-dominant-matrix","display_name":"Diagonally dominant matrix","score":0.43720000982284546},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42410001158714294},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4124999940395355},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.40139999985694885},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4009999930858612},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.39730000495910645}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8489999771118164},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.7203999757766724},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5467000007629395},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.48820000886917114},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.4797999858856201},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4684999883174896},{"id":"https://openalex.org/C84507854","wikidata":"https://www.wikidata.org/wiki/Q952222","display_name":"Diagonally dominant matrix","level":3,"score":0.43720000982284546},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4293000102043152},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42410001158714294},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4124999940395355},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.40139999985694885},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4009999930858612},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.39730000495910645},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.3871999979019165},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.3659999966621399},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3483000099658966},{"id":"https://openalex.org/C110342517","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Constant coefficients","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.32339999079704285},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.3224000036716461},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3212999999523163},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C64980692","wikidata":"https://www.wikidata.org/wiki/Q16191959","display_name":"Symbolic convergence theory","level":3,"score":0.26440000534057617},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.2615000009536743},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.2581999897956848},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.25130000710487366}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/18m1210460","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1210460","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1808.09595","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.09595","pdf_url":"https://arxiv.org/pdf/1808.09595","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/443523","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/443523","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"\u671f\u520a\u8bba\u6587"},{"id":"pmh:oai:irinsubria.uninsubria.it:11383/2119546","is_oa":false,"landing_page_url":"https://hdl.handle.net/11383/2119546","pdf_url":null,"source":{"id":"https://openalex.org/S4377196351","display_name":"IrInSubria (University of Insubria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I115752224","host_organization_name":"University of Insubria","host_organization_lineage":["https://openalex.org/I115752224"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1808.09595","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.09595","pdf_url":"https://arxiv.org/pdf/1808.09595","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7986504235","display_name":null,"funder_award_id":"11601206","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8655175202","display_name":null,"funder_award_id":"lzujbky-2019-80","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W221829734","https://openalex.org/W1758121264","https://openalex.org/W1970334228","https://openalex.org/W1970527624","https://openalex.org/W1975153608","https://openalex.org/W1984898295","https://openalex.org/W1993856828","https://openalex.org/W1994176509","https://openalex.org/W1999695483","https://openalex.org/W2006044588","https://openalex.org/W2012828992","https://openalex.org/W2015700994","https://openalex.org/W2017453755","https://openalex.org/W2020698763","https://openalex.org/W2028357997","https://openalex.org/W2059679865","https://openalex.org/W2062092992","https://openalex.org/W2066660517","https://openalex.org/W2066686577","https://openalex.org/W2084784234","https://openalex.org/W2085429036","https://openalex.org/W2086517326","https://openalex.org/W2121533457","https://openalex.org/W2145115300","https://openalex.org/W2148147555","https://openalex.org/W2165630134","https://openalex.org/W2312385896","https://openalex.org/W2313618896","https://openalex.org/W2395085125","https://openalex.org/W2623360684","https://openalex.org/W2685992850","https://openalex.org/W2748113844","https://openalex.org/W2758600160","https://openalex.org/W2947348673","https://openalex.org/W2963889991","https://openalex.org/W3099709074"],"related_works":[],"abstract_inverted_index":{"Nonlocal":[0],"problems":[1,33],"have":[2],"been":[3],"used":[4],"to":[5,120,172,186,234],"model":[6],"very":[7],"different":[8],"applied":[9],"scientific":[10],"phenomena":[11],"which":[12,177],"involve":[13],"the":[14,21,31,39,43,74,77,81,117,122,128,157,160,187,192,202,206,209,216,219,226,236,243,250,253],"fractional":[15,188],"Laplacian":[16,189],"when":[17,58,127],"one":[18],"looks":[19],"at":[20],"Levy":[22],"processes":[23],"and":[24,89,100,111,124,165,191],"stochastic":[25],"interfaces.":[26],"This":[27],"paper":[28],"deals":[29],"with":[30,60,225,238],"nonlocal":[32],"on":[34,200],"a":[35,67],"bounded":[36],"domain":[37],"where":[38,247],"stiffness":[40,75,129],"matrices":[41],"of":[42,73,80,156,205,208,218,252],"resulting":[44],"systems":[45,176],"are":[46,113,168,178,232],"Toeplitz":[47,71,180],"plus":[48],"tridiagonal":[49],"or":[50],"far":[51,132],"from":[52,133,153],"being":[53,134],"diagonally":[54,69,136,183],"dominant":[55,70,137,184],"as":[56],"occurs":[57],"dealing":[59],"linear":[61],"finite":[62],"element":[63],"approximations.":[64],"By":[65],"exploiting":[66],"weakly":[68,135,182],"property":[72],"matrices,":[76,159],"optimal":[78],"convergence":[79,207,217,237],"two-grid":[82,210],"method":[83,211],"is":[84,131,222,249],"well":[85],"established":[86],"in":[87,170],"[Fiorentino":[88],"Serra-Capizzano,":[90],"SIAM":[91,102],"T.":[92,103],"Sci.":[93],"Comput.,":[94],"17":[95],"(1996),":[96],"pp.":[97,109,145],"1068-1081;":[98],"Chen":[99],"Deng,":[101],"Matrix":[104],"Anal.":[105],"Appl.,":[106],"38":[107],"(2017),":[108],"869-890],":[110],"there":[112],"still":[114],"questions":[115],"about":[116],"best":[118],"ways":[119],"define":[121],"coarsening":[123],"interpolation":[125],"operators":[126],"matrix":[130],"[Stnben,":[138],"J.":[139],"Comput.":[140],"Appl.":[141],"Math.,":[142],"128":[143],"(2001),":[144],"281-309].":[146],"In":[147],"this":[148],"work,":[149],"using":[150],"spectral":[151],"indications":[152],"our":[154,198],"analysis":[155],"involved":[158],"simple":[161],"(traditional)":[162],"restriction":[163],"operator":[164,167],"prolongation":[166],"employed":[169],"order":[171],"handle":[173],"general":[174],"algebraic":[175],"neither":[179],"nor":[181],"corresponding":[185],"kernel":[190],"constant":[193,227],"kernel,":[194],"respectively.":[195],"We":[196],"focus":[197],"efforts":[199],"providing":[201],"detailed":[203],"proof":[204],"for":[212],"such":[213],"situations.":[214],"Moreover,":[215],"full":[220],"multigrid":[221],"also":[223],"discussed":[224],"kernel.":[228],"The":[229],"numerical":[230],"experiments":[231],"performed":[233],"verify":[235],"only":[239],"O(NlogN)":[240],"complexity":[241],"by":[242],"fast":[244],"Fourier":[245],"transform,":[246],"N":[248],"number":[251],"grid":[254],"points.":[255]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2018-09-07T00:00:00"}
