{"id":"https://openalex.org/W2010293595","doi":"https://doi.org/10.1137/100782516","title":"Spectral Chebyshev Collocation for the Poisson and Biharmonic Equations","display_name":"Spectral Chebyshev Collocation for the Poisson and Biharmonic Equations","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2010293595","doi":"https://doi.org/10.1137/100782516","mag":"2010293595"},"language":"en","primary_location":{"id":"doi:10.1137/100782516","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100782516","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/A5066709922","display_name":"Bernard Bialecki","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bernard Bialecki","raw_affiliation_strings":["bbialeck@mines.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"bbialeck@mines.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062580793","display_name":"Andr\u00e9as Karageorghis","orcid":"https://orcid.org/0000-0002-8399-6880"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andreas Karageorghis","raw_affiliation_strings":["andreask@ucy.ac.cy#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"andreask@ucy.ac.cy#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3383,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.60545482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"32","issue":"5","first_page":"2995","last_page":"3019"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9976000189781189,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9966999888420105,"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":0.8688339591026306},{"id":"https://openalex.org/keywords/biharmonic-equation","display_name":"Biharmonic equation","score":0.7905274629592896},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.5783326029777527},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.5349603295326233},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5315349698066711},{"id":"https://openalex.org/keywords/chebyshev-nodes","display_name":"Chebyshev nodes","score":0.4994161128997803},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.49501246213912964},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47689536213874817},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.47346749901771545},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4482915997505188},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.446382999420166},{"id":"https://openalex.org/keywords/poissons-equation","display_name":"Poisson's equation","score":0.44533661007881165},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.2050725519657135},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.19006061553955078},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.11931231617927551}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8688339591026306},{"id":"https://openalex.org/C145784156","wikidata":"https://www.wikidata.org/wiki/Q859808","display_name":"Biharmonic equation","level":3,"score":0.7905274629592896},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.5783326029777527},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.5349603295326233},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5315349698066711},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.4994161128997803},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.49501246213912964},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47689536213874817},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.47346749901771545},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4482915997505188},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.446382999420166},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.44533661007881165},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2050725519657135},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.19006061553955078},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.11931231617927551},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/100782516","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100782516","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1965342489","https://openalex.org/W1991835897","https://openalex.org/W1997701847","https://openalex.org/W2018211814","https://openalex.org/W2023688834","https://openalex.org/W2024738050","https://openalex.org/W2026684125","https://openalex.org/W2029206127","https://openalex.org/W2030348253","https://openalex.org/W2036614641","https://openalex.org/W2058987405","https://openalex.org/W2069259960","https://openalex.org/W2078752427","https://openalex.org/W2087273875","https://openalex.org/W2088090958","https://openalex.org/W2088123313","https://openalex.org/W2090179830","https://openalex.org/W2146245558","https://openalex.org/W2155216327","https://openalex.org/W2156010245","https://openalex.org/W2410898212","https://openalex.org/W4246480079","https://openalex.org/W4249437058"],"related_works":["https://openalex.org/W2135245226","https://openalex.org/W2979693432","https://openalex.org/W578875527","https://openalex.org/W2333103232","https://openalex.org/W2806218632","https://openalex.org/W2032873066","https://openalex.org/W3210472576","https://openalex.org/W3096143543","https://openalex.org/W2794114978","https://openalex.org/W3185419199"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,59,74],"concerned":[3],"with":[4],"the":[5,11,15,51,54,70,77,88,91,95,101],"spectral":[6,72,83,96],"Chebyshev":[7],"collocation":[8,24,102],"solution":[9,78],"of":[10,31,39,69,79,90,100],"Dirichlet":[12],"problems":[13],"for":[14,76,104],"Poisson":[16,71],"and":[17,46,94,97,106],"biharmonic":[18,52],"equations":[19],"in":[20],"a":[21,29,42,62,80],"square.":[22],"The":[23],"schemes":[25,103],"are":[26],"solved":[27,60],"at":[28],"cost":[30],"$2N^3+O(N^2\\log":[32],"N)$":[33],"operations":[34],"using":[35],"an":[36],"appropriate":[37],"set":[38],"basis":[40],"functions,":[41],"matrix":[43],"diagonalization":[44],"algorithm,":[45],"fast":[47],"Fourier":[48],"transforms.":[49],"For":[50],"problem,":[53],"resulting":[55],"Schur":[56],"complement":[57],"system":[58],"by":[61],"preconditioned":[63],"biconjugate":[64],"gradient":[65],"method.":[66],"An":[67],"application":[68],"preconditioner":[73],"discussed":[75],"variable":[81],"coefficient":[82],"problem.":[84],"Numerical":[85],"results":[86],"confirm":[87],"efficiency":[89],"proposed":[92],"algorithms":[93],"polynomial":[98],"accuracy":[99],"smooth":[105],"singular":[107],"solutions,":[108],"respectively.":[109]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
