{"id":"https://openalex.org/W2014836936","doi":"https://doi.org/10.1080/00207169508804376","title":"Numerical solution of non-separable elliptic equations by the iterative application of FFT methods","display_name":"Numerical solution of non-separable elliptic equations by the iterative application of FFT methods","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W2014836936","doi":"https://doi.org/10.1080/00207169508804376","mag":"2014836936"},"language":"en","primary_location":{"id":"doi:10.1080/00207169508804376","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169508804376","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"],"host_organization_lineage_names":["Taylor & Francis"],"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/A5086991591","display_name":"W. M. Pickering","orcid":null},"institutions":[{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"W. M. Pickering","raw_affiliation_strings":["Applied Mathematics Section , School of Mathematics and Statistics , The University, P.O. Box 597, Sheffield, S3 7RH, England"],"affiliations":[{"raw_affiliation_string":"Applied Mathematics Section , School of Mathematics and Statistics , The University, P.O. Box 597, Sheffield, S3 7RH, England","institution_ids":["https://openalex.org/I4210131439"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001050615","display_name":"P. J. Harley","orcid":null},"institutions":[{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. J. Harley","raw_affiliation_strings":["Applied Mathematics Section , School of Mathematics and Statistics , The University, P.O. Box 597, Sheffield, S3 7RH, England"],"affiliations":[{"raw_affiliation_string":"Applied Mathematics Section , School of Mathematics and Statistics , The University, P.O. Box 597, Sheffield, S3 7RH, England","institution_ids":["https://openalex.org/I4210131439"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086991591"],"corresponding_institution_ids":["https://openalex.org/I4210131439"],"apc_list":null,"apc_paid":null,"fwci":0.7053,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.66295896,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"55","issue":"3-4","first_page":"211","last_page":"222"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9993000030517578,"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":0.9993000030517578,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9991999864578247,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7853394746780396},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.7016873359680176},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.534125804901123},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.5285305380821228},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5113720297813416},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.49944400787353516},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.45492711663246155},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4468638300895691},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4233865737915039},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21893912553787231},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09535780549049377},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.07880041003227234}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7853394746780396},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.7016873359680176},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.534125804901123},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.5285305380821228},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5113720297813416},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.49944400787353516},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.45492711663246155},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4468638300895691},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4233865737915039},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21893912553787231},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09535780549049377},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.07880041003227234},{"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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169508804376","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169508804376","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"],"host_organization_lineage_names":["Taylor & Francis"],"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":17,"referenced_works":["https://openalex.org/W1541403646","https://openalex.org/W1965342489","https://openalex.org/W1984317560","https://openalex.org/W1990523337","https://openalex.org/W1991683746","https://openalex.org/W1995178279","https://openalex.org/W2001271893","https://openalex.org/W2019850180","https://openalex.org/W2023603353","https://openalex.org/W2036843998","https://openalex.org/W2045348487","https://openalex.org/W2047121664","https://openalex.org/W2068668112","https://openalex.org/W2070026366","https://openalex.org/W2093900303","https://openalex.org/W2432517183","https://openalex.org/W3214499564"],"related_works":["https://openalex.org/W4327521644","https://openalex.org/W2978884468","https://openalex.org/W2168413811","https://openalex.org/W2349221428","https://openalex.org/W2351377961","https://openalex.org/W1942228078","https://openalex.org/W2086942802","https://openalex.org/W2046073294","https://openalex.org/W2170408898","https://openalex.org/W2164136545"],"abstract_inverted_index":{"A":[0],"method":[1,106,157,194,283],"for":[2,73,131,158,265],"the":[3,15,19,40,55,62,79,88,94,105,152,176,188,210,220,231,245,269,277,282],"numerical":[4],"solution":[5,95],"of":[6,22,43,65,85,93,96,122,139,149,216,222,225,247,256,281],"non-separable":[7,160],"(self-adjoint)":[8],"elliptic":[9,161,310],"equations":[10,26,66,162,164],"is":[11,18,37,49,58,101,107,127,146,173,185],"described":[12],"in":[13,209,258,268,288],"which":[14,48,145],"basic":[16],"approach":[17,208,302],"iterative":[20,41,181,301],"application":[21,42],"direct":[23],"methods.":[24,45],"Such":[25],"may":[27,303],"be":[28,242,287,304],"transformed":[29,166],"into":[30],"Helmholtz":[31,35,56,168],"form":[32,138,169,224],"and":[33,78,125,154,170,203,239,276],"this":[34,97,137,183],"problem":[36],"solved":[38,186],"by":[39,69,187,235,295],"FFT":[44,70],"An":[46],"equation":[47,57,172,184,218],"\u2018near\u2019":[50],"(in":[51,228],"some":[52,259],"sense)":[53],"to":[54,87,109,167,199,230,286,306],"appropriately":[59],"chosen":[60],"from":[61],"general":[63,278,300,308],"class":[64],"soluble":[67],"directly":[68],"methods":[71],"(see,":[72],"example,":[74],"Le":[75],"Bail,":[76],"1972)":[77],"iteration":[80,113,123,140],"(of":[81],"block-Jacobi":[82],"form)":[83],"consists":[84],"corrections":[86],"relevant":[89],"Fourier":[90],"harmonic":[91],"amplitudes":[92],"\u2018nearby\u2019":[98,177],"equation.":[99,178],"It":[100],"also":[102,195],"shown":[103],"that":[104,244,293],"equivalent":[108],"a":[110,119,142,206,223,249,296],"D'":[111],"Yakonov-Gunn":[112],"[D'":[114],"Yakonov":[115],"(1961),":[116],"Gunn(1964)]":[117],"with":[118,134,272,292],"particular":[120],"choice":[121,215],"parameter":[124],"it":[126,240],"well":[128],"known":[129],"that,":[130],"self-adjoint":[132],"problems":[133],"smooth":[135],"coefficients,":[136],"has":[141],"convergence":[143,201,257],"rate":[144],"essentially":[147],"independent":[148],"grid-size.":[150],"In":[151],"Concus":[153,236],"Golub":[155],"(1973)":[156],"solving":[159],"such":[163,248],"are":[165,263],"Poisson's":[171],"employed":[174],"as":[175],"At":[179],"each":[180],"stage":[182],"Bunemann":[189],"(cyclic":[190],"reduction)":[191],"algorithm.":[192],"Their":[193],"uses":[196],"shifted":[197],"iterations":[198],"improve":[200,254],"rates":[202,255],"we":[204],"adopt":[205],"similar":[207],"present":[211],"study.":[212],"However,":[213],"our":[214],"nearby":[217],"allows":[219],"use":[221,246],"variable":[226,250],"shift":[227,233,251],"addition":[229],"constant":[232],"used":[234],"et":[237],"al.,)":[238],"will":[241],"demonstrated":[243],"can":[252],"considerably":[253],"examples.":[260],"Numerical":[261],"results":[262],"presented":[264],"illustrative":[266],"examples":[267],"unit":[270],"square":[271],"Dirichlet":[273],"boundary":[274],"conditions":[275],"computational":[279],"behaviour":[280],"was":[284],"found":[285],"very":[289],"good":[290],"agreement":[291],"predicted":[294],"theoretical":[297],"analysis.":[298],"The":[299],"extended":[305],"more":[307],"linear":[309],"equations.":[311]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
