{"id":"https://openalex.org/W2036614641","doi":"https://doi.org/10.1137/0911019","title":"Finite-Element Preconditioning for Pseudospectral Solutions of Elliptic Problems","display_name":"Finite-Element Preconditioning for Pseudospectral Solutions of Elliptic Problems","publication_year":1990,"publication_date":"1990-03-01","ids":{"openalex":"https://openalex.org/W2036614641","doi":"https://doi.org/10.1137/0911019","mag":"2036614641"},"language":"en","primary_location":{"id":"doi:10.1137/0911019","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0911019","pdf_url":null,"source":{"id":"https://openalex.org/S4210181992","display_name":"SIAM Journal on Scientific and Statistical Computing","issn_l":"0196-5204","issn":["0196-5204","2168-3417"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 and Statistical 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/A5111816784","display_name":"Michel Deville","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. O. Deville","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5062588575","display_name":"E. H. Mund","orcid":"https://orcid.org/0000-0003-3462-6004"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"E. H. Mund","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.5988,"has_fulltext":false,"cited_by_count":101,"citation_normalized_percentile":{"value":0.96218359,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"11","issue":"2","first_page":"311","last_page":"342"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994999766349792,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994000196456909,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9993000030517578,"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":0.8043920993804932},{"id":"https://openalex.org/keywords/pseudospectral-optimal-control","display_name":"Pseudospectral optimal control","score":0.6564810872077942},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6350593566894531},{"id":"https://openalex.org/keywords/gauss-pseudospectral-method","display_name":"Gauss pseudospectral method","score":0.48119741678237915},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4668481945991516},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.44626399874687195},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.44390690326690674},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44234076142311096},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4283137321472168},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.4142095744609833},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.41182056069374084},{"id":"https://openalex.org/keywords/pseudo-spectral-method","display_name":"Pseudo-spectral method","score":0.3658134937286377},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.11930438876152039},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.10323870182037354}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8043920993804932},{"id":"https://openalex.org/C154304650","wikidata":"https://www.wikidata.org/wiki/Q7255577","display_name":"Pseudospectral optimal control","level":5,"score":0.6564810872077942},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6350593566894531},{"id":"https://openalex.org/C71026131","wikidata":"https://www.wikidata.org/wiki/Q5527825","display_name":"Gauss pseudospectral method","level":5,"score":0.48119741678237915},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4668481945991516},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.44626399874687195},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.44390690326690674},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44234076142311096},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4283137321472168},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.4142095744609833},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.41182056069374084},{"id":"https://openalex.org/C177937620","wikidata":"https://www.wikidata.org/wiki/Q7254447","display_name":"Pseudo-spectral method","level":4,"score":0.3658134937286377},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.11930438876152039},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.10323870182037354},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.0},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0911019","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0911019","pdf_url":null,"source":{"id":"https://openalex.org/S4210181992","display_name":"SIAM Journal on Scientific and Statistical Computing","issn_l":"0196-5204","issn":["0196-5204","2168-3417"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 and Statistical Computing","raw_type":"journal-article"},{"id":"pmh:oai:dial.uclouvain.be:boreal:51909","is_oa":false,"landing_page_url":"http://hdl.handle.net/2078.1/51909","pdf_url":null,"source":{"id":"https://openalex.org/S4306400166","display_name":"Digital Access to Libraries","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800384882","host_organization_name":"Harris County Public Library","host_organization_lineage":["https://openalex.org/I2800384882"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific and Statistical Computing, Vol. 11, no. 2, p. 311-342 (1990)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1511154369","https://openalex.org/W1590879322","https://openalex.org/W1749747674","https://openalex.org/W1985144286","https://openalex.org/W1988233945","https://openalex.org/W1997701847","https://openalex.org/W2009524444","https://openalex.org/W2014289408","https://openalex.org/W2030348253","https://openalex.org/W2033702923","https://openalex.org/W2041523977","https://openalex.org/W2051567707","https://openalex.org/W2058304101","https://openalex.org/W2062618977","https://openalex.org/W2065006139","https://openalex.org/W2069736604","https://openalex.org/W2073732659","https://openalex.org/W2269031643","https://openalex.org/W3022074680","https://openalex.org/W4297937075","https://openalex.org/W4298060601","https://openalex.org/W4300934284","https://openalex.org/W4300938688"],"related_works":["https://openalex.org/W2550657075","https://openalex.org/W1512809069","https://openalex.org/W2761671048","https://openalex.org/W2357738898","https://openalex.org/W2029764875","https://openalex.org/W2281601070","https://openalex.org/W2143234151","https://openalex.org/W2166683827","https://openalex.org/W2356744059","https://openalex.org/W4387187495"],"abstract_inverted_index":{"A":[0],"preconditioning":[1,115],"technique":[2,23],"for":[3,91],"pseudospectral":[4,22],"solutions":[5],"of":[6,43,77,95,121],"elliptic":[7],"problems":[8,62],"based":[9,30],"on":[10,31],"quadrangular":[11],"finite-element":[12,50,112],"algorithms":[13],"is":[14,24,81,131],"analyzed,":[15],"which":[16],"exhibits":[17],"excellent":[18],"convergence":[19,100],"properties.":[20],"The":[21,109],"implemented":[25],"through":[26],"a":[27,92,106,125],"collocation":[28],"grid":[29],"Gauss\u2013Lobatto":[32],"quadrature":[33],"nodes":[34],"associated":[35],"to":[36,89,124],"the":[37,49,74,78,83,119,122],"Jacobi":[38],"orthogonal":[39],"polynomials.":[40],"Various":[41],"types":[42],"basis":[44],"functions":[45],"are":[46,63,116],"used":[47],"in":[48,65,105],"preconditioner":[51],"(i.e.,":[52],"low-order":[53],"Lagrange":[54],"or":[55],"cubic":[56],"Hermite":[57],"elements).":[58],"Dirichlet":[59],"and":[60,67,86,113],"Neumann":[61],"investigated":[64],"one-":[66],"two-space":[68],"dimensions.":[69],"Numerical":[70],"results":[71],"show":[72],"that":[73],"eigenvalue":[75],"spectrum":[76],"iteration":[79],"matrix":[80],"inside":[82],"unit":[84],"circle":[85],"even,":[87],"close":[88],"zero":[90],"wide":[93],"range":[94],"operators.":[96],"This":[97],"property":[98],"ensures":[99],"until":[101],"roundoff":[102],"error":[103],"level":[104],"few":[107],"iterations.":[108],"differences":[110],"between":[111],"finite-difference":[114],"analyzed.":[117],"Finally,":[118],"application":[120],"algorithm":[123],"problem":[126],"exhibiting":[127],"geometric":[128],"induced":[129],"singularities":[130],"discussed.":[132]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}