{"id":"https://openalex.org/W2054052891","doi":"https://doi.org/10.1137/s1064827596303491","title":"Approximate Schur Complement Preconditioning of the Lowest-Order Nodal Discretizations","display_name":"Approximate Schur Complement Preconditioning of the Lowest-Order Nodal Discretizations","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2054052891","doi":"https://doi.org/10.1137/s1064827596303491","mag":"2054052891"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827596303491","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827596303491","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":true,"oa_status":"green","oa_url":"https://www.osti.gov/biblio/433355","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082681568","display_name":"D. Moulton","orcid":"https://orcid.org/0000-0002-9456-0871"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. David Moulton","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Jim E. Morel","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jim E. Morel","raw_affiliation_strings":["Univ. of British Columbia, Vancouver, British Columbia (Canada)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. of British Columbia, Vancouver, British Columbia (Canada)","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"last","author":{"id":null,"display_name":"Uri M. Ascher","orcid":null},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Uri M. Ascher","raw_affiliation_strings":["Los Alamos National Lab., NM (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Los Alamos National Lab., NM (United States)","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.533,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.65944222,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"19","issue":"1","first_page":"185","last_page":"205"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10514","display_name":"Numerical methods in engineering","score":0.998199999332428,"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":0.9977999925613403,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.8774113655090332},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.7773122191429138},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7709218263626099},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6634949445724487},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5875484347343445},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4841904938220978},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3337525725364685},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18799474835395813},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.15404093265533447},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.06972295045852661}],"concepts":[{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.8774113655090332},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.7773122191429138},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7709218263626099},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6634949445724487},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5875484347343445},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4841904938220978},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3337525725364685},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18799474835395813},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.15404093265533447},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.06972295045852661},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s1064827596303491","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827596303491","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.31.6970","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.6970","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.cs.ubc.ca/pub/local/ascher/papers/mma.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.54.2704","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.2704","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.iam.ubc.ca/tr/1996/iam96-06.ps.gz","raw_type":"text"},{"id":"pmh:oai:osti.gov:433355","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/433355","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null}],"best_oa_location":{"id":"pmh:oai:osti.gov:433355","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/433355","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W84303516","https://openalex.org/W1493124821","https://openalex.org/W1500537472","https://openalex.org/W1967011851","https://openalex.org/W1972099897","https://openalex.org/W1983066726","https://openalex.org/W1999331305","https://openalex.org/W2031182879","https://openalex.org/W2038535655","https://openalex.org/W2042435167","https://openalex.org/W2051345161","https://openalex.org/W2055251260","https://openalex.org/W2060128553","https://openalex.org/W2062547854","https://openalex.org/W2086164570","https://openalex.org/W2088799043","https://openalex.org/W2147243899","https://openalex.org/W2172093368","https://openalex.org/W2246442169","https://openalex.org/W2491027544","https://openalex.org/W3149667697","https://openalex.org/W3157524294"],"related_works":["https://openalex.org/W2804034492","https://openalex.org/W2138306359","https://openalex.org/W2040165403","https://openalex.org/W1965116625","https://openalex.org/W993433986","https://openalex.org/W1990747776","https://openalex.org/W2171218546","https://openalex.org/W2018155758","https://openalex.org/W2543276709","https://openalex.org/W2153295992"],"abstract_inverted_index":{"Certain":[0],"classes":[1],"of":[2,17,24,59,72,87,116],"nodal":[3],"methods":[4,9],"and":[5,14,43,131],"mixed-hybrid":[6,79],"finite":[7,80,128],"element":[8,81],"lead":[10],"to":[11,57,112,148,157],"equivalent,":[12],"robust,":[13],"accurate":[15],"discretizations":[16,26,52,130],"second-order":[18],"elliptic":[19],"PDEs.":[20],"However,":[21],"widespread":[22],"popularity":[23],"these":[25,51,117,152],"has":[27],"been":[28],"hindered":[29],"by":[30,77,103],"the":[31,60,69,73,78,113,146,149],"awkward":[32],"linear":[33,74],"systems":[34],"which":[35,46,123],"result.":[36],"The":[37],"present":[38],"work":[39],"overcomes":[40],"this":[41,101,142],"awkwardness":[42],"develops":[44],"preconditioners":[45,118],"yield":[47],"solution":[48],"algorithms":[49],"for":[50,63],"with":[53,94,126,135],"an":[54],"efficiency":[55],"comparable":[56],"that":[58],"multigrid":[61,139],"method":[62],"standard":[64,127],"discretizations.":[65],"Our":[66],"approach":[67],"exploits":[68],"natural":[70],"partitioning":[71],"system":[75],"obtained":[76,93],"method.":[82],"By":[83],"eliminating":[84],"different":[85],"subsets":[86],"unknowns,":[88],"two":[89],"Schur":[90],"complements":[91],"are":[92,154],"known":[95],"structure.":[96],"Replacing":[97],"key":[98],"matrices":[99],"in":[100],"structure":[102,122],"lumped":[104],"approximations,":[105],"we":[106,144],"define":[107],"three":[108,158],"optimal":[109,114],"preconditioners.":[110],"Central":[111],"performance":[115],"is":[119,124],"their":[120],"sparsity":[121],"compatible":[125],"difference":[129],"hence":[132],"treated":[133],"adequately":[134],"only":[136],"a":[137],"single":[138],"cycle.":[140],"In":[141],"paper":[143],"restrict":[145],"discussion":[147],"two-dimensional":[150],"case;":[151],"techniques":[153],"readily":[155],"extended":[156],"dimensions.":[159]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}