{"id":"https://openalex.org/W3126561592","doi":"https://doi.org/10.1002/nla.2362","title":"Cell\u2010by\u2010cell approximate Schur complement technique in preconditioning of meshfree discretized piezoelectric equations","display_name":"Cell\u2010by\u2010cell approximate Schur complement technique in preconditioning of meshfree discretized piezoelectric equations","publication_year":2021,"publication_date":"2021-02-08","ids":{"openalex":"https://openalex.org/W3126561592","doi":"https://doi.org/10.1002/nla.2362","mag":"3126561592"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.2362","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5080152964","display_name":"Yang Cao","orcid":"https://orcid.org/0000-0002-5519-5197"},"institutions":[{"id":"https://openalex.org/I199305430","display_name":"Nantong University","ror":"https://ror.org/02afcvw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I199305430"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Cao","raw_affiliation_strings":["School of Transportation and Civil Engineering, Nantong University, Nantong, P.R. China"],"affiliations":[{"raw_affiliation_string":"School of Transportation and Civil Engineering, Nantong University, Nantong, P.R. China","institution_ids":["https://openalex.org/I199305430"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042698904","display_name":"Maya Neytcheva","orcid":"https://orcid.org/0000-0002-6719-4984"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Maya Neytcheva","raw_affiliation_strings":["Department of Information Technology, Uppsala University, Uppsala, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Information Technology, Uppsala University, Uppsala, Sweden","institution_ids":["https://openalex.org/I123387679"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042698904"],"corresponding_institution_ids":["https://openalex.org/I123387679"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430,"provenance":"doaj"},"apc_paid":null,"fwci":0.547,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.457119,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":76,"max":78},"biblio":{"volume":"28","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":1.0,"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":1.0,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9978,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9958,"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/krylov-subspace","display_name":"Krylov subspace","score":0.46896067}],"concepts":[{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.9119869},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.68364906},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6748581},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.46896067},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43946612},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43936113},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.34284437},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.086407214},{"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.2362","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.65,"display_name":"Peace, justice, and strong institutions","id":"https://metadata.un.org/sdg/16"}],"grants":[{"funder":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China","award_id":"11771225, 11572210"},{"funder":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det","award_id":"2017\u201003749"}],"datasets":[],"versions":[],"referenced_works_count":41,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1518160170","https://openalex.org/W1518562996","https://openalex.org/W1541162015","https://openalex.org/W18716960","https://openalex.org/W1989229028","https://openalex.org/W1992395804","https://openalex.org/W2012758668","https://openalex.org/W2019810268","https://openalex.org/W2020064379","https://openalex.org/W2026039932","https://openalex.org/W2032821273","https://openalex.org/W2037416344","https://openalex.org/W2040003476","https://openalex.org/W2050206349","https://openalex.org/W2060327589","https://openalex.org/W2071700284","https://openalex.org/W2071875410","https://openalex.org/W2082197559","https://openalex.org/W2084732065","https://openalex.org/W2108617145","https://openalex.org/W2108953660","https://openalex.org/W2116353269","https://openalex.org/W2119393586","https://openalex.org/W2130641059","https://openalex.org/W2131592900","https://openalex.org/W2134773145","https://openalex.org/W2141870784","https://openalex.org/W2142136198","https://openalex.org/W2146739464","https://openalex.org/W2148822556","https://openalex.org/W2167512083","https://openalex.org/W2259362360","https://openalex.org/W2302242104","https://openalex.org/W2403418182","https://openalex.org/W2417514618","https://openalex.org/W2481312347","https://openalex.org/W2765311738","https://openalex.org/W2899782685","https://openalex.org/W3154445565","https://openalex.org/W836818425"],"related_works":["https://openalex.org/W2789837637","https://openalex.org/W2524243948","https://openalex.org/W2106635645","https://openalex.org/W2074780612","https://openalex.org/W2069496135","https://openalex.org/W2032899988","https://openalex.org/W1966164811","https://openalex.org/W1751968827","https://openalex.org/W1660483802","https://openalex.org/W1596255161"],"abstract_inverted_index":{"Abstract":[0],"The":[1,92,158],"radial":[2],"point":[3,51],"interpolation":[4],"meshfree":[5,107],"discretization":[6,108],"is":[7,46,115,150,167,201],"a":[8,63,67,111,176,183,198],"very":[9,55,136],"efficient":[10],"numerical":[11],"framework":[12],"for":[13,65,89],"the":[14,20,34,39,42,82,103,106,118,128,147,154,161,164,192,204,214],"analysis":[15],"of":[16,48,69,84,105,146,163,194,203,206,208,213],"piezoelectricity,":[17],"in":[18,78,102,141],"which":[19,133],"fundamental":[21],"electrostatic":[22],"equations":[23,149],"governing":[24],"piezoelectric":[25,40,148,177,184],"media":[26],"are":[27,97,124],"solved":[28],"without":[29],"mesh":[30],"generation.":[31],"Due":[32],"to":[33,75,80,127,135,152,196],"mechanical\u2010electrical":[35],"coupling":[36],"property":[37],"and":[38,53,99,109,160,182],"constant,":[41],"discrete":[43],"linear":[44],"system":[45],"sparse,":[47],"generalized":[49],"saddle":[50],"form":[52],"often":[54],"ill":[56],"conditioned.":[57],"In":[58,143],"this":[59],"work,":[60],"we":[61],"propose":[62],"technique":[64],"constructing":[66],"family":[68],"cell\u2010by\u2010cell":[70],"approximate":[71,93,120],"Schur":[72,94,121,130],"complement":[73,95,122,131],"matrices,":[74],"be":[76],"used":[77,140],"preconditioning":[79],"accelerate":[81],"convergence":[83,138],"Krylov":[85],"subspace":[86],"iteration":[87],"methods":[88],"such":[90],"problems.":[91],"matrices":[96,123],"simply":[98],"cheaply":[100],"constructed":[101],"process":[104],"have":[110],"sparse":[112],"structure.":[113],"It":[114],"proved":[116],"that":[117,191],"so\u2010constructed":[119],"spectrally":[125],"equivalent":[126],"exact":[129],"matrix,":[132],"leads":[134],"fast":[137],"when":[139],"preconditioning.":[142],"addition,":[144],"nondimensionalization":[145],"considered":[151],"make":[153],"computations":[155],"more":[156],"stable.":[157],"robustness":[159],"efficiency":[162],"proposed":[165],"preconditioners":[166],"illustrated":[168],"numerically":[169],"on":[170],"two":[171],"test":[172],"problems,":[173],"arising":[174],"from":[175],"strip":[178,185],"shear":[179],"deformation":[180],"problem":[181,216],"bending":[186],"problem.":[187],"Numerical":[188],"results":[189],"show":[190],"number":[193,205],"iterations":[195],"achieve":[197],"given":[199],"tolerance":[200],"independent":[202],"degrees":[207],"freedom":[209],"as":[210,212],"well":[211],"various":[215],"parameters.":[217]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3126561592","counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2025-01-21T03:00:11.792504","created_date":"2021-02-15"}