{"id":"https://openalex.org/W7125368201","doi":"https://doi.org/10.1137/25m1749311","title":"Block Triangular Preconditioners for Double Saddle-Point Linear Systems Arising in the Mixed Form of Poroelasticity Equations","display_name":"Block Triangular Preconditioners for Double Saddle-Point Linear Systems Arising in the Mixed Form of Poroelasticity Equations","publication_year":2026,"publication_date":"2026-02-05","ids":{"openalex":"https://openalex.org/W7125368201","doi":"https://doi.org/10.1137/25m1749311"},"language":"en","primary_location":{"id":"doi:10.1137/25m1749311","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1749311","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://epubs.siam.org/doi/10.1137/25M1749311","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123176635","display_name":"Luca Bergamaschi","orcid":null},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Luca Bergamaschi","raw_affiliation_strings":["Department of Civil, Environmental, and Architectural Engineering, University of Padua, Italy"],"raw_orcid":"https://orcid.org/0000-0001-8273-9674","affiliations":[{"raw_affiliation_string":"Department of Civil, Environmental, and Architectural Engineering, University of Padua, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034165194","display_name":"Massimiliano Ferronato","orcid":"https://orcid.org/0000-0002-5077-1394"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Massimiliano Ferronato","raw_affiliation_strings":["Department of Civil, Environmental, and Architectural Engineering, University of Padua, Italy"],"raw_orcid":"https://orcid.org/0000-0002-5077-1394","affiliations":[{"raw_affiliation_string":"Department of Civil, Environmental, and Architectural Engineering, University of Padua, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5123212938","display_name":"\u00c1ngeles Mart\u00ednez","orcid":null},"institutions":[{"id":"https://openalex.org/I142444530","display_name":"University of Trieste","ror":"https://ror.org/02n742c10","country_code":"IT","type":"education","lineage":["https://openalex.org/I142444530"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"\u00c1ngeles Mart\u00ednez","raw_affiliation_strings":["Corresponding author. Department of Mathematics, Informatics and Geosciences, University of Trieste, Italy"],"raw_orcid":"https://orcid.org/0000-0003-4826-1114","affiliations":[{"raw_affiliation_string":"Corresponding author. Department of Mathematics, Informatics and Geosciences, University of Trieste, Italy","institution_ids":["https://openalex.org/I142444530"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12196523,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"47","issue":"1","first_page":"132","last_page":"157"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9387000203132629,"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":0.9387000203132629,"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":0.04340000078082085,"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/T12303","display_name":"Tensor decomposition and applications","score":0.0026000000070780516,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6919999718666077},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.6833999752998352},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6740999817848206},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6299999952316284},{"id":"https://openalex.org/keywords/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.48019999265670776},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4666000008583069},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.448199987411499},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4440000057220459},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.4120999872684479},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.40630000829696655}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8756999969482422},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6919999718666077},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.6833999752998352},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6740999817848206},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6299999952316284},{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.48019999265670776},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4666000008583069},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46549999713897705},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.448199987411499},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4440000057220459},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.4120999872684479},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.40630000829696655},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4000000059604645},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.3944999873638153},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.3831000030040741},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.37630000710487366},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.3700000047683716},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.3375000059604645},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.33500000834465027},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3124000132083893},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.29280000925064087},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.2919999957084656},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.27469998598098755},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.27160000801086426},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C84507854","wikidata":"https://www.wikidata.org/wiki/Q952222","display_name":"Diagonally dominant matrix","level":3,"score":0.26489999890327454},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.2639000117778778},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.25859999656677246}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/25m1749311","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1749311","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arts.units.it:11368/3129718","is_oa":false,"landing_page_url":"https://hdl.handle.net/11368/3129718","pdf_url":null,"source":{"id":"https://openalex.org/S4306400480","display_name":"ArTS Archivio della ricerca di Trieste (University of Trieste https://www.units.it/)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142444530","host_organization_name":"University of Trieste","host_organization_lineage":["https://openalex.org/I142444530"],"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":"info:eu-repo/semantics/article"},{"id":"pmh:oai:www.research.unipd.it:11577/3575325","is_oa":true,"landing_page_url":"https://epubs.siam.org/doi/10.1137/25M1749311","pdf_url":null,"source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:www.research.unipd.it:11577/3575325","is_oa":true,"landing_page_url":"https://epubs.siam.org/doi/10.1137/25M1749311","pdf_url":null,"source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0,82],"this":[1],"paper,":[2],"we":[3],"study":[4],"a":[5,56,72,95],"class":[6],"of":[7,30,60,74,91,94,109,125,132],"inexact":[8],"block":[9,139],"triangular":[10],"preconditioners":[11,128],"for":[12,45],"double":[13,47],"saddle-point":[14,48],"symmetric":[15],"linear":[16],"systems":[17],"arising":[18],"from":[19],"the":[20,36,61,67,84,92,107,110,123,126,130,145],"mixed":[21,25],"finite":[22,27],"element":[23,28],"and":[24,77,121],"hybrid":[26],"discretization":[29],"Biot's":[31],"poroelasticity":[32],"equations.":[33],"We":[34],"extend":[35],"theoretical":[37,111],"results":[38,102],"presented":[39],"in":[40,71,89,129,135],"(Balani":[41],"et":[42],"al.,":[43],"2023)":[44],"general":[46],"problems":[49],"with":[50,98,137,144],"nonzero":[51],"diagonal":[52,140],"blocks,":[53],"by":[54],"developing":[55],"novel":[57],"spectral":[58],"analysis":[59],"preconditioned":[62],"matrix.":[63],"This":[64],"shows":[65],"that":[66],"complex":[68],"eigenvalues":[69,86],"lie":[70],"circle":[73],"center":[75],"(1,0)":[76],"radius":[78],"smaller":[79],"than":[80],"1.":[81],"contrast,":[83],"real":[85,99],"are":[87,103],"described":[88],"terms":[90],"roots":[93],"third-degree":[96],"polynomial":[97],"coefficients.":[100],"Numerical":[101],"reported":[104],"to":[105,117],"show":[106],"quality":[108],"bounds,":[112],"which":[113],"generally":[114],"turn":[115],"out":[116],"be":[118],"quite":[119],"tight,":[120],"illustrate":[122],"efficiency":[124],"proposed":[127],"acceleration":[131],"GMRES,":[133],"especially":[134],"comparison":[136],"similar":[138],"preconditioning":[141],"strategies":[142],"along":[143],"MINRES":[146],"iteration.":[147]},"counts_by_year":[],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2026-01-23T00:00:00"}
