{"id":"https://openalex.org/W7165638138","doi":"https://doi.org/10.1137/25m1731253","title":"An Efficient Preconditioner for Mixed-Dimensional Contact Poromechanics Based on the Fixed Stress Splitting Scheme","display_name":"An Efficient Preconditioner for Mixed-Dimensional Contact Poromechanics Based on the Fixed Stress Splitting Scheme","publication_year":2026,"publication_date":"2026-06-23","ids":{"openalex":"https://openalex.org/W7165638138","doi":"https://doi.org/10.1137/25m1731253"},"language":"en","primary_location":{"id":"doi:10.1137/25m1731253","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1731253","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2501.07441","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093734312","display_name":"Yury Zabegaev","orcid":"https://orcid.org/0009-0006-7095-3044"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Yury Zabegaev","raw_affiliation_strings":["Center for Modeling of Coupled Subsurface Dynamics, Department of Mathematics, University of Bergen, Bergen, Norway"],"raw_orcid":"https://orcid.org/0009-0006-7095-3044","affiliations":[{"raw_affiliation_string":"Center for Modeling of Coupled Subsurface Dynamics, Department of Mathematics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023075206","display_name":"Inga Berre","orcid":"https://orcid.org/0000-0002-0212-7959"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Inga Berre","raw_affiliation_strings":["Center for Modeling of Coupled Subsurface Dynamics, Department of Mathematics, University of Bergen, Bergen, Norway"],"raw_orcid":"https://orcid.org/0000-0002-0212-7959","affiliations":[{"raw_affiliation_string":"Center for Modeling of Coupled Subsurface Dynamics, Department of Mathematics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016158002","display_name":"Eirik Keilegavlen","orcid":"https://orcid.org/0000-0002-0333-9507"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Eirik Keilegavlen","raw_affiliation_strings":["Center for Modeling of Coupled Subsurface Dynamics, Department of Mathematics, University of Bergen, Bergen, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Modeling of Coupled Subsurface Dynamics, Department of Mathematics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101419280","display_name":"Kundan Kumar","orcid":"https://orcid.org/0000-0002-3784-4819"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Kundan Kumar","raw_affiliation_strings":["Center for Modeling of Coupled Subsurface Dynamics, Department of Mathematics, University of Bergen, Bergen, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Modeling of Coupled Subsurface Dynamics, Department of Mathematics, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4432739"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.83100931,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"48","issue":"3","first_page":"A1785","last_page":"A1810"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.26919999718666077,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.26919999718666077,"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/T11366","display_name":"Elasticity and Material Modeling","score":0.13220000267028809,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10514","display_name":"Numerical methods in engineering","score":0.07590000331401825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.6359999775886536},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5715000033378601},{"id":"https://openalex.org/keywords/poromechanics","display_name":"Poromechanics","score":0.5486000180244446},{"id":"https://openalex.org/keywords/stress","display_name":"Stress (linguistics)","score":0.382999986410141},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.36910000443458557},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3384000062942505}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7281000018119812},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.6359999775886536},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5715000033378601},{"id":"https://openalex.org/C181965411","wikidata":"https://www.wikidata.org/wiki/Q2314330","display_name":"Poromechanics","level":4,"score":0.5486000180244446},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4925000071525574},{"id":"https://openalex.org/C21036866","wikidata":"https://www.wikidata.org/wiki/Q181767","display_name":"Stress (linguistics)","level":2,"score":0.382999986410141},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3790000081062317},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.36910000443458557},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3384000062942505},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.33640000224113464},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30720001459121704},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C2988766672","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference scheme","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C2987355758","wikidata":"https://www.wikidata.org/wiki/Q25037251","display_name":"Operator splitting","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2531999945640564},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/25m1731253","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1731253","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:arXiv.org:2501.07441","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2501.07441","pdf_url":"https://arxiv.org/pdf/2501.07441","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2501.07441","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2501.07441","pdf_url":"https://arxiv.org/pdf/2501.07441","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4281890445","display_name":null,"funder_award_id":"308733","funder_id":"https://openalex.org/F4320323299","funder_display_name":"Norges Forskningsr\u00e5d"}],"funders":[{"id":"https://openalex.org/F4320323299","display_name":"Norges Forskningsr\u00e5d","ror":"https://ror.org/00epmv149"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W7165638138.pdf"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1530030810","https://openalex.org/W1969593637","https://openalex.org/W1972326999","https://openalex.org/W1973776666","https://openalex.org/W1990759037","https://openalex.org/W1998570005","https://openalex.org/W2001032894","https://openalex.org/W2034584048","https://openalex.org/W2044686992","https://openalex.org/W2044751804","https://openalex.org/W2052138618","https://openalex.org/W2094293004","https://openalex.org/W2112311198","https://openalex.org/W2121005322","https://openalex.org/W2141870784","https://openalex.org/W2265775362","https://openalex.org/W2292681641","https://openalex.org/W2470472984","https://openalex.org/W2575247701","https://openalex.org/W2883853367","https://openalex.org/W2889279000","https://openalex.org/W2898271452","https://openalex.org/W2901819592","https://openalex.org/W2911701814","https://openalex.org/W2916712392","https://openalex.org/W2921485495","https://openalex.org/W2944273318","https://openalex.org/W2962796483","https://openalex.org/W2964076483","https://openalex.org/W2973116097","https://openalex.org/W2976101081","https://openalex.org/W2996279215","https://openalex.org/W3049070198","https://openalex.org/W3092750238","https://openalex.org/W3199777780","https://openalex.org/W3212743457","https://openalex.org/W4229059513","https://openalex.org/W4280488160","https://openalex.org/W4294266227","https://openalex.org/W4299968561","https://openalex.org/W4302775077","https://openalex.org/W4313528170","https://openalex.org/W4385977944","https://openalex.org/W4390959581"],"related_works":[],"abstract_inverted_index":{"Numerical":[0],"simulation":[1,50],"of":[2,42,48,104,111,121,154,184,206,214],"fracture":[3,171],"contact":[4,40,93,106,156,178],"poromechanics":[5,37,130],"is":[6,78,97],"essential":[7],"for":[8,56],"various":[9],"applications,":[10],"including":[11],"CO2":[12],"sequestration,":[13],"geothermal":[14],"energy":[15],"production":[16],"and":[17,38,46,92,170,191,204],"underground":[18],"gas":[19],"storage.":[20],"Modeling":[21],"this":[22,133],"problem":[23],"accurately":[24],"presents":[25],"significant":[26],"challenges":[27],"due":[28],"to":[29,127,166],"the":[30,49,57,62,101,105,112,118,122,129,151,155,162,168,177,182,185,207],"complex":[31],"physics":[32],"involved":[33],"in":[34,69],"strongly":[35],"coupled":[36],"frictional":[39],"mechanics":[41,107,157,179],"fractures.":[43],"The":[44,95,202],"robustness":[45,205],"efficiency":[47],"heavily":[51],"depends":[52],"on":[53],"a":[54,109,137,146,199,212],"preconditioner":[55,77,138],"linear":[58,147],"solver,":[59],"which":[60,116,149],"addresses":[61,150],"Jacobian":[63],"matrices":[64],"arising":[65],"from":[66],"Newton's":[67],"method":[68,208],"fully":[70],"implicit":[71],"time-stepping":[72],"schemes.":[73],"Developing":[74],"an":[75],"effective":[76],"difficult":[79],"because":[80],"it":[81,194],"must":[82],"decouple":[83,128],"three":[84],"interdependent":[85],"subproblems:":[86],"momentum":[87],"balance,":[88,91],"fluid":[89],"mass":[90],"mechanics.":[94],"challenge":[96],"further":[98],"compounded":[99],"by":[100],"saddle-point":[102],"structure":[103],"problem,":[108],"result":[110],"Augmented":[113],"Lagrange":[114],"formulation,":[115],"hinders":[117],"direct":[119],"application":[120],"well-established":[123],"fixed":[124,163,187],"stress":[125,164],"approximation":[126],"subproblem.":[131,158],"In":[132],"work,":[134],"we":[135],"propose":[136],"hat":[139],"combines":[140],"nested":[141],"Schur":[142],"complement":[143],"approximations":[144],"with":[145],"transformation,":[148],"singular":[152],"nature":[153],"This":[159],"approach":[160],"extends":[161],"scheme":[165,190],"both":[167],"matrix":[169],"subdomains.":[172],"We":[173],"investigate":[174],"analytically":[175],"how":[176,193],"subproblem":[180],"affects":[181],"convergence":[183],"proposed":[186],"stress-based":[188],"iterative":[189],"demonstrate":[192],"can":[195],"be":[196],"translated":[197],"into":[198],"practical":[200],"preconditioner.":[201],"scalability":[203],"are":[209],"validated":[210],"through":[211],"series":[213],"numerical":[215],"experiments.":[216]},"counts_by_year":[],"updated_date":"2026-06-24T06:22:24.138952","created_date":"2026-06-24T00:00:00"}
