{"id":"https://openalex.org/W2030447882","doi":"https://doi.org/10.1137/08072749x","title":"Iterative Solution of Piecewise Linear Systems and Applications to Flows in Porous Media","display_name":"Iterative Solution of Piecewise Linear Systems and Applications to Flows in Porous Media","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2030447882","doi":"https://doi.org/10.1137/08072749x","mag":"2030447882"},"language":"en","primary_location":{"id":"doi:10.1137/08072749x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/08072749x","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036669637","display_name":"Luigi Brugnano","orcid":"https://orcid.org/0000-0002-6290-4107"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Luigi Brugnano","raw_affiliation_strings":["luigi.brugnano@unifi.it#TAB#"],"affiliations":[{"raw_affiliation_string":"luigi.brugnano@unifi.it#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023914916","display_name":"V Casulli","orcid":"https://orcid.org/0000-0002-2398-9339"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vincenzo Casulli","raw_affiliation_strings":["vincenzo.casulli@unitn.it#TAB#"],"affiliations":[{"raw_affiliation_string":"vincenzo.casulli@unitn.it#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036669637"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5518,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.9292121,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"31","issue":"3","first_page":"1858","last_page":"1873"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9988999962806702,"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/T11416","display_name":"Numerical methods for differential equations","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.813498854637146},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7994530200958252},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7181484699249268},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5877455472946167},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5413117408752441},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.5205827355384827},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5179969072341919},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5042866468429565},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4919013977050781},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4890962243080139},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47466376423835754},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47260433435440063},{"id":"https://openalex.org/keywords/constant-function","display_name":"Constant function","score":0.462380588054657},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4326291084289551},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.41574087738990784},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4116935133934021},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21741995215415955},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.1572175920009613},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08058664202690125},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07857018709182739}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.813498854637146},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7994530200958252},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7181484699249268},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5877455472946167},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5413117408752441},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.5205827355384827},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5179969072341919},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5042866468429565},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4919013977050781},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4890962243080139},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47466376423835754},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47260433435440063},{"id":"https://openalex.org/C153658351","wikidata":"https://www.wikidata.org/wiki/Q746264","display_name":"Constant function","level":3,"score":0.462380588054657},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4326291084289551},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.41574087738990784},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4116935133934021},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21741995215415955},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.1572175920009613},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08058664202690125},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07857018709182739},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/08072749x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/08072749x","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:10.1.1.484.6373","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.484.6373","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.math.unifi.it/users/brugnano/preprint/SISC-072749R.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.718.687","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.718.687","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.math.unifi.it/users/brugnano/papers/sisc_31_%282009%29_1858-1873.pdf","raw_type":"text"},{"id":"pmh:oai:flore.unifi.it:2158/324985","is_oa":false,"landing_page_url":"http://hdl.handle.net/2158/324985","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.unitn.it:11572/79800","is_oa":false,"landing_page_url":"http://hdl.handle.net/11572/79800","pdf_url":null,"source":{"id":"https://openalex.org/S4306401913","display_name":"Institutional Research Information System (Universit\u00e0 degli Studi di Trento)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193223587","host_organization_name":"University of Trento","host_organization_lineage":["https://openalex.org/I193223587"],"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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1488435683","https://openalex.org/W1506342804","https://openalex.org/W1512127157","https://openalex.org/W1975941105","https://openalex.org/W1981745143","https://openalex.org/W1982391474","https://openalex.org/W2020863487","https://openalex.org/W2033798957","https://openalex.org/W2053643774","https://openalex.org/W2060151887","https://openalex.org/W2071145489","https://openalex.org/W2087322512","https://openalex.org/W2104679917","https://openalex.org/W2148498476","https://openalex.org/W2295470351"],"related_works":["https://openalex.org/W2133947431","https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W3208509670","https://openalex.org/W2051018371","https://openalex.org/W2888635693","https://openalex.org/W2109304297","https://openalex.org/W2048747447","https://openalex.org/W2100864966","https://openalex.org/W2490196280"],"abstract_inverted_index":{"The":[0,39,60],"correct":[1],"numerical":[2,94],"modeling":[3,102],"of":[4,14,26,54,81,103],"free-surface":[5],"hydrodynamic":[6],"problems":[7],"often":[8],"requires":[9],"to":[10,48,64,73],"have":[11,65],"the":[12,27,41,55,100],"solution":[13,28,76],"special":[15],"linear":[16,52],"systems":[17],"whose":[18],"coefficient":[19],"matrix":[20],"is":[21],"a":[22,50,66,78,92],"piecewise":[23,51],"constant":[24],"function":[25],"itself.":[29],"In":[30],"doing":[31],"so,":[32],"one":[33],"may":[34],"fulfill":[35],"relevant":[36],"physical":[37],"constraints.":[38],"existence,":[40],"uniqueness,":[42],"and":[43],"two":[44],"constructive":[45],"iterative":[46],"methods":[47,61],"solve":[49],"system":[53],"form":[56],"$\\max[\\boldsymbol{l},\\min(\\boldsymbol{u},\\mathbf{x})]+T\\mathbf{x}=\\mathbf{b}$":[57],"are":[58,62,97],"analyzed.":[59],"shown":[63],"finite":[67,79],"termination":[68],"property;":[69],"i.e.,":[70],"they":[71,85],"converge":[72,86],"an":[74],"exact":[75],"in":[77,105],"number":[80],"steps":[82],"and,":[83],"actually,":[84],"very":[87],"quickly,":[88],"as":[89],"confirmed":[90],"by":[91],"few":[93],"tests,":[95],"which":[96],"derived":[98],"from":[99],"mathematical":[101],"flows":[104],"porous":[106],"media.":[107]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}