{"id":"https://openalex.org/W3112068269","doi":"https://doi.org/10.1007/s10915-020-01372-0","title":"Preconditioning Techniques for the Numerical Solution of Flow in Fractured Porous Media","display_name":"Preconditioning Techniques for the Numerical Solution of Flow in Fractured Porous Media","publication_year":2020,"publication_date":"2020-12-11","ids":{"openalex":"https://openalex.org/W3112068269","doi":"https://doi.org/10.1007/s10915-020-01372-0","mag":"3112068269"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-020-01372-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-020-01372-0","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s10915-020-01372-0","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063675442","display_name":"Paola F. Antonietti","orcid":"https://orcid.org/0000-0002-2138-3878"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Paola F. Antonietti","raw_affiliation_strings":["MOX, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy","MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MOX, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046736304","display_name":"Jacopo De Ponti","orcid":null},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Jacopo De Ponti","raw_affiliation_strings":["MOX, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy","MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MOX, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030787381","display_name":"Luca Formaggia","orcid":"https://orcid.org/0000-0003-2628-1683"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Luca Formaggia","raw_affiliation_strings":["MOX, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy","MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy"],"raw_orcid":"https://orcid.org/0000-0003-2628-1683","affiliations":[{"raw_affiliation_string":"MOX, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048895792","display_name":"Anna Scotti","orcid":"https://orcid.org/0000-0002-1859-0024"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Anna Scotti","raw_affiliation_strings":["MOX, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy","MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MOX, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"MOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5030787381","https://openalex.org/A5046736304","https://openalex.org/A5048895792","https://openalex.org/A5063675442"],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.7202,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.67492318,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"86","issue":"1","first_page":null,"last_page":null},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9991999864578247,"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":0.9979000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.837489128112793},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7863452434539795},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.6631045937538147},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5312751531600952},{"id":"https://openalex.org/keywords/darcys-law","display_name":"Darcy's law","score":0.5156984925270081},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5121185779571533},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5074414610862732},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4949764609336853},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.49484843015670776},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.45066913962364197},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4354018568992615},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4148682951927185},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.4130278527736664},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3405168950557709},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.31336334347724915},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.23198950290679932},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17479223012924194},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16893219947814941},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.06080067157745361}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.837489128112793},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7863452434539795},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.6631045937538147},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5312751531600952},{"id":"https://openalex.org/C183447037","wikidata":"https://www.wikidata.org/wiki/Q392416","display_name":"Darcy's law","level":4,"score":0.5156984925270081},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5121185779571533},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5074414610862732},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4949764609336853},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.49484843015670776},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.45066913962364197},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4354018568992615},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4148682951927185},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4130278527736664},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3405168950557709},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31336334347724915},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.23198950290679932},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17479223012924194},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16893219947814941},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.06080067157745361},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10915-020-01372-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-020-01372-0","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:re.public.polimi.it:11311/1155462","is_oa":true,"landing_page_url":"http://hdl.handle.net/11311/1155462","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10915-020-01372-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-020-01372-0","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3039731318","display_name":null,"funder_award_id":"201744KLJL","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G8495165288","display_name":null,"funder_award_id":"SIR RBSI14VT0S","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W178921856","https://openalex.org/W592911714","https://openalex.org/W1530030810","https://openalex.org/W1549748890","https://openalex.org/W1646924155","https://openalex.org/W1673742782","https://openalex.org/W1964990176","https://openalex.org/W1968754888","https://openalex.org/W1969974650","https://openalex.org/W1972081361","https://openalex.org/W1973709085","https://openalex.org/W1988443077","https://openalex.org/W1991785777","https://openalex.org/W2001067676","https://openalex.org/W2010549570","https://openalex.org/W2018850201","https://openalex.org/W2029367872","https://openalex.org/W2030683327","https://openalex.org/W2033877479","https://openalex.org/W2042387166","https://openalex.org/W2042694208","https://openalex.org/W2043994920","https://openalex.org/W2048972778","https://openalex.org/W2051917325","https://openalex.org/W2073237186","https://openalex.org/W2080233464","https://openalex.org/W2081622703","https://openalex.org/W2083875017","https://openalex.org/W2085581918","https://openalex.org/W2089024363","https://openalex.org/W2094293004","https://openalex.org/W2094336633","https://openalex.org/W2097964994","https://openalex.org/W2098763399","https://openalex.org/W2116404756","https://openalex.org/W2121613024","https://openalex.org/W2124633526","https://openalex.org/W2133248904","https://openalex.org/W2140153041","https://openalex.org/W2141870784","https://openalex.org/W2147874172","https://openalex.org/W2168914934","https://openalex.org/W2188276974","https://openalex.org/W2404390473","https://openalex.org/W2552188572","https://openalex.org/W2615979748","https://openalex.org/W2627064343","https://openalex.org/W2724697992","https://openalex.org/W2734812188","https://openalex.org/W2797266132","https://openalex.org/W2804722640","https://openalex.org/W2907521988","https://openalex.org/W2908252308","https://openalex.org/W2962837672","https://openalex.org/W2963898481","https://openalex.org/W2964307594","https://openalex.org/W3004023006","https://openalex.org/W3008420272","https://openalex.org/W3008798357","https://openalex.org/W3040088525","https://openalex.org/W3080755743","https://openalex.org/W3100761649","https://openalex.org/W4211094263","https://openalex.org/W4231405723","https://openalex.org/W4293028925","https://openalex.org/W6687471308"],"related_works":["https://openalex.org/W2330640442","https://openalex.org/W2392533133","https://openalex.org/W2617981106","https://openalex.org/W4251142058","https://openalex.org/W1965041963","https://openalex.org/W2766044013","https://openalex.org/W2007426143","https://openalex.org/W2384221708","https://openalex.org/W2171402820","https://openalex.org/W2044635454"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"work":[2],"deals":[3],"with":[4],"the":[5,10,34,50,57,64,82,94,97],"efficient":[6],"iterative":[7,78],"solution":[8],"of":[9,12,20,37,63,69,77,96],"system":[11],"equations":[13],"stemming":[14],"from":[15],"mimetic":[16,44],"finite":[17,45,54],"difference":[18],"discretization":[19],"a":[21,38,67],"hybrid-dimensional":[22],"mixed":[23,39],"Darcy":[24],"problem":[25],"modeling":[26],"flow":[27,48],"in":[28,49,66],"fractured":[29],"porous":[30],"media.":[31],"We":[32],"investigate":[33],"spectral":[35],"properties":[36,95],"discrete":[40,84],"formulation":[41],"based":[42],"on":[43,88],"differences":[46],"for":[47,56],"bulk":[51],"matrix":[52],"and":[53,59],"volumes":[55],"fractures,":[58],"present":[60],"an":[61],"approximation":[62],"factors":[65],"set":[68],"approximate":[70],"block":[71],"factorization":[72],"preconditioners":[73],"that":[74],"accelerates":[75],"convergence":[76],"solvers":[79],"applied":[80],"to":[81],"resulting":[83],"system.":[85],"Numerical":[86],"tests":[87],"significant":[89],"three-dimensional":[90],"cases":[91],"have":[92],"assessed":[93],"proposed":[98],"preconditioners.":[99]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}