{"id":"https://openalex.org/W4285100302","doi":"https://doi.org/10.1145/3539781.3539796","title":"On the construction of AMG prolongation through energy minimization","display_name":"On the construction of AMG prolongation through energy minimization","publication_year":2022,"publication_date":"2022-06-27","ids":{"openalex":"https://openalex.org/W4285100302","doi":"https://doi.org/10.1145/3539781.3539796"},"language":"en","primary_location":{"id":"doi:10.1145/3539781.3539796","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3539781.3539796","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Platform for Advanced Scientific Computing Conference","raw_type":"proceedings-article"},"type":"conference-paper","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/A5030722968","display_name":"Giovanni Isotton","orcid":"https://orcid.org/0000-0002-1548-2378"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giovanni Isotton","raw_affiliation_strings":["M3E S.r.l., Padova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"M3E S.r.l., Padova, Italy","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086445027","display_name":"Andrea Franceschini","orcid":"https://orcid.org/0000-0003-4395-5125"},"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":"Andrea Franceschini","raw_affiliation_strings":["University of Padova, Padova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Padova, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066565638","display_name":"Carlo Janna","orcid":"https://orcid.org/0000-0001-7286-8122"},"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":"Carlo Janna","raw_affiliation_strings":["University of Padova Padova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Padova Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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":0.08400413,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"37","issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9995999932289124,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9944000244140625,"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/mathematical-optimization","display_name":"Mathematical optimization","score":0.5709857940673828},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5653723478317261},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5215299129486084},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5200942754745483},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.5017244815826416},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4925616383552551},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45549023151397705},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4213102459907532},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4194273352622986},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.4182608425617218},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40955930948257446},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3761642575263977},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.35188135504722595},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.1950511932373047},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.1229654848575592}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5709857940673828},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5653723478317261},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5215299129486084},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5200942754745483},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.5017244815826416},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4925616383552551},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45549023151397705},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4213102459907532},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4194273352622986},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.4182608425617218},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40955930948257446},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3761642575263977},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.35188135504722595},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.1950511932373047},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.1229654848575592},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3539781.3539796","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3539781.3539796","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Platform for Advanced Scientific Computing Conference","raw_type":"proceedings-article"},{"id":"pmh:oai:www.research.unipd.it:11577/3453022","is_oa":false,"landing_page_url":"http://hdl.handle.net/11577/3453022","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8999999761581421}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1966756606","https://openalex.org/W1967983557","https://openalex.org/W1981142209","https://openalex.org/W2009250131","https://openalex.org/W2031859223","https://openalex.org/W2032718616","https://openalex.org/W2042913171","https://openalex.org/W2069340633","https://openalex.org/W2075536798","https://openalex.org/W2095318027","https://openalex.org/W2106088594","https://openalex.org/W2141870784","https://openalex.org/W2142304406","https://openalex.org/W2252040419","https://openalex.org/W2335262827","https://openalex.org/W2531839392","https://openalex.org/W2605147253","https://openalex.org/W2808718522","https://openalex.org/W2908144813","https://openalex.org/W2912759508","https://openalex.org/W2946073031","https://openalex.org/W2963109303","https://openalex.org/W2963889991","https://openalex.org/W2964264054","https://openalex.org/W3098359859","https://openalex.org/W3202697353"],"related_works":["https://openalex.org/W2018388178","https://openalex.org/W2106635645","https://openalex.org/W2074780612","https://openalex.org/W1596255161","https://openalex.org/W2032899988","https://openalex.org/W2171218546","https://openalex.org/W2069496135","https://openalex.org/W2524243948","https://openalex.org/W1991081991","https://openalex.org/W1751968827"],"abstract_inverted_index":{"Algebraic":[0],"Multigrid":[1],"(AMG)":[2],"is":[3,16,34,54,105,146,165],"a":[4,42,57,135,208,246],"very":[5],"popular":[6],"iterative":[7,212],"method":[8],"used":[9],"in":[10,21,83,167],"several":[11],"applications.":[12],"This":[13,53],"wide":[14],"diffusion":[15,78],"due":[17,175],"to":[18,40,94,107,121,176,187,200,223,231],"its":[19,35,154,178],"effectiveness":[20],"solving":[22],"linear":[23],"systems":[24],"arising":[25,73],"from":[26,74],"PDEs":[27],"discretization.":[28],"The":[29],"key":[30],"feature":[31],"of":[32,46],"AMG":[33,110,169],"optimality,":[36],"i.e.,":[37],"the":[38,47,61,64,84,109,144,148,158,168,215,226,238],"ability":[39],"guarantee":[41],"convergence":[43,239],"rate":[44,240],"independent":[45],"mesh":[48],"size":[49],"for":[50,67],"different":[51],"problems.":[52],"obtained":[55],"through":[56,192],"good":[58],"interplay":[59],"between":[60],"smoother":[62],"and":[63,88,126,153,180,195,214],"interpolation.":[65],"Unfortunately,":[66],"difficult":[68,181],"problems,":[69],"such":[70],"as":[71,134],"those":[72],"structural":[75],"mechanics":[76],"or":[77],"problems":[79],"with":[80],"large":[81],"jumps":[82],"coefficients,":[85],"standard":[86],"smoothers":[87],"interpolation":[89],"techniques":[90],"are":[91],"not":[92],"enough":[93],"ensure":[95],"fast":[96],"convergence.":[97],"In":[98,112,139,198],"these":[99],"cases,":[100],"an":[101,117,122],"improved":[102],"prolongation":[103,119,149],"operator":[104,159],"required":[106],"enhance":[108],"effectiveness.":[111],"this":[113,129,202],"work,":[114],"we":[115,141,184,204,235],"present":[116],"updated":[118],"according":[120],"energy":[123,163,189],"minimization":[124,130,137,164,190],"criterion":[125],"show":[127],"how":[128,237],"can":[131,220,241],"be":[132,151,221,242],"seen":[133],"constrained":[136],"problem.":[138],"detail,":[140],"have":[142],"that":[143],"constraint":[145],"twofold:":[147],"must":[150,156],"sparse,":[152],"range":[155],"represent":[157],"near-kernel.":[160],"Even":[161],"though":[162],"well-known":[166],"community,":[170],"it":[171],"has":[172],"little":[173],"application":[174],"both":[177],"cost":[179],"implementation.":[182,197],"Here,":[183],"would":[185],"like":[186],"make":[188],"feasible":[191],"suitable":[193],"preconditioned":[194,222],"effective":[196],"particular,":[199],"solve":[201],"problem,":[203],"propose":[205],"two":[206],"strategies:":[207],"restricted":[209],"Krylov":[210],"subspace":[211],"procedure":[213],"null-space":[216],"method.":[217],"Both":[218],"approaches":[219],"speed":[224],"up":[225],"setup":[227,248],"time.":[228],"Finally,":[229],"thanks":[230],"some":[232],"numerical":[233],"experiments,":[234],"demonstrate":[236],"significantly":[243],"increased":[244],"at":[245],"reasonable":[247],"cost.":[249]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
