{"id":"https://openalex.org/W1845641575","doi":"https://doi.org/10.1137/140980260","title":"AmgX: A Library for GPU Accelerated Algebraic Multigrid and Preconditioned Iterative Methods","display_name":"AmgX: A Library for GPU Accelerated Algebraic Multigrid and Preconditioned Iterative Methods","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1845641575","doi":"https://doi.org/10.1137/140980260","mag":"1845641575"},"language":"en","primary_location":{"id":"doi:10.1137/140980260","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140980260","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/A5038603364","display_name":"Maxim Naumov","orcid":"https://orcid.org/0000-0002-6102-2903"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Naumov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069136720","display_name":"M. Arsaev","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Arsaev","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013846372","display_name":"Patrice Castonguay","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. Castonguay","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079416691","display_name":"Jonathan Cohen","orcid":"https://orcid.org/0000-0003-1004-5598"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Cohen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076943072","display_name":"Julien Demouth","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Demouth","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073670556","display_name":"Joe Eaton","orcid":"https://orcid.org/0000-0001-7540-995X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Eaton","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009435664","display_name":"Simon K. Layton","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Layton","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022474130","display_name":"N. Markovskiy","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"N. Markovskiy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048478302","display_name":"Istv\u00e1n Z. Reguly","orcid":"https://orcid.org/0000-0002-4385-4204"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"I. Reguly","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039599159","display_name":"Nikolai Sakharnykh","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"N. Sakharnykh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027226268","display_name":"V. Sellappan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V. Sellappan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5047006398","display_name":"Robert Strzodka","orcid":"https://orcid.org/0000-0003-0468-0472"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. Strzodka","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":12,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2708,"has_fulltext":false,"cited_by_count":157,"citation_normalized_percentile":{"value":0.92103611,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"37","issue":"5","first_page":"S602","last_page":"S626"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.9958999752998352,"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/multigrid-method","display_name":"Multigrid method","score":0.8042668104171753},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.6589978933334351},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.623050332069397},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.6152418255805969},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5443025827407837},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4757649302482605},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.45721814036369324},{"id":"https://openalex.org/keywords/lu-decomposition","display_name":"LU decomposition","score":0.45328667759895325},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.4355371594429016},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43396320939064026},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4315856099128723},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3296085298061371},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.15999051928520203},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.13346821069717407}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.8042668104171753},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.6589978933334351},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.623050332069397},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.6152418255805969},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5443025827407837},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4757649302482605},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.45721814036369324},{"id":"https://openalex.org/C123213974","wikidata":"https://www.wikidata.org/wiki/Q833089","display_name":"LU decomposition","level":4,"score":0.45328667759895325},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.4355371594429016},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43396320939064026},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4315856099128723},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3296085298061371},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.15999051928520203},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.13346821069717407},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140980260","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140980260","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321679","display_name":"Ministry of Economy, Trade and Industry","ror":"https://ror.org/055tm7f07"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W207622524","https://openalex.org/W345637930","https://openalex.org/W1506342804","https://openalex.org/W1522512418","https://openalex.org/W1525132831","https://openalex.org/W1575701986","https://openalex.org/W1790422192","https://openalex.org/W1907157228","https://openalex.org/W1961194538","https://openalex.org/W1966448113","https://openalex.org/W1975464357","https://openalex.org/W1985263109","https://openalex.org/W1987896015","https://openalex.org/W1994182141","https://openalex.org/W1997497072","https://openalex.org/W2007389171","https://openalex.org/W2017217780","https://openalex.org/W2041876368","https://openalex.org/W2047702967","https://openalex.org/W2048255281","https://openalex.org/W2048748322","https://openalex.org/W2053486661","https://openalex.org/W2057901401","https://openalex.org/W2065607954","https://openalex.org/W2070232376","https://openalex.org/W2075536798","https://openalex.org/W2083116175","https://openalex.org/W2083715026","https://openalex.org/W2089437293","https://openalex.org/W2089711159","https://openalex.org/W2099957444","https://openalex.org/W2100061495","https://openalex.org/W2132612821","https://openalex.org/W2139131733","https://openalex.org/W2142304406","https://openalex.org/W2148202071","https://openalex.org/W2153179908","https://openalex.org/W2167512083","https://openalex.org/W2189553231","https://openalex.org/W2243781021","https://openalex.org/W2471174275","https://openalex.org/W2610857016","https://openalex.org/W2945154147","https://openalex.org/W2973296080","https://openalex.org/W3098342588","https://openalex.org/W3106161546","https://openalex.org/W3145128584"],"related_works":["https://openalex.org/W2018388178","https://openalex.org/W144270911","https://openalex.org/W2149246659","https://openalex.org/W2770497004","https://openalex.org/W2119553411","https://openalex.org/W2116573255","https://openalex.org/W2575167716","https://openalex.org/W1534644390","https://openalex.org/W2902881413","https://openalex.org/W4254160523"],"abstract_inverted_index":{"The":[0,74,104,132,155],"solution":[1,40],"of":[2,41,56,65,94,108,124],"large":[3,28,32],"sparse":[4],"linear":[5],"systems":[6],"arises":[7],"in":[8,43,134,159,181],"many":[9,107],"applications,":[10],"such":[11],"as":[12],"computational":[13],"fluid":[14],"dynamics":[15],"and":[16,54,70,80,87,96,101,111,146,188],"oil":[17],"reservoir":[18],"simulation.":[19],"In":[20,47],"realistic":[21],"cases":[22],"the":[23,39,52,57,109,125,135,144,160,175,182],"matrices":[24],"are":[25],"often":[26,148],"so":[27],"that":[29],"they":[30],"require":[31],"scale":[33,191],"distributed":[34,66],"parallel":[35,139,151],"computing":[36],"to":[37],"obtain":[38],"interest":[42],"a":[44,92,167,171],"reasonable":[45],"time.":[46],"this":[48,197],"paper":[49],"we":[50],"discuss":[51],"design":[53],"implementation":[55,173],"AmgX":[58,75,161],"library,":[59],"which":[60,118],"provides":[61],"drop-in":[62],"GPU":[63,169],"acceleration":[64],"algebraic":[67],"multigrid":[68,127],"(AMG)":[69],"preconditioned":[71,113],"iterative":[72,116],"methods.":[73],"library":[76,105,162],"implements":[77],"both":[78,186],"classical":[79],"aggregation-based":[81],"AMG":[82,156],"methods":[83,128],"with":[84,91,122],"different":[85],"selector":[86],"interpolation":[88],"strategies,":[89],"along":[90],"variety":[93],"smoothers":[95,145],"preconditioners,":[97],"including":[98],"block-Jacobi,":[99],"Gauss--Seidel,":[100],"incomplete-LU":[102],"factorization.":[103],"contains":[106],"standard":[110],"flexible":[112],"Krylov":[114],"subspace":[115],"methods,":[117],"can":[119],"be":[120,179],"combined":[121],"any":[123],"available":[126],"or":[129],"simpler":[130],"preconditioners.":[131],"parallelism":[133],"aggregation":[136],"scheme":[137],"exploits":[138],"graph":[140,152],"matching":[141],"techniques,":[142],"while":[143],"preconditioners":[147],"rely":[149],"on":[150,166,174],"coloring":[153],"algorithms.":[154],"algorithm":[157],"implemented":[158],"achieves":[163],"$2$--$5\\times$":[164],"speedup":[165],"single":[168],"against":[170],"competitive":[172],"CPU.":[176],"As":[177],"will":[178],"shown":[180],"numerical":[183],"experiments":[184],"section,":[185],"setup":[187],"solve":[189],"phases":[190],"well":[192],"across":[193],"multiple":[194],"nodes,":[195],"sustaining":[196],"performance":[198],"advantage.":[199]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":32},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":23},{"year":2022,"cited_by_count":19},{"year":2021,"cited_by_count":23},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}