{"id":"https://openalex.org/W3084410321","doi":"https://doi.org/10.1137/19m1249060","title":"A Highly Parallel Multilevel Newton--Krylov--Schwarz Method with Subspace-Based Coarsening and Partition-Based Balancing for the Multigroup Neutron Transport Equation on Three-Dimensional Unstructured Meshes","display_name":"A Highly Parallel Multilevel Newton--Krylov--Schwarz Method with Subspace-Based Coarsening and Partition-Based Balancing for the Multigroup Neutron Transport Equation on Three-Dimensional Unstructured Meshes","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3084410321","doi":"https://doi.org/10.1137/19m1249060","mag":"3084410321"},"language":"en","primary_location":{"id":"doi:10.1137/19m1249060","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1249060","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/A5103149505","display_name":"Fande Kong","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fande Kong","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-4275-7418","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100352466","display_name":"Yaqi Wang","orcid":"https://orcid.org/0000-0002-3737-3498"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yaqi Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026662743","display_name":"Derek Gaston","orcid":"https://orcid.org/0000-0001-9659-9094"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Derek R. Gaston","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025181525","display_name":"Cody Permann","orcid":"https://orcid.org/0000-0001-5336-2863"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cody J. Permann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087599270","display_name":"Andrew E. Slaughter","orcid":"https://orcid.org/0000-0002-4935-6812"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrew E. Slaughter","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037282372","display_name":"Alexander Lindsay","orcid":"https://orcid.org/0000-0002-6988-2123"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexander D. Lindsay","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036938995","display_name":"Mark D. DeHart","orcid":"https://orcid.org/0000-0002-4686-4301"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mark D. DeHart","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5081586956","display_name":"Richard Martineau","orcid":"https://orcid.org/0000-0002-9328-2777"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Richard C. Martineau","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5103149505"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5827,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.74050591,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"42","issue":"5","first_page":"C193","last_page":"C220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987000226974487,"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":0.9987000226974487,"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":0.9983999729156494,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9976999759674072,"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/krylov-subspace","display_name":"Krylov subspace","score":0.7934213876724243},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.7615804076194763},{"id":"https://openalex.org/keywords/neutron-transport","display_name":"Neutron transport","score":0.7030308842658997},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6628115773200989},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.5915930271148682},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.48762646317481995},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4767666459083557},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.47504496574401855},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47488850355148315},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.4372996687889099},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4367785155773163},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4191315174102783},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.40917906165122986},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38805487751960754},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3068222999572754},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.2705995440483093},{"id":"https://openalex.org/keywords/neutron","display_name":"Neutron","score":0.19232875108718872},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14107048511505127},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12012043595314026},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10234200954437256}],"concepts":[{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.7934213876724243},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.7615804076194763},{"id":"https://openalex.org/C66963500","wikidata":"https://www.wikidata.org/wiki/Q3338735","display_name":"Neutron transport","level":3,"score":0.7030308842658997},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6628115773200989},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.5915930271148682},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.48762646317481995},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4767666459083557},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.47504496574401855},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47488850355148315},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.4372996687889099},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4367785155773163},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4191315174102783},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.40917906165122986},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38805487751960754},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3068222999572754},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2705995440483093},{"id":"https://openalex.org/C152568617","wikidata":"https://www.wikidata.org/wiki/Q2348","display_name":"Neutron","level":2,"score":0.19232875108718872},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14107048511505127},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12012043595314026},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10234200954437256},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1249060","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1249060","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":[{"score":0.46000000834465027,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G2402323868","display_name":null,"funder_award_id":"DE-AC07-05ID14517","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W69485787","https://openalex.org/W1812682958","https://openalex.org/W1964004732","https://openalex.org/W1966281943","https://openalex.org/W1975464357","https://openalex.org/W1978588246","https://openalex.org/W1978804357","https://openalex.org/W1988200181","https://openalex.org/W1988580765","https://openalex.org/W2011655084","https://openalex.org/W2039789965","https://openalex.org/W2056730433","https://openalex.org/W2073897969","https://openalex.org/W2074809615","https://openalex.org/W2092862307","https://openalex.org/W2100061495","https://openalex.org/W2140153041","https://openalex.org/W2152342464","https://openalex.org/W2171303908","https://openalex.org/W2259663966","https://openalex.org/W2302274267","https://openalex.org/W2498468807","https://openalex.org/W2590799653","https://openalex.org/W2603805256","https://openalex.org/W2757798042","https://openalex.org/W2767992360","https://openalex.org/W2774746823","https://openalex.org/W2806383593","https://openalex.org/W2945154147","https://openalex.org/W2963972078","https://openalex.org/W2985958607","https://openalex.org/W3105271077"],"related_works":["https://openalex.org/W2042846224","https://openalex.org/W3157581606","https://openalex.org/W2113830538","https://openalex.org/W2358905935","https://openalex.org/W2942315554","https://openalex.org/W2804461272","https://openalex.org/W2040391781","https://openalex.org/W2382988560","https://openalex.org/W2024149451","https://openalex.org/W4322732133"],"abstract_inverted_index":{"The":[0,88],"multigroup":[1,22],"neutron":[2,23,100,148],"transport":[3,24,101,149,249],"equation":[4,25,31],"is":[5,26,32,43,54,91,121,135,155,184,207,226],"crucial":[6],"for":[7,98,199,233],"studying":[8],"the":[9,21,30,39,46,94,104,143,147,176,188,192,197,223,252,264],"motion":[10],"of":[11,20,73,93,106,119,142,146,191,214,246],"neutrons":[12],"and":[13,45,82,112],"their":[14],"interaction":[15],"with":[16,228,241],"materials.":[17],"Numerical":[18],"simulation":[19],"computationally":[27],"challenging":[28],"because":[29],"defined":[33],"on":[34,237,263],"a":[35,59,66,74,78,83,116,125,132,138,166,211,234,242],"high-dimensional":[36],"phase":[37],"space,":[38],"computational":[40],"spatial":[41],"domain":[42],"complex,":[44],"materials":[47],"are":[48,256,272],"heterogeneous.":[49],"A":[50,180,202],"scalable":[51,227],"parallel":[52,68,189],"solver":[53,267],"required":[55],"to":[56,157,186,209],"address":[57],"such":[58],"challenge.":[60],"In":[61],"this":[62],"paper,":[63],"we":[64,164],"study":[65],"highly":[67],"Newton--Krylov--Schwarz":[69],"(NKS)":[70],"method":[71,90],"consisting":[72],"Newton-based":[75],"eigenvalue":[76],"solver,":[77],"Krylov":[79],"subspace":[80],"method,":[81],"novel":[84,126],"multilevel":[85,89,133,170],"Schwarz":[86],"preconditioner.":[87],"one":[92],"most":[95],"popular":[96],"preconditioners":[97],"accelerating":[99],"calculations,":[102],"but":[103],"construction":[105],"coarse":[107],"spaces":[108],"can":[109],"be":[110],"expensive":[111],"often":[113],"unscalable":[114],"when":[115,174,268],"large":[117,212],"number":[118,213],"processors":[120,232,271],"used.":[122],"We":[123,220],"propose":[124],"matrix":[127,140,145],"coarsening":[128,153,178],"algorithm":[129,154,194,206,225,255],"in":[130,169],"which":[131],"hierarchy":[134],"constructed":[136],"using":[137,175,251],"single-component":[139],"instead":[141],"full":[144],"equation.":[150],"This":[151],"new":[152],"referred":[156],"as":[158,258,260],"\u201csubspace-based":[159],"coarsening.\u201d":[160],"Above":[161],"8,000":[162,270],"processors,":[163],"show":[165],"13x":[167],"enhancement":[168],"preconditioner":[171],"setup":[172],"time":[173],"subspace-based":[177],"method.":[179],"partition-based":[181],"balancing":[182],"strategy":[183],"studied":[185],"enhance":[187],"efficiency":[190],"NKS":[193,254,266],"by":[195],"equalizing":[196],"work":[198],"each":[200],"processor.":[201],"hierarchical":[203],"mesh":[204],"partitioning":[205],"employed":[208],"generate":[210],"submeshes":[215],"while":[216],"minimizing":[217],"off-node":[218],"communication.":[219],"demonstrate":[221],"that":[222],"proposed":[224],"more":[229],"than":[230],"10,000":[231],"realistic":[235],"application":[236],"three-dimensional":[238],"unstructured":[239],"meshes":[240],"few":[243],"billion":[244],"degrees":[245],"freedom.":[247],"Neutron":[248],"calculations":[250],"improved":[253],"twice":[257],"fast":[259],"those":[261],"based":[262],"unmodified":[265],"over":[269],"employed.":[273]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2026-05-12T08:28:47.272897","created_date":"2025-10-10T00:00:00"}
