{"id":"https://openalex.org/W2196186329","doi":"https://doi.org/10.1137/140974602","title":"Solvers for $\\mathcal{O} (N)$ Electronic Structure in the Strong Scaling Limit","display_name":"Solvers for $\\mathcal{O} (N)$ Electronic Structure in the Strong Scaling Limit","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2196186329","doi":"https://doi.org/10.1137/140974602","mag":"2196186329"},"language":"en","primary_location":{"id":"doi:10.1137/140974602","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140974602","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":true,"oa_status":"green","oa_url":"https://www.osti.gov/biblio/1329852","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102962662","display_name":"Nicolas Bock","orcid":"https://orcid.org/0009-0004-5143-2820"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Nicolas Bock","raw_affiliation_strings":["Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division"],"affiliations":[{"raw_affiliation_string":"Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027657365","display_name":"William Matthew Challacombe","orcid":null},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matt Challacombe","raw_affiliation_strings":["Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division"],"affiliations":[{"raw_affiliation_string":"Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051465480","display_name":"Laxmikant V. Kal\u00e9","orcid":"https://orcid.org/0000-0001-9673-8445"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Laxmikant V. Kal\u00e9","raw_affiliation_strings":["Univ. of Illinois, Urbana-Champaign, IL (United States). Parallel Programming Lab"],"affiliations":[{"raw_affiliation_string":"Univ. of Illinois, Urbana-Champaign, IL (United States). Parallel Programming Lab","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102962662"],"corresponding_institution_ids":["https://openalex.org/I1343871089"],"apc_list":null,"apc_paid":null,"fwci":1.5926,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.80953923,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"38","issue":"1","first_page":"C1","last_page":"C21"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11809","display_name":"Advanced NMR Techniques and Applications","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11809","display_name":"Advanced NMR Techniques and Applications","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10002","display_name":"Advanced Chemical Physics Studies","score":0.9926000237464905,"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"}},{"id":"https://openalex.org/T11177","display_name":"Spectroscopy and Quantum Chemical Studies","score":0.9921000003814697,"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/mathematics","display_name":"Mathematics","score":0.6729994416236877},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.6329634785652161},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5695444941520691},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5323382616043091},{"id":"https://openalex.org/keywords/approx","display_name":"Approx","score":0.48913222551345825},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4570299983024597},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.45244190096855164},{"id":"https://openalex.org/keywords/scaling-limit","display_name":"Scaling limit","score":0.43233442306518555},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.41902586817741394},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.41487616300582886},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3881373405456543},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17148065567016602},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16802754998207092},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1487140655517578},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1474502682685852},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1109357476234436}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6729994416236877},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6329634785652161},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5695444941520691},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5323382616043091},{"id":"https://openalex.org/C2777894999","wikidata":"https://www.wikidata.org/wiki/Q4781758","display_name":"Approx","level":2,"score":0.48913222551345825},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4570299983024597},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.45244190096855164},{"id":"https://openalex.org/C24084028","wikidata":"https://www.wikidata.org/wiki/Q7429781","display_name":"Scaling limit","level":3,"score":0.43233442306518555},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.41902586817741394},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.41487616300582886},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3881373405456543},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17148065567016602},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16802754998207092},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1487140655517578},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1474502682685852},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1109357476234436},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"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:10.1137/140974602","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140974602","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:osti.gov:1329852","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1329852","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null}],"best_oa_location":{"id":"pmh:oai:osti.gov:1329852","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1329852","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null},"sustainable_development_goals":[{"score":0.5400000214576721,"id":"https://metadata.un.org/sdg/6","display_name":"Clean water and sanitation"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320309151","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":102,"referenced_works":["https://openalex.org/W57462620","https://openalex.org/W105839681","https://openalex.org/W578415018","https://openalex.org/W1527992869","https://openalex.org/W1570967635","https://openalex.org/W1589986168","https://openalex.org/W1645422644","https://openalex.org/W1755261299","https://openalex.org/W1963497281","https://openalex.org/W1965092590","https://openalex.org/W1965798822","https://openalex.org/W1966406013","https://openalex.org/W1972362643","https://openalex.org/W1975326268","https://openalex.org/W1978005976","https://openalex.org/W1985621235","https://openalex.org/W1987874655","https://openalex.org/W1989559941","https://openalex.org/W1991470918","https://openalex.org/W1997813198","https://openalex.org/W1997881210","https://openalex.org/W1998284301","https://openalex.org/W1998388190","https://openalex.org/W2001543152","https://openalex.org/W2002401010","https://openalex.org/W2005129866","https://openalex.org/W2007628141","https://openalex.org/W2008305564","https://openalex.org/W2009036829","https://openalex.org/W2011461657","https://openalex.org/W2012679265","https://openalex.org/W2015372451","https://openalex.org/W2016851069","https://openalex.org/W2019104854","https://openalex.org/W2019675177","https://openalex.org/W2020428152","https://openalex.org/W2021064626","https://openalex.org/W2024076906","https://openalex.org/W2026448279","https://openalex.org/W2027353946","https://openalex.org/W2030976617","https://openalex.org/W2031260715","https://openalex.org/W2035137413","https://openalex.org/W2035303153","https://openalex.org/W2035824740","https://openalex.org/W2037993052","https://openalex.org/W2038339443","https://openalex.org/W2038535655","https://openalex.org/W2043485146","https://openalex.org/W2050053200","https://openalex.org/W2053997903","https://openalex.org/W2055120144","https://openalex.org/W2055578689","https://openalex.org/W2056999868","https://openalex.org/W2060573894","https://openalex.org/W2061369241","https://openalex.org/W2074429597","https://openalex.org/W2080322127","https://openalex.org/W2080353445","https://openalex.org/W2081898709","https://openalex.org/W2087609676","https://openalex.org/W2087772053","https://openalex.org/W2089437293","https://openalex.org/W2092577788","https://openalex.org/W2098379190","https://openalex.org/W2099887980","https://openalex.org/W2120145199","https://openalex.org/W2120229493","https://openalex.org/W2121817924","https://openalex.org/W2122796755","https://openalex.org/W2122948532","https://openalex.org/W2134237243","https://openalex.org/W2139316564","https://openalex.org/W2140085532","https://openalex.org/W2141514639","https://openalex.org/W2141895027","https://openalex.org/W2143981217","https://openalex.org/W2146558186","https://openalex.org/W2159161022","https://openalex.org/W2160011226","https://openalex.org/W2162169073","https://openalex.org/W2163041510","https://openalex.org/W2164331678","https://openalex.org/W2164754386","https://openalex.org/W2165787742","https://openalex.org/W2168425706","https://openalex.org/W2171695156","https://openalex.org/W2172139828","https://openalex.org/W2230728100","https://openalex.org/W2332437841","https://openalex.org/W2494991931","https://openalex.org/W2949165561","https://openalex.org/W2950119333","https://openalex.org/W2963315512","https://openalex.org/W2963425983","https://openalex.org/W2964167564","https://openalex.org/W3102666199","https://openalex.org/W3121465581","https://openalex.org/W3145412265","https://openalex.org/W4241766299","https://openalex.org/W4247459116","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2277483927","https://openalex.org/W1867383269","https://openalex.org/W2064404759","https://openalex.org/W399943172","https://openalex.org/W4378770497","https://openalex.org/W2049584446","https://openalex.org/W2300902614","https://openalex.org/W2079781215","https://openalex.org/W1568782638","https://openalex.org/W2029082315"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,32,53,78],"hybrid":[3],"OpenMP/Charm\\tt++":[4],"framework":[5],"for":[6,132,154],"solving":[7],"the":[8,17,25,38,60,96],"$\\mathcal{O}":[9],"(N)$":[10],"self-consistent-field":[11],"eigenvalue":[12],"problem":[13],"with":[14,52,100,106,159],"parallelism":[15],"in":[16,95],"strong":[18,157],"scaling":[19,125],"regime,":[20],"$P\\gg{N}$,":[21],"where":[22],"$P$":[23],"is":[24,31,50],"number":[26,39],"of":[27,34,40,92,98,128],"cores,":[28],"and":[29,59,66,76,90,119,151],"$N$":[30],"measure":[33],"system":[35,161],"size,":[36],"i.e.,":[37],"matrix":[41,63],"rows/columns,":[42],"basis":[43],"functions,":[44],"atoms,":[45],"molecules,":[46],"etc.":[47],"This":[48],"result":[49],"achieved":[51],"nested":[54],"approach":[55],"to":[56,88],"spectral":[57],"projection":[58],"sparse":[61],"approximate":[62],"multiply":[64],"[Bock":[65],"Challacombe,":[67],"SIAM":[68],"J.":[69],"Sci.":[70],"Comput.,":[71],"35":[72],"(2013),":[73],"pp.":[74],"C72--C98],":[75],"involves":[77],"recursive,":[79],"task-parallel":[80],"algorithm,":[81],"often":[82],"employed":[83],"by":[84],"generalized":[85,107],"$N$-Body":[86,108],"solvers,":[87,109],"occlusion":[89],"culling":[91],"negligible":[93],"products":[94],"case":[97],"matrices":[99],"decay.":[101],"Employing":[102],"classic":[103],"technologies":[104],"associated":[105],"including":[110],"overdecomposition,":[111],"recursive":[112],"task":[113],"parallelism,":[114],"orderings":[115],"that":[116],"preserve":[117],"locality,":[118],"persistence-based":[120],"load":[121],"balancing,":[122],"we":[123],"obtain":[124],"beyond":[126],"hundreds":[127],"cores":[129],"per":[130],"molecule":[131],"small":[133],"water":[134],"clusters":[135],"([H${}_2$O]${}_N$,":[136],"$N":[137],"\\in":[138],"\\{":[139,146],"30,":[140],"90,":[141],"150":[142],"\\}$,":[143],"$P/N":[144],"\\approx":[145],"819,":[147],"273,":[148],"164":[149],"\\}$)":[150],"find":[152],"support":[153],"an":[155],"increasingly":[156],"scalability":[158],"increasing":[160],"size":[162],"$N$.":[163]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}