{"id":"https://openalex.org/W3113413164","doi":"https://doi.org/10.1137/20m1387985","title":"Optimal and Low-Memory Near-Optimal Preconditioning of Fully Implicit Runge--Kutta Schemes for Parabolic PDEs","display_name":"Optimal and Low-Memory Near-Optimal Preconditioning of Fully Implicit Runge--Kutta Schemes for Parabolic PDEs","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3113413164","doi":"https://doi.org/10.1137/20m1387985","mag":"3113413164"},"language":"en","primary_location":{"id":"doi:10.1137/20m1387985","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1387985","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2012.12779","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033515755","display_name":"Xiangmin Jiao","orcid":"https://orcid.org/0000-0002-7111-9813"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiangmin Jiao","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-7111-9813","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066857796","display_name":"Xuebin Wang","orcid":"https://orcid.org/0000-0002-0809-6014"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xuebin Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100728174","display_name":"Qiao Chen","orcid":"https://orcid.org/0000-0001-9895-8935"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qiao Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1769,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.72750253,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"43","issue":"5","first_page":"A3527","last_page":"A3551"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994999766349792,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991000294685364,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.6959813237190247},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6591731309890747},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6031867861747742},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4740681052207947},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.44106048345565796},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.4322136342525482},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4282175302505493},{"id":"https://openalex.org/keywords/incomplete-lu-factorization","display_name":"Incomplete LU factorization","score":0.41572141647338867},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3811154365539551},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.374175488948822},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.2638620138168335},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.17746996879577637},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16791588068008423},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07309028506278992}],"concepts":[{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.6959813237190247},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6591731309890747},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6031867861747742},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4740681052207947},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.44106048345565796},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.4322136342525482},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4282175302505493},{"id":"https://openalex.org/C134978465","wikidata":"https://www.wikidata.org/wiki/Q1654069","display_name":"Incomplete LU factorization","level":4,"score":0.41572141647338867},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3811154365539551},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.374175488948822},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2638620138168335},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.17746996879577637},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16791588068008423},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07309028506278992},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1387985","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1387985","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:arXiv.org:2012.12779","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.12779","pdf_url":"https://arxiv.org/pdf/2012.12779","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"mag:3113413164","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2012.12779","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2012.12779","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2012.12779","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2012.12779","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.12779","pdf_url":"https://arxiv.org/pdf/2012.12779","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2332202595","display_name":null,"funder_award_id":"462974","funder_id":"https://openalex.org/F4320338304","funder_display_name":"Los Alamos National Laboratory"},{"id":"https://openalex.org/G7941388931","display_name":null,"funder_award_id":"28451","funder_id":"https://openalex.org/F4320312918","funder_display_name":"Empire State Development"}],"funders":[{"id":"https://openalex.org/F4320312918","display_name":"Empire State Development","ror":"https://ror.org/00ppzen87"},{"id":"https://openalex.org/F4320338304","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W73123583","https://openalex.org/W321261355","https://openalex.org/W1506342804","https://openalex.org/W1509923322","https://openalex.org/W1519422254","https://openalex.org/W1543750907","https://openalex.org/W1576347883","https://openalex.org/W1598578620","https://openalex.org/W1601728065","https://openalex.org/W1794639636","https://openalex.org/W1912260502","https://openalex.org/W1954725639","https://openalex.org/W1964070472","https://openalex.org/W1975696503","https://openalex.org/W1977542511","https://openalex.org/W1981220107","https://openalex.org/W1986437112","https://openalex.org/W1991915199","https://openalex.org/W1998953621","https://openalex.org/W1999698136","https://openalex.org/W2000650590","https://openalex.org/W2010029092","https://openalex.org/W2014730252","https://openalex.org/W2024029196","https://openalex.org/W2033886849","https://openalex.org/W2041876368","https://openalex.org/W2044557804","https://openalex.org/W2044858286","https://openalex.org/W2046492835","https://openalex.org/W2055987340","https://openalex.org/W2059371748","https://openalex.org/W2069849438","https://openalex.org/W2073555064","https://openalex.org/W2080097309","https://openalex.org/W2099093654","https://openalex.org/W2109119560","https://openalex.org/W2122049987","https://openalex.org/W2140153041","https://openalex.org/W2150003608","https://openalex.org/W2156095889","https://openalex.org/W2164374667","https://openalex.org/W2212370034","https://openalex.org/W2334722666","https://openalex.org/W2581973763","https://openalex.org/W2592996154","https://openalex.org/W2613462647","https://openalex.org/W2740885083","https://openalex.org/W2798909945","https://openalex.org/W2964180189","https://openalex.org/W3013202496","https://openalex.org/W3082287790"],"related_works":["https://openalex.org/W2553881380","https://openalex.org/W2988877209","https://openalex.org/W3120401416","https://openalex.org/W1834935215","https://openalex.org/W1997843647","https://openalex.org/W2949868289","https://openalex.org/W2950871635","https://openalex.org/W3120903577","https://openalex.org/W2310734763","https://openalex.org/W3211735279","https://openalex.org/W3100356286","https://openalex.org/W2991261427","https://openalex.org/W2895787496","https://openalex.org/W2766623188","https://openalex.org/W949628637","https://openalex.org/W3045084124","https://openalex.org/W273993589","https://openalex.org/W1600186676","https://openalex.org/W2083063368","https://openalex.org/W2462359089"],"abstract_inverted_index":{"Runge-Kutta":[0],"(RK)":[1],"schemes,":[2,12],"especially":[3],"Gauss-Legendre":[4],"and":[5,28,72,81,129,186,195,206,212],"some":[6],"other":[7,199],"fully":[8],"implicit":[9,46],"RK":[10,47],"(FIRK)":[11],"are":[13],"desirable":[14,118],"for":[15,41,86],"the":[16,100,140,170,178,213,217,226],"time":[17],"integration":[18],"of":[19,120,203,216,221,229],"parabolic":[20],"partial":[21],"differential":[22],"equations":[23],"due":[24],"to":[25,37,44,176],"their":[26],"A-stability":[27],"high-order":[29],"accuracy.":[30],"However,":[31],"it":[32,124],"is":[33,122,208],"significantly":[34,197],"more":[35],"challenging":[36],"construct":[38],"optimal":[39,59],"preconditioners":[40,60,80,172,200],"them":[42,211],"compared":[43],"diagonally":[45],"(or":[48,131],"DIRK)":[49],"schemes.":[50],"To":[51],"address":[52],"this":[53],"challenge,":[54],"we":[55],"first":[56],"introduce":[57],"mathematically":[58],"called":[61],"block":[62,67,73,171],"complex":[63],"Schur":[64,69,105],"decomposition":[65,70,106],"(BCSD),":[66],"real":[68,104],"(BRSD),":[71],"Jordan":[74,82],"form":[75,83],"(BJF),":[76],"motivated":[77],"by":[78,98],"block-circulant":[79],"solution":[84],"techniques":[85,146],"IRK.":[87],"We":[88,138,168,190],"then":[89],"derive":[90],"an":[91,108,148,165],"efficient,":[92],"near-optimal":[93],"singly-diagonal":[94],"approximate":[95,139],"BRSD":[96],"(SABRSD)":[97],"approximating":[99],"quasi-triangular":[101],"matrix":[102,111],"in":[103,143,173,181,201,219],"using":[107,147,183],"optimized":[109],"upper-triangular":[110],"with":[112,151,164,210],"a":[113,161],"single":[114],"diagonal":[115,141],"value.":[116],"A":[117],"feature":[119],"SABRSD":[121,207],"that":[123,192],"has":[125],"comparable":[126],"memory":[127],"requirements":[128],"factorization":[130,150],"setup)":[132],"cost":[133,223],"as":[134,156],"singly":[135],"DIRK":[136],"(SDIRK).":[137],"blocks":[142],"these":[144],"preconditioning":[145],"incomplete":[149],"(near)":[152],"linear":[153],"complexity,":[154],"such":[155],"multilevel":[157],"ILU,":[158],"ILU(0),":[159],"or":[160],"multigrid":[162],"method":[163],"ILU-based":[166],"smoother.":[167],"apply":[169],"right-preconditioned":[174],"GMRES":[175,204],"solve":[177],"advection-diffusion":[179],"equation":[180],"3D":[182],"finite":[184,187],"element":[185],"difference":[188],"methods.":[189],"show":[191],"BCSD,":[193],"BRSD,":[194],"BJF":[196],"outperform":[198],"terms":[202,220],"iterations,":[205],"competitive":[209],"prior":[214],"state":[215],"art":[218],"computational":[222],"while":[224],"requiring":[225],"least":[227],"amount":[228],"memory.":[230]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
