{"id":"https://openalex.org/W2000509730","doi":"https://doi.org/10.1137/120900745","title":"A Framework for the Automation of Generalized Stability Theory","display_name":"A Framework for the Automation of Generalized Stability Theory","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2000509730","doi":"https://doi.org/10.1137/120900745","mag":"2000509730"},"language":"en","primary_location":{"id":"doi:10.1137/120900745","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120900745","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/A5102855060","display_name":"Patrick E. Farrell","orcid":"https://orcid.org/0000-0002-1241-7060"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"P. E. Farrell","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Oxford OX2 6GG, UK"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Oxford OX2 6GG, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076491283","display_name":"Colin J. Cotter","orcid":"https://orcid.org/0000-0001-7962-8324"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"C. J. Cotter","raw_affiliation_strings":["Department of Mathematics, Imperial College London, London, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College London, London, UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013806448","display_name":"Simon W. Funke","orcid":"https://orcid.org/0000-0003-4709-8415"},"institutions":[{"id":"https://openalex.org/I2799829267","display_name":"Simula Research Laboratory","ror":"https://ror.org/00vn06n10","country_code":"NO","type":"facility","lineage":["https://openalex.org/I2799829267"]},{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB","NO"],"is_corresponding":false,"raw_author_name":"S. W. Funke","raw_affiliation_strings":["Imperial College Lon-don, London, UK","Center for Biomedical Computing, Simula Research Laboratory, Oslo, Norway, and Applied Mod-elling and Computation Group, Department of Earth Science and Engineering,"],"affiliations":[{"raw_affiliation_string":"Imperial College Lon-don, London, UK","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Center for Biomedical Computing, Simula Research Laboratory, Oslo, Norway, and Applied Mod-elling and Computation Group, Department of Earth Science and Engineering,","institution_ids":["https://openalex.org/I2799829267"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102855060"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":0.63300915,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.68400864,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"36","issue":"1","first_page":"C25","last_page":"C48"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9915000200271606,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9915000200271606,"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/T12603","display_name":"NMR spectroscopy and applications","score":0.9886999726295471,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9846000075340271,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6038332581520081},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5215520858764648},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5203779935836792},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.4982130527496338},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4881163537502289},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.44065284729003906},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4114390015602112},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3599560856819153},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3563149869441986},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30034664273262024},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22762340307235718},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1759032905101776}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6038332581520081},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5215520858764648},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5203779935836792},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.4982130527496338},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4881163537502289},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.44065284729003906},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4114390015602112},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3599560856819153},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3563149869441986},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30034664273262024},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22762340307235718},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1759032905101776},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120900745","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120900745","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:spiral.imperial.ac.uk:10044/1/12885","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/12885","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"C48","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6225080052","display_name":null,"funder_award_id":"EP/I00405X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7247996769","display_name":null,"funder_award_id":"EP/K030930/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7554227835","display_name":null,"funder_award_id":"EP/L000407/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":74,"referenced_works":["https://openalex.org/W73123583","https://openalex.org/W90568776","https://openalex.org/W149522324","https://openalex.org/W166268883","https://openalex.org/W400678491","https://openalex.org/W1479681228","https://openalex.org/W1493632573","https://openalex.org/W1569090332","https://openalex.org/W1576347883","https://openalex.org/W1585773866","https://openalex.org/W1596195796","https://openalex.org/W1946796247","https://openalex.org/W1964217357","https://openalex.org/W1966397236","https://openalex.org/W1969598406","https://openalex.org/W1969870848","https://openalex.org/W1973154786","https://openalex.org/W1979836673","https://openalex.org/W1981632256","https://openalex.org/W1983452151","https://openalex.org/W1983655899","https://openalex.org/W1988068819","https://openalex.org/W1988314016","https://openalex.org/W1990518285","https://openalex.org/W1996465851","https://openalex.org/W2000530301","https://openalex.org/W2006640177","https://openalex.org/W2009076876","https://openalex.org/W2010914491","https://openalex.org/W2011655084","https://openalex.org/W2026106782","https://openalex.org/W2037465123","https://openalex.org/W2038249383","https://openalex.org/W2038516800","https://openalex.org/W2039951169","https://openalex.org/W2046195637","https://openalex.org/W2046528357","https://openalex.org/W2046971416","https://openalex.org/W2047340075","https://openalex.org/W2051171886","https://openalex.org/W2057235791","https://openalex.org/W2063518967","https://openalex.org/W2064807134","https://openalex.org/W2067136705","https://openalex.org/W2073955633","https://openalex.org/W2082261407","https://openalex.org/W2083530498","https://openalex.org/W2085273914","https://openalex.org/W2087278911","https://openalex.org/W2095621348","https://openalex.org/W2096163705","https://openalex.org/W2100418324","https://openalex.org/W2106565812","https://openalex.org/W2107979247","https://openalex.org/W2108674668","https://openalex.org/W2111153312","https://openalex.org/W2117686912","https://openalex.org/W2124889948","https://openalex.org/W2128095813","https://openalex.org/W2130411680","https://openalex.org/W2133088826","https://openalex.org/W2134957132","https://openalex.org/W2135486411","https://openalex.org/W2137020736","https://openalex.org/W2138565515","https://openalex.org/W2139832333","https://openalex.org/W2165198298","https://openalex.org/W2167657634","https://openalex.org/W2186310920","https://openalex.org/W2535658559","https://openalex.org/W3099270997","https://openalex.org/W3101743426","https://openalex.org/W4232726482","https://openalex.org/W4247323812"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2732220824","https://openalex.org/W2117054131","https://openalex.org/W2005557375","https://openalex.org/W836021966"],"abstract_inverted_index":{"The":[0,244],"traditional":[1],"approach":[2,41],"to":[3,12,22,60,195,209,215,232],"investigating":[4],"the":[5,14,24,27,31,44,48,52,61,64,69,83,89,93,103,119,123,127,135,163,186,197,211,216,227,249],"stability":[6,46,76,104,167,228],"of":[7,26,47,54,63,71,88,92,105,165,179,241,248],"a":[8,17,72,143,160,174,180,237],"physical":[9],"system":[10],"is":[11,141,153,192],"linearize":[13],"equations":[15],"about":[16],"steady":[18],"base":[19],"solution,":[20],"and":[21,50,131,138,146,201,246,262],"examine":[23],"eigenvalues":[25],"linearized":[28,90],"operator.":[29],"Over":[30],"past":[32],"several":[33],"decades,":[34],"it":[35],"has":[36,97,115],"been":[37,116],"recognized":[38],"that":[39,121],"this":[40,156],"only":[42],"determines":[43],"asymptotic":[45],"system,":[49,188],"neglects":[51],"possibility":[53],"transient":[55],"perturbation":[56],"growth":[57,223],"arising":[58],"due":[59],"nonnormality":[62],"system.":[65,94],"This":[66],"observation":[67],"motivated":[68],"development":[70],"more":[73,112,238],"powerful":[74,235],"generalized":[75,166],"theory":[77],"(GST),":[78],"which":[79,169],"focuses":[80],"instead":[81],"on":[82],"singular":[84],"value":[85],"decomposition":[86],"(SVD)":[87],"propagator":[91],"While":[95],"GST":[96],"had":[98],"significant":[99],"successes":[100],"in":[101,107,185],"understanding":[102],"phenomena":[106],"geophysical":[108,257],"fluid":[109,258],"dynamics,":[110,259],"its":[111,132],"widespread":[113],"applicability":[114],"hampered":[117],"by":[118],"fact":[120],"computing":[122],"SVD":[124],"requires":[125],"both":[126],"tangent":[128,136,199],"linear":[129,137],"operator":[130],"adjoint:":[133],"deriving":[134],"adjoint":[139,202],"models":[140,205],"usually":[142],"considerable":[144],"challenge,":[145],"manually":[147],"embedding":[148],"them":[149],"inside":[150],"an":[151],"eigensolver":[152],"laborious.":[154],"In":[155],"paper,":[157],"we":[158,230],"present":[159],"framework":[161,250],"for":[162],"automation":[164],"theory,":[168],"overcomes":[170],"these":[171,204,234],"difficulties.":[172],"Given":[173],"compact":[175],"high-level":[176],"symbolic":[177],"representation":[178],"finite":[181],"element":[182],"discretization":[183],"implemented":[184],"FEniCS":[187],"efficient":[189],"C++":[190],"code":[191],"automatically":[193],"generated":[194],"assemble":[196],"forward,":[198],"linear,":[200],"models;":[203],"are":[206,251],"then":[207],"used":[208],"calculate":[210],"optimally":[212],"growing":[213],"perturbations":[214],"forward":[217],"model,":[218],"as":[219,221],"well":[220],"their":[222],"rates.":[224],"By":[225],"automating":[226],"computations,":[229],"hope":[231],"make":[233],"tools":[236],"routine":[239],"part":[240],"computational":[242],"analysis.":[243],"efficiency":[245],"generality":[247],"demonstrated,":[252],"with":[253],"applications":[254],"drawn":[255],"from":[256],"phase":[260],"separation,":[261],"quantum":[263],"mechanics.":[264]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}