{"id":"https://openalex.org/W4414878598","doi":"https://doi.org/10.1016/j.jcp.2026.115001","title":"DFPI: Generic deflation for accelerating fixed-point iterations via dynamic extraction from Krylov subspaces","display_name":"DFPI: Generic deflation for accelerating fixed-point iterations via dynamic extraction from Krylov subspaces","publication_year":2026,"publication_date":"2026-05-04","ids":{"openalex":"https://openalex.org/W4414878598","doi":"https://doi.org/10.1016/j.jcp.2026.115001"},"language":"en","primary_location":{"id":"doi:10.1016/j.jcp.2026.115001","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jcp.2026.115001","pdf_url":null,"source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Physics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.jcp.2026.115001","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5116007040","display_name":"J\u00e9r\u00e9my Kalfoun","orcid":null},"institutions":[{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I4210155595","display_name":"MNM Consulting (France)","ror":"https://ror.org/05t7drw06","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210155595"]},{"id":"https://openalex.org/I4387152683","display_name":"Math\u00e9matiques et Informatique pour la Complexit\u00e9 et les Syst\u00e8mes","ror":"https://ror.org/03q29s414","country_code":null,"type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4387152683"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jeremy Kalfoun","raw_affiliation_strings":["ICON Technology & Process Consulting (France)","F\u00e9d\u00e9ration de Math\u00e9matiques de CentraleSup\u00e9lec (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","Universit\u00e9 Paris-Saclay (B\u00e2timent Br\u00e9guet, 3 Rue Joliot Curie 2e \u00e9t, 91190 Gif-sur-Yvette - France)","MICS - Math\u00e9matiques et Informatique pour la Complexit\u00e9 et les Syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ICON Technology & Process Consulting (France)","institution_ids":["https://openalex.org/I4210155595"]},{"raw_affiliation_string":"F\u00e9d\u00e9ration de Math\u00e9matiques de CentraleSup\u00e9lec (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","institution_ids":["https://openalex.org/I4210107720"]},{"raw_affiliation_string":"Universit\u00e9 Paris-Saclay (B\u00e2timent Br\u00e9guet, 3 Rue Joliot Curie 2e \u00e9t, 91190 Gif-sur-Yvette - France)","institution_ids":["https://openalex.org/I277688954"]},{"raw_affiliation_string":"MICS - Math\u00e9matiques et Informatique pour la Complexit\u00e9 et les Syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","institution_ids":["https://openalex.org/I4387152683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067004107","display_name":"Guillaume Pierrot","orcid":null},"institutions":[{"id":"https://openalex.org/I4210155595","display_name":"MNM Consulting (France)","ror":"https://ror.org/05t7drw06","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210155595"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Guillaume Pierrot","raw_affiliation_strings":["ICON Technology & Process Consulting (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ICON Technology & Process Consulting (France)","institution_ids":["https://openalex.org/I4210155595"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049553661","display_name":"John Cagnol","orcid":"https://orcid.org/0000-0002-5447-3335"},"institutions":[{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I4387152683","display_name":"Math\u00e9matiques et Informatique pour la Complexit\u00e9 et les Syst\u00e8mes","ror":"https://ror.org/03q29s414","country_code":null,"type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4387152683"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"John Cagnol","raw_affiliation_strings":["Universit\u00e9 Paris-Saclay (B\u00e2timent Br\u00e9guet, 3 Rue Joliot Curie 2e \u00e9t, 91190 Gif-sur-Yvette - France)","F\u00e9d\u00e9ration de Math\u00e9matiques de CentraleSup\u00e9lec (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","MICS - Math\u00e9matiques et Informatique pour la Complexit\u00e9 et les Syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)"],"raw_orcid":"https://orcid.org/0000-0002-5447-3335","affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris-Saclay (B\u00e2timent Br\u00e9guet, 3 Rue Joliot Curie 2e \u00e9t, 91190 Gif-sur-Yvette - France)","institution_ids":["https://openalex.org/I277688954"]},{"raw_affiliation_string":"F\u00e9d\u00e9ration de Math\u00e9matiques de CentraleSup\u00e9lec (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","institution_ids":["https://openalex.org/I4210107720"]},{"raw_affiliation_string":"MICS - Math\u00e9matiques et Informatique pour la Complexit\u00e9 et les Syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","institution_ids":["https://openalex.org/I4387152683"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5116007040"],"corresponding_institution_ids":["https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210155595","https://openalex.org/I4387152683"],"apc_list":{"value":3750,"currency":"USD","value_usd":3750},"apc_paid":{"value":3750,"currency":"USD","value_usd":3750},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01948298,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"562","issue":null,"first_page":"115001","last_page":"115001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991999864578247,"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":0.9991999864578247,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.964900016784668,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9327999949455261,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.7630000114440918},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.7408999800682068},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5993000268936157},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5706999897956848},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.5295000076293945},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5026999711990356},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.45820000767707825},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4410000145435333},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.3840999901294708}],"concepts":[{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.7630000114440918},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.7408999800682068},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5993000268936157},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5706999897956848},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5297999978065491},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5295000076293945},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5026999711990356},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.45820000767707825},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45329999923706055},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4521999955177307},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4410000145435333},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4072999954223633},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39480000734329224},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.3840999901294708},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.33180001378059387},{"id":"https://openalex.org/C120553275","wikidata":"https://www.wikidata.org/wiki/Q4903720","display_name":"Biconjugate gradient stabilized method","level":3,"score":0.3127000033855438},{"id":"https://openalex.org/C163834973","wikidata":"https://www.wikidata.org/wiki/Q2004891","display_name":"Numerical linear algebra","level":3,"score":0.31049999594688416},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.3075999915599823},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.30630001425743103},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2919999957084656},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.28929999470710754},{"id":"https://openalex.org/C91394653","wikidata":"https://www.wikidata.org/wiki/Q5161159","display_name":"Conjugate residual method","level":4,"score":0.28459998965263367},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C2776865275","wikidata":"https://www.wikidata.org/wiki/Q311666","display_name":"Projector","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C102893441","wikidata":"https://www.wikidata.org/wiki/Q1063089","display_name":"Richardson extrapolation","level":3,"score":0.2506999969482422}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1016/j.jcp.2026.115001","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jcp.2026.115001","pdf_url":null,"source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Physics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2502.20121","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2502.20121","pdf_url":"https://arxiv.org/pdf/2502.20121","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"pmh:oai:arXiv.org:2502.20121","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2502.20121","pdf_url":"https://arxiv.org/pdf/2502.20121","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"pmh:oai:HAL:hal-04970544v1","is_oa":false,"landing_page_url":"https://cnrs.hal.science/hal-04970544","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2025","raw_type":"Preprints, Working Papers, ..."},{"id":"pmh:oai:HAL:hal-05610398v1","is_oa":false,"landing_page_url":"https://hal.science/hal-05610398","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Physics, In press, pp.115001. &#x27E8;10.1016/j.jcp.2026.115001&#x27E9;","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.2502.20121","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2502.20121","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"}],"best_oa_location":{"id":"doi:10.1016/j.jcp.2026.115001","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jcp.2026.115001","pdf_url":null,"source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Physics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W2140153041","https://openalex.org/W2084363278","https://openalex.org/W1990351032","https://openalex.org/W2052579356","https://openalex.org/W3157603860","https://openalex.org/W2028989647","https://openalex.org/W2079308547","https://openalex.org/W2068485378","https://openalex.org/W2613879078","https://openalex.org/W4200373490","https://openalex.org/W2128836543","https://openalex.org/W2006340150","https://openalex.org/W2364308289","https://openalex.org/W2046402929","https://openalex.org/W2033635206","https://openalex.org/W2015805170","https://openalex.org/W2061784001","https://openalex.org/W816806891","https://openalex.org/W1966801132","https://openalex.org/W3039557128","https://openalex.org/W2155216327","https://openalex.org/W2112979995","https://openalex.org/W2063263929","https://openalex.org/W2083232784"],"related_works":[],"abstract_inverted_index":{"Iterative":[0],"algorithms":[1],"are":[2],"instrumental":[3],"in":[4,22],"modern":[5],"numerical":[6,210],"simulation":[7],"for":[8,56,70,98],"solving":[9],"systems":[10],"arising":[11],"from":[12],"the":[13,68,99,122,146,153,157,163,174,187,193],"discretization":[14],"of":[15,82,102,148,176,218],"PDEs.":[16],"They":[17],"face":[18],"however":[19],"significant":[20],"challenges":[21],"industrial":[23],"applications,":[24],"such":[25,44,59,113],"as":[26,45,60,114,184,186],"slow":[27],"convergence,":[28],"limit":[29],"cycle":[30],"oscillations,":[31],"or":[32],"iterations":[33,47,126],"blow-up.":[34],"An":[35],"ideal":[36],"preconditioner":[37],"is":[38,76,138,199],"rarely":[39],"available":[40],"and":[41,79,110,117,120,127,135,156],"naive":[42],"approaches":[43],"Richardson":[46,125],"often":[48],"fail":[49],"to":[50],"converge":[51],"on":[52,152,162,215],"complex":[53],"cases,":[54],"calling":[55],"generic":[57],"sophistications":[58],"deflation":[61],"techniques":[62,112],"and/or":[63],"Krylov":[64,128],"subspaces":[65],"approaches.":[66],"However":[67,196],"quest":[69],"an":[71],"optimal":[72],"general":[73,167],"linear":[74,103],"solver":[75],"still":[77],"open":[78],"a":[80,88,149,177,202,206,216],"matter":[81],"active":[83],"research.":[84],"This":[85],"paper":[86],"introduces":[87],"new":[89],"theoretical":[90],"framework,":[91],"called":[92],"DFPI":[93,137],"(Deflated":[94],"Fixed":[95],"Point":[96],"Iterations)":[97],"iterative":[100],"solution":[101],"systems.":[104],"It":[105],"unifies":[106],"several":[107],"existing":[108],"acceleration":[109],"stabilization":[111],"RPM,":[115],"BoostConv":[116],"Anderson":[118],"acceleration,":[119],"bridges":[121],"gap":[123],"between":[124],"subspace":[129],"methods,":[130],"including":[131],"GMRES,":[132],"PCG,":[133],"BiCGStab":[134],"variants.":[136],"structured":[139],"around":[140],"two":[141],"key":[142],"building":[143],"blocks":[144],":":[145],"choice":[147,175],"projection":[150,179,188],"operator,":[151],"one":[154],"hand":[155],"trouble":[158],"vectors":[159],"recruitment":[160],"strategy,":[161],"other":[164],"hand.":[165],"A":[166],"convergence":[168],"result":[169],"will":[170,212],"be":[171,213],"presented,":[172],"showing":[173],"specific":[178],"operator":[180],"has":[181],"minimal":[182],"impact":[183],"long":[185],"space":[189],"remains":[190],"invariant":[191],"by":[192],"iteration":[194],"matrix.":[195],"when":[197],"this":[198],"not":[200],"guaranteed,":[201],"minimization":[203],"principle":[204],"becomes":[205],"must":[207],"have.":[208],"Finally":[209],"comparisons":[211],"conducted":[214],"variety":[217],"relevant":[219],"CFD":[220],"cases.":[221]},"counts_by_year":[],"updated_date":"2026-05-09T06:09:20.037420","created_date":"2025-10-07T00:00:00"}
