{"id":"https://openalex.org/W4402271415","doi":"https://doi.org/10.1090/mcom/4015","title":"Average energy dissipation rates of explicit exponential Runge-Kutta methods for gradient flow problems","display_name":"Average energy dissipation rates of explicit exponential Runge-Kutta methods for gradient flow problems","publication_year":2024,"publication_date":"2024-09-05","ids":{"openalex":"https://openalex.org/W4402271415","doi":"https://doi.org/10.1090/mcom/4015"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4015","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4015","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/A5052651480","display_name":"Hong-lin Liao","orcid":"https://orcid.org/0000-0003-0777-6832"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hong-lin Liao","raw_affiliation_strings":["School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, People\u2019s Republic of China; ormalfont and Key Laboratory of Mathematical Modeling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing 211106, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, People\u2019s Republic of China; ormalfont and Key Laboratory of Mathematical Modeling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing 211106, People\u2019s Republic of China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101778644","display_name":"Xuping Wang","orcid":"https://orcid.org/0000-0003-2909-4007"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuping Wang","raw_affiliation_strings":["School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, People\u2019s Republic of China","institution_ids":["https://openalex.org/I9842412"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5052651480"],"corresponding_institution_ids":["https://openalex.org/I9842412"],"apc_list":null,"apc_paid":null,"fwci":6.8847,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.97831273,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"94","issue":"354","first_page":"1721","last_page":"1759"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9998000264167786,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9995999932289124,"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/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.8434483408927917},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.7736297845840454},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5517796277999878},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5290074944496155},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.491345077753067},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.4645732641220093},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4638848900794983},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4303928315639496},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3675028085708618},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3001376688480377},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.11987742781639099},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11019933223724365},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.10699528455734253}],"concepts":[{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.8434483408927917},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.7736297845840454},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5517796277999878},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5290074944496155},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.491345077753067},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.4645732641220093},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4638848900794983},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4303928315639496},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3675028085708618},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3001376688480377},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.11987742781639099},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11019933223724365},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.10699528455734253}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/4015","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4015","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8100000023841858,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W586282074","https://openalex.org/W1483804921","https://openalex.org/W1970532716","https://openalex.org/W1970906109","https://openalex.org/W1989097818","https://openalex.org/W2005061077","https://openalex.org/W2010652522","https://openalex.org/W2014219947","https://openalex.org/W2027319740","https://openalex.org/W2032171614","https://openalex.org/W2033254215","https://openalex.org/W2049165066","https://openalex.org/W2080330641","https://openalex.org/W2088535056","https://openalex.org/W2090704787","https://openalex.org/W2106565812","https://openalex.org/W2164743984","https://openalex.org/W2314914323","https://openalex.org/W2588054282","https://openalex.org/W2914074116","https://openalex.org/W3026935255","https://openalex.org/W3108780065","https://openalex.org/W3151605865","https://openalex.org/W3155723199","https://openalex.org/W3159813613","https://openalex.org/W3160679425","https://openalex.org/W4206255168","https://openalex.org/W4211077197","https://openalex.org/W4225659843","https://openalex.org/W4226324972","https://openalex.org/W4389473729","https://openalex.org/W4391786284","https://openalex.org/W4404695384","https://openalex.org/W4405677240"],"related_works":["https://openalex.org/W4206768127","https://openalex.org/W2347486132","https://openalex.org/W4213270568","https://openalex.org/W4301315183","https://openalex.org/W2157764110","https://openalex.org/W2316789606","https://openalex.org/W2350340797","https://openalex.org/W2083551655","https://openalex.org/W4244999877","https://openalex.org/W4293224283"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2],"unified":[3],"theoretical":[4],"framework":[5,31],"to":[6,33,95,155],"examine":[7],"the":[8,29,35,43,49,56,67,74,97,130,135,139,145],"energy":[9,69,99,141,146],"dissipation":[10,70,86,100,142,147],"properties":[11],"at":[12],"all":[13],"stages":[14],"of":[15,28,38,46,102,122,137],"explicit":[16],"exponential":[17],"Runge-Kutta":[18],"(EERK)":[19],"methods":[20,94,117,128],"for":[21,91],"gradient":[22],"flow":[23],"problems.":[24],"The":[25],"main":[26,57],"part":[27],"novel":[30],"is":[32,78,88],"construct":[34],"differential":[36],"form":[37],"EERK":[39,63,104,116,123,127],"method":[40,47,64,105],"by":[41],"using":[42],"difference":[44],"coefficients":[45],"and":[48,144],"so-called":[50],"discrete":[51],"orthogonal":[52],"convolution":[53],"kernels.":[54],"As":[55],"result,":[58],"we":[59],"prove":[60],"that":[61,107],"an":[62,103],"can":[65,109],"preserve":[66],"original":[68,140],"law":[71,143],"unconditionally":[72],"if":[73],"associated":[75],"differentiation":[76],"matrix":[77],"positive":[79],"semi-definite.":[80],"A":[81],"simple":[82],"indicator,":[83],"namely":[84],"average":[85],"rate,":[87],"also":[89,153],"introduced":[90],"these":[92],"multi-stage":[93],"evaluate":[96],"overall":[98],"rate":[101],"such":[106],"one":[108],"choose":[110],"proper":[111],"parameters":[112],"in":[113,129],"some":[114],"parameterized":[115],"or":[118],"compare":[119],"different":[120],"kinds":[121],"methods.":[124],"Some":[125,149],"existing":[126],"literature":[131],"are":[132,152],"evaluated":[133],"from":[134],"perspective":[136],"preserving":[138],"rate.":[148],"numerical":[150],"examples":[151],"included":[154],"support":[156],"our":[157],"theory.":[158]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":1}],"updated_date":"2025-12-27T23:08:20.325037","created_date":"2025-10-10T00:00:00"}
