{"id":"https://openalex.org/W7214032302","doi":"https://doi.org/10.48550/arxiv.2609.23045","title":"Asymptotic preservation of an exponential Euler method under Hamiltonian fast advection with multiple critical points","display_name":"Asymptotic preservation of an exponential Euler method under Hamiltonian fast advection with multiple critical points","publication_year":2026,"publication_date":"2026-09-19","ids":{"openalex":"https://openalex.org/W7214032302","doi":"https://doi.org/10.48550/arxiv.2609.23045"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.23045","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23045","pdf_url":"https://arxiv.org/pdf/2609.23045","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.23045","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062043413","display_name":"Jianbo Cui","orcid":"https://orcid.org/0000-0003-4615-4390","observed_orcids":["https://orcid.org/0000-0003-4615-4390"]},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Cui, Jianbo","raw_affiliation_strings":["Department of Applied Mathematics , The Hong Kong Polytechnic University , Hung Hom , Kowloon , Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , The Hong Kong Polytechnic University , Hung Hom , Kowloon , Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152460540","display_name":"Guozhen Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Li, Guozhen","raw_affiliation_strings":["Department of Applied Mathematics , The Hong Kong Polytechnic University , Hung Hom , Kowloon , Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , The Hong Kong Polytechnic University , Hung Hom , Kowloon , Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037860907","display_name":"Derui Sheng","orcid":"https://orcid.org/0000-0002-8665-9038","observed_orcids":["https://orcid.org/0000-0002-8665-9038"]},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Sheng, Derui","raw_affiliation_strings":["Department of Applied Mathematics , The Hong Kong Polytechnic University , Hung Hom , Kowloon , Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , The Hong Kong Polytechnic University , Hung Hom , Kowloon , Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I14243506"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.8560000061988831,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.8560000061988831,"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/T11416","display_name":"Numerical methods for differential equations","score":0.0843999981880188,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.032600000500679016,"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/multiple-critical-points","display_name":"multiple critical points","score":0.9399999976158142},{"id":"https://openalex.org/keywords/metric-graphs","display_name":"metric graphs","score":0.6330000162124634},{"id":"https://openalex.org/keywords/strong-convergence","display_name":"strong convergence","score":0.7770000100135803},{"id":"https://openalex.org/keywords/weighted-l2-estimates","display_name":"weighted L2 estimates","score":0.8539999723434448}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8130999803543091},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5418999791145325},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5054000020027161},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5},{"id":"https://openalex.org/C5072599","wikidata":"https://www.wikidata.org/wiki/Q379788","display_name":"Advection","level":2,"score":0.48010000586509705},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4717000126838684},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4359999895095825},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.4032000005245209},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.3873000144958496},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.38589999079704285},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.38089999556541443},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.35510000586509705},{"id":"https://openalex.org/C2777634741","wikidata":"https://www.wikidata.org/wiki/Q768993","display_name":"Wasserstein metric","level":2,"score":0.34279999136924744},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.33719998598098755},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.31150001287460327},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.31049999594688416},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.3077999949455261},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.304500013589859},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.2992999851703644},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.2973000109195709},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.2856999933719635},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.2728999853134155},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C136864674","wikidata":"https://www.wikidata.org/wiki/Q477921","display_name":"Hamiltonian mechanics","level":3,"score":0.2596000134944916},{"id":"https://openalex.org/C38976095","wikidata":"https://www.wikidata.org/wiki/Q752641","display_name":"Asymmetry","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.2508000135421753}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.23045","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23045","pdf_url":"https://arxiv.org/pdf/2609.23045","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.23045","doi":"https://doi.org/10.48550/arxiv.2609.23045","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.23045","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.23045","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23045","pdf_url":"https://arxiv.org/pdf/2609.23045","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1357208708","display_name":null,"funder_award_id":"P0041274","funder_id":"https://openalex.org/F4320322598","funder_display_name":"Hong Kong Polytechnic University"},{"id":"https://openalex.org/G1479870695","display_name":null,"funder_award_id":"12522119","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G663028628","display_name":null,"funder_award_id":"12301526","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8651657396","display_name":null,"funder_award_id":"P0045336","funder_id":"https://openalex.org/F4320322598","funder_display_name":"Hong Kong Polytechnic University"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321523","display_name":"Chalmers Tekniska H\u00f6gskola","ror":"https://ror.org/040wg7k59"},{"id":"https://openalex.org/F4320322598","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214032302.pdf","grobid_xml":"https://content.openalex.org/works/W7214032302.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4394906840","https://openalex.org/W2999402452","https://openalex.org/W2948629959","https://openalex.org/W7147286778","https://openalex.org/W4404850155","https://openalex.org/W7212059947","https://openalex.org/W3184385953","https://openalex.org/W2331301548","https://openalex.org/W4392658957","https://openalex.org/W2558895487"],"abstract_inverted_index":{"We":[0],"establish":[1],"the":[2,6,26,29,47,52,61,70,77,116,120,124,130,135],"asymptotic-preserving":[3,121],"property":[4,122],"of":[5,51,76],"exponential":[7,54],"Euler":[8,55],"method":[9],"for":[10,99],"stochastic":[11,34],"reaction-diffusion-advection":[12],"equations":[13],"in":[14,123],"$\\mathbb":[15],"R^2$":[16],"under":[17,107],"fast":[18],"Hamiltonian":[19],"advection":[20],"with":[21,115],"multiple":[22,65],"critical":[23],"points.":[24],"In":[25],"fast-advection":[27,117],"limit,":[28],"dynamics":[30],"reduces":[31],"to":[32,97],"a":[33,39,81,91,108],"partial":[35],"differential":[36],"equation":[37],"on":[38],"noncompact":[40],"metric":[41],"graph.":[42],"A":[43],"key":[44],"ingredient":[45],"is":[46,58],"strong":[48],"convergence":[49,93,138],"analysis":[50],"limiting":[53],"scheme,":[56],"which":[57],"complicated":[59],"by":[60],"graph's":[62],"noncompactness,":[63],"its":[64],"edges":[66],"and":[67,69,73,85,104,133],"vertices,":[68],"nonuniform":[71],"ellipticity":[72],"vertex":[74],"degeneracy":[75],"graph":[78],"operator.":[79],"Using":[80],"weighted":[82,100],"$L^2$":[83,101],"framework":[84],"analytic-semigroup":[86],"smoothing":[87],"estimates,":[88],"we":[89],"prove":[90],"temporal":[92,137],"order":[94],"arbitrarily":[95],"close":[96],"$1/2$":[98,106],"initial":[102],"data":[103],"exactly":[105],"half-order":[109],"fractional-domain":[110],"condition.":[111],"Combining":[112],"these":[113],"estimates":[114],"limits":[118],"yields":[119],"multiple-critical-point":[125],"setting.":[126],"Numerical":[127],"experiments":[128],"illustrate":[129],"asymptotic":[131],"behavior":[132],"confirm":[134],"predicted":[136],"rate.":[139]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-23T00:00:00"}