{"id":"https://openalex.org/W4306412372","doi":"https://doi.org/10.1137/22m147952x","title":"Hamiltonian-Preserving Discontinuous Galerkin Methods for the Liouville Equation With Discontinuous Potential","display_name":"Hamiltonian-Preserving Discontinuous Galerkin Methods for the Liouville Equation With Discontinuous Potential","publication_year":2022,"publication_date":"2022-10-01","ids":{"openalex":"https://openalex.org/W4306412372","doi":"https://doi.org/10.1137/22m147952x"},"language":"en","primary_location":{"id":"doi:10.1137/22m147952x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m147952x","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/A5002727544","display_name":"Boyang Ye","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Boyang Ye","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017812804","display_name":"Shi Jin","orcid":"https://orcid.org/0000-0002-8635-7435"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shi Jin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021293562","display_name":"Yulong Xing","orcid":"https://orcid.org/0000-0002-3504-6194"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yulong Xing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5064601117","display_name":"Xinghui Zhong","orcid":"https://orcid.org/0000-0003-3681-9598"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xinghui Zhong","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-3681-9598","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11628572,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"44","issue":"5","first_page":"A3317","last_page":"A3340"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9990000128746033,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9990000128746033,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987000226974487,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9965000152587891,"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/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.8028115034103394},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7543613910675049},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5424677729606628},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4765130281448364},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4693741798400879},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.46155428886413574},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3861194849014282},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.19614070653915405},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.16869434714317322},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09548807144165039}],"concepts":[{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.8028115034103394},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7543613910675049},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5424677729606628},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4765130281448364},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4693741798400879},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.46155428886413574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3861194849014282},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.19614070653915405},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.16869434714317322},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09548807144165039},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m147952x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m147952x","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2421126317","display_name":null,"funder_award_id":"11871428","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3998814077","display_name":null,"funder_award_id":"DMS-1753581","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7627071985","display_name":null,"funder_award_id":"12031013","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1600997507","https://openalex.org/W1971728915","https://openalex.org/W1982465309","https://openalex.org/W1995266347","https://openalex.org/W2018277869","https://openalex.org/W2026836732","https://openalex.org/W2028550140","https://openalex.org/W2035974650","https://openalex.org/W2048742304","https://openalex.org/W2052104757","https://openalex.org/W2056490794","https://openalex.org/W2068039185","https://openalex.org/W2070533863","https://openalex.org/W2071858499","https://openalex.org/W2073649388","https://openalex.org/W2074900879","https://openalex.org/W2081339714","https://openalex.org/W2101638790","https://openalex.org/W2105705213","https://openalex.org/W2111427335","https://openalex.org/W2139971200","https://openalex.org/W2166039818","https://openalex.org/W2167159842","https://openalex.org/W2170690815","https://openalex.org/W2530578203","https://openalex.org/W2963271011","https://openalex.org/W3010292040","https://openalex.org/W3140310139","https://openalex.org/W4247811167","https://openalex.org/W4252060206"],"related_works":["https://openalex.org/W623557396","https://openalex.org/W2120874885","https://openalex.org/W1965109456","https://openalex.org/W2244225468","https://openalex.org/W968924973","https://openalex.org/W2435162739","https://openalex.org/W2003988341","https://openalex.org/W3087073411","https://openalex.org/W2064065738","https://openalex.org/W4285308861"],"abstract_inverted_index":{"Numerically":[0],"solving":[1],"the":[2,15,21,24,35,40,59,89,103,107,112,119,123,128,131,134,138,157,168,173],"Liouville":[3,60],"equation":[4,61],"in":[5,65,153],"classical":[6,116],"mechanics":[7],"with":[8,62,74],"a":[9,28,52,115],"discontinuous":[10,54,63],"potential":[11,25,64,120,135],"often":[12],"leads":[13],"to":[14,19,34,100,110,148,166],"challenges":[16],"of":[17,77,91,106,114,130,172],"how":[18],"preserve":[20],"Hamiltonian":[22,132],"across":[23,133],"barrier":[26,121,136],"and":[27,47,79,88,96,137,141,151,170],"severe":[29],"time":[30],"step":[31],"constraint":[32],"according":[33],"Courant--Friedrichs--Lewy":[36],"condition.":[37,143],"Motivated":[38],"by":[39,45],"Hamiltonian-preserving":[41,53],"finite":[42],"volume":[43],"schemes":[44],"Jin":[46],"Wen":[48],"[21],":[49],"we":[50],"introduce":[51],"Galerkin":[55],"(DG)":[56],"scheme":[57,145],"for":[58],"this":[66],"paper.":[67],"The":[68],"DG":[69,108],"method":[70],"can":[71],"be":[72,149],"designed":[73],"arbitrary":[75],"order":[76],"accuracy":[78,169],"offers":[80],"many":[81],"advantages":[82],"including":[83],"easy":[84],"adaptivity,":[85],"compact":[86],"stencils,":[87],"ability":[90],"handling":[92],"complicated":[93],"boundary":[94],"conditions":[95],"interfaces.":[97],"We":[98],"propose":[99],"carefully":[101],"design":[102],"numerical":[104,124,175],"fluxes":[105],"methods":[109],"build":[111],"behavior":[113],"particle":[117],"at":[118],"into":[122],"scheme,":[125],"which":[126],"ensures":[127],"continuity":[129],"correct":[139],"transmission":[140],"reflection":[142],"Our":[144],"is":[146,160],"proved":[147],"positive":[150],"stable":[152],"$L^1$":[154],"norm":[155],"if":[156],"positivity-preserving":[158],"limiter":[159],"applied.":[161],"Numerical":[162],"examples":[163],"are":[164],"provided":[165],"illustrate":[167],"effectiveness":[171],"proposed":[174],"scheme.":[176]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}