{"id":"https://openalex.org/W2116046842","doi":"https://doi.org/10.1137/070709505","title":"A Hybrid Phase-Flow Method for Hamiltonian Systems with Discontinuous Hamiltonians","display_name":"A Hybrid Phase-Flow Method for Hamiltonian Systems with Discontinuous Hamiltonians","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2116046842","doi":"https://doi.org/10.1137/070709505","mag":"2116046842"},"language":"en","primary_location":{"id":"doi:10.1137/070709505","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070709505","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/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":["jin@math.wisc.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"jin@math.wisc.edu#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107874398","display_name":"Hao Wu","orcid":"https://orcid.org/0009-0004-2341-4764"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao Wu","raw_affiliation_strings":["hwu04@mails.tsinghua.edu.cn and zhuang@math.tsinghua.edu.cn#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"hwu04@mails.tsinghua.edu.cn and zhuang@math.tsinghua.edu.cn#TAB#","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065270536","display_name":"Zhongyi Huang","orcid":"https://orcid.org/0000-0002-5623-4864"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongyi Huang","raw_affiliation_strings":["Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4961,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.8980367,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"31","issue":"2","first_page":"1303","last_page":"1321"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9986000061035156,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9986000061035156,"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":0.9980999827384949,"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/T11965","display_name":"Quantum, superfluid, helium dynamics","score":0.9965000152587891,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7383751273155212},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6821042895317078},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6660690307617188},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.544222354888916},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.531958818435669},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5311445593833923},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.49005258083343506},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.48086029291152954},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4679777920246124},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3098323345184326},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2088778018951416},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.20358595252037048},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.142412930727005}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7383751273155212},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6821042895317078},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6660690307617188},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.544222354888916},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.531958818435669},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5311445593833923},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.49005258083343506},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.48086029291152954},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4679777920246124},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3098323345184326},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2088778018951416},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.20358595252037048},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.142412930727005},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/070709505","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070709505","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:CiteSeerX.psu:10.1.1.294.9491","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.294.9491","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.wisc.edu/~jin/PS/hpfpm.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.73.7646","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.73.7646","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.wisc.edu/~jin/PS/hpfpm.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1530404001","https://openalex.org/W1544770838","https://openalex.org/W1552159942","https://openalex.org/W1558736232","https://openalex.org/W1638501928","https://openalex.org/W1910233272","https://openalex.org/W1978588812","https://openalex.org/W1979604227","https://openalex.org/W1983797262","https://openalex.org/W1995266347","https://openalex.org/W2001888406","https://openalex.org/W2023082994","https://openalex.org/W2026073961","https://openalex.org/W2035974650","https://openalex.org/W2039914675","https://openalex.org/W2052104757","https://openalex.org/W2054662916","https://openalex.org/W2064476366","https://openalex.org/W2068039185","https://openalex.org/W2073649388","https://openalex.org/W2083916485","https://openalex.org/W2150077991","https://openalex.org/W2167159842","https://openalex.org/W2169501376","https://openalex.org/W2491804397","https://openalex.org/W2892948875","https://openalex.org/W3141151088"],"related_works":["https://openalex.org/W2186864281","https://openalex.org/W4255427455","https://openalex.org/W1966025497","https://openalex.org/W68941528","https://openalex.org/W4206451355","https://openalex.org/W1553604823","https://openalex.org/W8322802","https://openalex.org/W2195994862","https://openalex.org/W314331466","https://openalex.org/W2149122936"],"abstract_inverted_index":{"In":[0,15],"this":[1],"paper,":[2],"we":[3],"propose":[4],"a":[5,69,83,100,107],"new":[6],"phase-flow":[7,18,66,93],"method":[8,19,67,94,109],"for":[9,56,113],"Hamiltonian":[10,60,71,97],"systems":[11],"with":[12,99],"discontinuous":[13,70],"Hamiltonians.":[14],"the":[16,32,40,43,51,59,65,75,87,90,114],"original":[17],"introduced":[20],"by":[21],"Ying":[22],"and":[23,73],"Cand\u00e8s":[24],"[J.":[25],"Comput.":[26],"Phys.,":[27],"220":[28],"(2006),":[29],"pp.":[30],"184\u2013215],":[31],"phase":[33,52],"map":[34,53],"should":[35],"be":[36,111],"smooth":[37],"to":[38,95],"ensure":[39],"accuracy":[41],"of":[42,81,89,103,116],"interpolation.":[44],"Such":[45,106],"an":[46],"interpolation":[47],"is":[48,54,61],"inaccurate":[49],"if":[50],"nonsmooth,":[55],"example,":[57],"when":[58],"discontinuous.":[62],"We":[63],"modify":[64],"using":[68],"solver":[72],"establish":[74],"stability":[76],"(for":[77],"piecewise":[78],"constant":[79],"potentials)":[80],"such":[82],"solver.":[84],"This":[85],"extends":[86],"applicability":[88],"highly":[91],"efficient":[92],"singular":[96],"systems,":[98],"mild":[101],"increase":[102],"algorithm":[104],"complexity.":[105],"particle":[108],"can":[110],"useful":[112],"computation":[115],"high":[117],"frequency":[118],"waves":[119],"through":[120],"interfaces.":[121]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}