{"id":"https://openalex.org/W3206956769","doi":"https://doi.org/10.3390/sym13101930","title":"Symplectic All-at-Once Method for Hamiltonian Systems","display_name":"Symplectic All-at-Once Method for Hamiltonian Systems","publication_year":2021,"publication_date":"2021-10-14","ids":{"openalex":"https://openalex.org/W3206956769","doi":"https://doi.org/10.3390/sym13101930","mag":"3206956769"},"language":"en","primary_location":{"id":"doi:10.3390/sym13101930","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13101930","pdf_url":"https://www.mdpi.com/2073-8994/13/10/1930/pdf?version=1634527845","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/10/1930/pdf?version=1634527845","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085261208","display_name":"Beibei Zhu","orcid":"https://orcid.org/0000-0002-8775-0108"},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bei-Bei Zhu","raw_affiliation_strings":["School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5120850130","display_name":"Yong-Liang Zhao","orcid":"https://orcid.org/0009-0007-3823-5357"},"institutions":[{"id":"https://openalex.org/I63354593","display_name":"Sichuan Normal University","ror":"https://ror.org/043dxc061","country_code":"CN","type":"education","lineage":["https://openalex.org/I63354593"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong-Liang Zhao","raw_affiliation_strings":["School of Mathematical Sciences, Sichuan Normal University, Chengdu 610068, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Sichuan Normal University, Chengdu 610068, China","institution_ids":["https://openalex.org/I63354593"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085261208"],"corresponding_institution_ids":["https://openalex.org/I92403157"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3124,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56223464,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"13","issue":"10","first_page":"1930","last_page":"1930"},"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":0.9994000196456909,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/symplectic-geometry","display_name":"Symplectic geometry","score":0.8165313005447388},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.7580918073654175},{"id":"https://openalex.org/keywords/symplectic-integrator","display_name":"Symplectic integrator","score":0.5898335576057434},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5530515313148499},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5105829834938049},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45643770694732666},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40899163484573364},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3284251093864441},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3023386001586914},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22758567333221436},{"id":"https://openalex.org/keywords/symplectic-manifold","display_name":"Symplectic manifold","score":0.2259964644908905}],"concepts":[{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.8165313005447388},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.7580918073654175},{"id":"https://openalex.org/C207646825","wikidata":"https://www.wikidata.org/wiki/Q7661847","display_name":"Symplectic integrator","level":4,"score":0.5898335576057434},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5530515313148499},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5105829834938049},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45643770694732666},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40899163484573364},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3284251093864441},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3023386001586914},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22758567333221436},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.2259964644908905}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13101930","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13101930","pdf_url":"https://www.mdpi.com/2073-8994/13/10/1930/pdf?version=1634527845","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a56db8bf02fe49ae87001d2989f5c761","is_oa":true,"landing_page_url":"https://doaj.org/article/a56db8bf02fe49ae87001d2989f5c761","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 10, p 1930 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/10/1930/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13101930","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13101930","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13101930","pdf_url":"https://www.mdpi.com/2073-8994/13/10/1930/pdf?version=1634527845","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.8199999928474426,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G2953579065","display_name":null,"funder_award_id":"11901564","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3206956769.pdf","grobid_xml":"https://content.openalex.org/works/W3206956769.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W587555435","https://openalex.org/W1506342804","https://openalex.org/W1607460358","https://openalex.org/W1945420166","https://openalex.org/W1965757759","https://openalex.org/W1986367849","https://openalex.org/W2001569514","https://openalex.org/W2025692268","https://openalex.org/W2045621460","https://openalex.org/W2045701663","https://openalex.org/W2046608570","https://openalex.org/W2084367325","https://openalex.org/W2115291951","https://openalex.org/W2129191879","https://openalex.org/W2340680806","https://openalex.org/W2341074930","https://openalex.org/W2421968726","https://openalex.org/W2563511547","https://openalex.org/W2610765273","https://openalex.org/W2809985151","https://openalex.org/W2943648831","https://openalex.org/W2947056241","https://openalex.org/W3026890537","https://openalex.org/W3164559554","https://openalex.org/W3199556142","https://openalex.org/W4213034854","https://openalex.org/W6641835042","https://openalex.org/W6661766136","https://openalex.org/W6808754384"],"related_works":["https://openalex.org/W1974002951","https://openalex.org/W1574778259","https://openalex.org/W1970254086","https://openalex.org/W4297992868","https://openalex.org/W2390276644","https://openalex.org/W3011215806","https://openalex.org/W25827740","https://openalex.org/W2064282017","https://openalex.org/W2027000851","https://openalex.org/W4298036990"],"abstract_inverted_index":{"The":[0,29],"all-at-once":[1,49],"technique":[2,17],"has":[3],"attracted":[4],"many":[5],"researchers\u2019":[6],"interest":[7],"in":[8],"recent":[9],"years.":[10],"In":[11,39],"this":[12,16],"paper,":[13],"we":[14],"combine":[15],"with":[18,61],"a":[19,51],"classical":[20,78],"symplectic":[21,79],"and":[22],"symmetric":[23],"method":[24,72],"for":[25],"solving":[26,47],"Hamiltonian":[27,59],"systems.":[28],"solutions":[30],"at":[31,37],"all":[32],"time":[33],"steps":[34],"are":[35,66],"obtained":[36],"one-shot.":[38],"order":[40],"to":[41,68],"reduce":[42],"the":[43,48,77],"computational":[44],"cost":[45],"of":[46,58,63],"system,":[50],"fast":[52],"algorithm":[53],"is":[54,73],"designed.":[55],"Numerical":[56],"experiments":[57],"systems":[60],"degrees":[62],"freedom":[64],"n\u22643":[65],"provided":[67],"show":[69],"that":[70],"our":[71],"more":[74],"efficient":[75],"than":[76],"method.":[80]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
