{"id":"https://openalex.org/W7168249423","doi":"https://doi.org/10.48550/arxiv.2607.10652","title":"Symplectic Hamiltonian Direct Discontinuous Galerkin Method for Wave Propagation","display_name":"Symplectic Hamiltonian Direct Discontinuous Galerkin Method for Wave Propagation","publication_year":2026,"publication_date":"2026-07-12","ids":{"openalex":"https://openalex.org/W7168249423","doi":"https://doi.org/10.48550/arxiv.2607.10652"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.10652","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.10652","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.10652","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140663204","display_name":"Haomiao Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Haomiao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5140608052","display_name":"Yumiao Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Yumiao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5140603996","display_name":"Jiaxin Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Jiaxin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5140701476","display_name":"Tiegang Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Tiegang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5140653269","display_name":"Kun Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Kun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9168000221252441,"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":0.9168000221252441,"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":0.06019999831914902,"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":0.007600000128149986,"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":0.8090000152587891},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5845999717712402},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5810999870300293},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5189999938011169},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5157999992370605},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.44339999556541443},{"id":"https://openalex.org/keywords/hamiltonian-mechanics","display_name":"Hamiltonian mechanics","score":0.40119999647140503},{"id":"https://openalex.org/keywords/bilinear-form","display_name":"Bilinear form","score":0.38989999890327454}],"concepts":[{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.8090000152587891},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7318999767303467},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5845999717712402},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5810999870300293},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5407999753952026},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5189999938011169},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5157999992370605},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.44339999556541443},{"id":"https://openalex.org/C136864674","wikidata":"https://www.wikidata.org/wiki/Q477921","display_name":"Hamiltonian mechanics","level":3,"score":0.40119999647140503},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.38989999890327454},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35199999809265137},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.3352000117301941},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3228999972343445},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C135661100","wikidata":"https://www.wikidata.org/wiki/Q1049064","display_name":"Symplectomorphism","level":3,"score":0.3073999881744385},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.29589998722076416},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.29330000281333923},{"id":"https://openalex.org/C44886760","wikidata":"https://www.wikidata.org/wiki/Q1758425","display_name":"Wave propagation","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2856999933719635},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C207646825","wikidata":"https://www.wikidata.org/wiki/Q7661847","display_name":"Symplectic integrator","level":4,"score":0.26499998569488525},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.2540999948978424},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2540000081062317}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.10652","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.10652","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.10652","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.10652","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,45,67],"symplectic":[4,92,101,145],"Hamiltonian":[5,47,69,146],"direct":[6],"discontinuous":[7],"Galerkin":[8],"(DDG)":[9],"method":[10,59,65,112,148],"for":[11,109,123,131],"approximating":[12],"wave":[13,21,116],"propagation":[14],"problems,":[15],"including":[16,73],"the":[17,31,34,42,55,61,74,96,110,119,124,127,132,137,144],"linear":[18],"and":[19,60,77,126,141,154],"semilinear":[20,115],"equations.":[22],"Within":[23],"an":[24],"auxiliary-variable-free":[25],"DG":[26],"framework,":[27],"we":[28,88],"prove":[29],"that":[30,51,143],"symmetry":[32],"of":[33,44],"numerical":[35],"flux":[36],"bilinear":[37],"form":[38],"is":[39],"equivalent":[40],"to":[41,114],"existence":[43],"discrete":[46,68,91],"structure.":[48],"It":[49],"follows":[50],"methods":[52,79],"such":[53],"as":[54],"symmetric":[56,62],"interior":[57],"penalty":[58],"DDG":[63,147],"(SDDG)":[64],"admit":[66],"structure,":[70,87],"whereas":[71],"schemes":[72,93],"Baumann--Oden,":[75],"DDG,":[76],"BR2":[78],"do":[80],"not":[81],"possess":[82],"this":[83,86],"property.":[84],"Exploiting":[85],"construct":[89],"fully":[90],"by":[94],"combining":[95],"SDDG":[97,111],"spatial":[98],"discretization":[99],"with":[100],"time":[102],"integrators.":[103],"We":[104],"further":[105],"derive":[106],"error":[107],"estimates":[108],"applied":[113],"equations,":[117],"showing":[118],"optimal":[120],"convergence":[121,129,139],"rate":[122,130],"displacement":[125],"suboptimal":[128],"velocity.":[133],"Numerical":[134],"experiments":[135],"validate":[136],"theoretical":[138],"rates":[140],"demonstrate":[142],"achieves":[149],"superior":[150],"long-time":[151],"energy":[152],"conservation":[153],"accuracy.":[155]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-15T00:00:00"}