Symplectic Hamiltonian Finite Element Methods for Semilinear Wave Propagation

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dc.contributor.authorSanchez, Manuel A.
dc.contributor.authorValenzuela, Joaquin
dc.date.accessioned2025-01-20T17:05:46Z
dc.date.available2025-01-20T17:05:46Z
dc.date.issued2024
dc.description.abstractThis paper presents Hamiltonian finite element methods for approximating semilinear wave propagation problems, including the nonlinear Klein-Gordon and sine-Gordon equations. The aim is to obtain accurate high-order approximations while conserving physical quantities of interest such as energy. To achieve conservation properties at a discrete level, we propose semidiscrete schemes based on two Hamiltonian structures of the equation. These include Mixed finite element methods, discontinuous Galerkin methods, and hybridizable discontinuous Galerkin methods (HDG). In particular, we propose a new class of DG methods using time operators to define the numerical traces, ultimately leading to an energy-conserving scheme. Time discretization uses Symplectic explicit-partitioned and diagonally-implicit Runge-Kutta schemes. Furthermore, the paper showcases several numerical examples that demonstrate the accuracy and energy conservation properties of the approximations, along with the simulation of soliton cloning.
dc.description.funderAgencia Nacional de Investigacin y Desarrollo
dc.fuente.origenWOS
dc.identifier.doi10.1007/s10915-024-02519-z
dc.identifier.eissn1573-7691
dc.identifier.issn0885-7474
dc.identifier.urihttps://doi.org/10.1007/s10915-024-02519-z
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/90745
dc.identifier.wosidWOS:001205445400004
dc.issue.numero3
dc.language.isoen
dc.revistaJournal of scientific computing
dc.rightsacceso restringido
dc.subjectDiscontinuous Galerkin methods
dc.subjectHybrid/mixed methods
dc.subjectSemilinear wave equation Hamiltonian systems
dc.subjectNonlinear Klein-Gordon equation
dc.subjectSine-Gordon equation
dc.titleSymplectic Hamiltonian Finite Element Methods for Semilinear Wave Propagation
dc.typeartículo
dc.volumen99
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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