Symplectic Hamiltonian finite element methods for electromagnetics

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dc.contributor.authorSanchez, Manuel A.
dc.contributor.authorDu, Shukai
dc.contributor.authorCockburn, Bernardo
dc.contributor.authorNguyen, Ngoc-Cuong
dc.contributor.authorPeraire, Jaime
dc.date.accessioned2025-01-20T21:06:19Z
dc.date.available2025-01-20T21:06:19Z
dc.date.issued2022
dc.description.abstractWe present several high-order accurate finite element methods for the Maxwell's equations which provide time-invariant, non-drifting approximations to the total electric and magnetic charges, and to the total energy. We devise these methods by taking advantage of the Hamiltonian structures of the Maxwell's equations as follows. First, we introduce spatial discretizations of the Maxwell's equations using mixed finite element, discontinuous Galerkin, and hybridizable discontinuous Galerkin methods to obtain a semi-discrete system of equations which display discrete versions of the Hamiltonian structure of the Maxwell's equations. Then we discretize the resulting semi-discrete system in time by using a symplectic integrator. This ensures the conservation properties of the fully discrete system of equations. For the Symplectic Hamiltonian HDG method, we present numerical experiments which confirm its optimal orders of convergence for all variables and its conservation properties for the total linear and angular momenta, as well as the total energy. Finally, we discuss the extension of our results to other boundary conditions and to numerical schemes defined by different weak formulations.(c) 2022 Elsevier B.V. All rights reserved.
dc.fuente.origenWOS
dc.identifier.doi10.1016/j.cma.2022.114969
dc.identifier.eissn1879-2138
dc.identifier.issn0045-7825
dc.identifier.urihttps://doi.org/10.1016/j.cma.2022.114969
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/93346
dc.identifier.wosidWOS:000802531600004
dc.language.isoen
dc.revistaComputer methods in applied mechanics and engineering
dc.rightsacceso restringido
dc.subjectTime-dependent Maxwell?s equations
dc.subjectSymplectic Hamiltonian finite element methods
dc.subjectMixed methods
dc.subjectDiscontinuous Galerkin methods
dc.subjectHybridizable discontinuous Galerkin methods
dc.titleSymplectic Hamiltonian finite element methods for electromagnetics
dc.typeartículo
dc.volumen396
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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