Discontinuous Galerkin Methods with Time-Operators in Their Numerical Traces for Time-Dependent Electromagnetics

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dc.contributor.authorCockburn, Bernardo
dc.contributor.authorDu, Shukai
dc.contributor.authorSanchez, Manuel A.
dc.date.accessioned2025-01-20T21:07:24Z
dc.date.available2025-01-20T21:07:24Z
dc.date.issued2022
dc.description.abstractWe present a new class of discontinuous Galerkin methods for the space discretization of the time-dependent Maxwell equations whose main feature is the use of time derivatives and/or time integrals in the stabilization part of their numerical traces. These numerical traces are chosen in such a way that the resulting semidiscrete schemes exactly conserve a discrete version of the energy. We introduce four model ways of achieving this and show that, when using the mid-point rule to march in time, the fully discrete schemes also conserve the discrete energy. Moreover, we propose a new three-step technique to devise fully discrete schemes of arbitrary order of accuracy which conserve the energy in time. The first step consists in transforming the semidiscrete scheme into a Hamiltonian dynamical system. The second step consists in applying a symplectic time-marching method to this dynamical system in order to guarantee that the resulting fully discrete method conserves the discrete energy in time. The third and last step consists in reversing the above-mentioned transformation to rewrite the fully discrete scheme in terms of the original variables.
dc.fuente.origenWOS
dc.identifier.doi10.1515/cmam-2021-0215
dc.identifier.eissn1609-9389
dc.identifier.issn1609-4840
dc.identifier.urihttps://doi.org/10.1515/cmam-2021-0215
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/93412
dc.identifier.wosidWOS:000797796400001
dc.issue.numero4
dc.language.isoen
dc.pagina.final796
dc.pagina.inicio775
dc.revistaComputational methods in applied mathematics
dc.rightsacceso restringido
dc.subjectTime-Dependent Maxwell's Equations
dc.subjectDiscontinuous Galerkin Methods
dc.subjectEnergy-Conserving Methods
dc.titleDiscontinuous Galerkin Methods with Time-Operators in Their Numerical Traces for Time-Dependent Electromagnetics
dc.typeartículo
dc.volumen22
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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