Locally Implicit Discontinuous Galerkin Methods for Time-Domain Maxwell’s Equations

L. Moya ()
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L. Moya: Inria Sophia Antipolis – Méditerranée

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 129-137 from Springer

Abstract: Abstract An attractive feature of discontinuous Galerkin (DG) spatial discretization is the possibility of using locally refined space grids to handle geometrical details. However, when combined with an explicit integration method to numerically solve a time-dependent partial differential equation, this readily leads to unduly large step size restrictions caused by the smallest grid elements. If the local refinement is strongly localized such that the ratio of fine to coarse elements is small, the unduly step size restrictions can be overcome by blending an implicit and an explicit scheme where only solution variables living at fine elements are implicitly treated. The counterpart of this approach is having to solve a linear system per time step. But due to the assumed small fine to coarse elements ratio, the overhead will also be small while the solution can be advanced in time with step sizes determined by the coarse elements. We propose to present two locally implicit methods for the time-domain Maxwell’s equations. Our purpose is to compare the two with DG spatial discretization so that the most efficient one can be advocated for future use. Finally we will present a preliminary numerical investigation to increase the order of convergence.

Keywords: Discontinuous Galerkin; Discontinuous Galerkin Method; Convergence Order; Fine Element; Richardson Extrapolation (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-33134-3_14

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DOI: 10.1007/978-3-642-33134-3_14

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