Browsing Department of Applied Mathematics by browse.metadata.advisor "Chun, Sehun"
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- ItemThe implementation of the discontinuous Galerkin method for two-dimensional Maxwell equations in Nektar++(Stellenbosch : Stellenbosch University, 2016-03) Sall, Mamadou Baïlo; Chun, Sehun; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics)ENGLISH ABSTRACT : Maxwell's equations consist of various laws of electromagnetism and can be written in two different modes in two dimensions: the transverse electric(TE) mode and the transverse magnetic(TM) mode. Various methods have been developed in Computational electromagnetics for numerical simulations of electrodynamic applications. In this thesis, a spectral/hp discontinuous Galerkin(DG) scheme is implemented for Maxwell's equations in TE as well as in TM polarization, in Nektar++ a spectral/hp object-oriented open-source software. The DG space discretization leads to a semi-discrete scheme to be integrated in time with the Runge-Kutta method, and two numerical fluxes are used to interconnect elements in the mesh namely the centered and the upwind numerical fluxes. To show the p-convergence and the h-convergence of the scheme, numerical tests in TE and TM modes are performed in linear and isotropic media, followed by an application to the scattering of an electromagnetic wave by a circular cylinder and a rectangular perfect electric conductor. For both modes, the induced current on the surface of the scatterer is computed, using the total field/scattered field formulation.