The implementation of the discontinuous Galerkin method for two-dimensional Maxwell equations in Nektar++

Sall, Mamadou Baïlo (2016-03)

Thesis (MSc)--Stellenbosch University, 2016

Thesis

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.

AFRIKAANSE OPSOMMING : Die Maxwell vergelykings bestaan uit verskeie wette van elektromagnetisme, en kan geskryf word in twee verskillende modusse in twee dimensies: die dwars elektriese (DE) modus en die dwars magnetiese (DM) modus. In komputasionele elektromagnetisme is verskeie metodes al ontwikkel om elektrodinamiese toepassings numeries te simuleer. In hierdie tesis word 'n spektrale diskontinue Galerkin (DG) skema geïmplementeer vir Maxwell vergelykings in dwars elektriese sowel as dwars magnetiese polarisasie, in Nektar++, 'n spektrale oopbronsagteware. Die DG ruimtelike diskretisering lei tot 'n semidiskrete skema wat in tyd geïntegreer word met die Runge-Kutta metode, en twee numeriese uxusse word gebruik om elemente in die maas te interkonnekteer, naamlik die gesentreerde en die upwind numeriese uxusse. Om die p-konvergensie en h-konvergensie van die skema te wys, word numeriese toetse in die DE en DM modusse uitgevoer in lineêre en isotropiese media, gevolg deur 'n toepassing op die verstrooiing van 'n elektromagnetiese golf deur 'n ronde silinder en 'n reghoekige volmaakte elektriese geleier. Vir altwee modusse word die geïnduseerde stroom op die oppervlak van die verstrooier uitgewerk deur gebruik te maak van die totaleveld/verstrooiingsveld formulering.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/98575
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