Sien, Neoh Soon
(2019)
Improved Residual Distributionschemes For The Maxwell’s.
PhD thesis, Universiti Sains Malaysia.
Abstract
Electrodynamics have innumerable applications, one of which is to locate
embedded object, for example in a human body using electromagnetic scattering.
The wireless telecommunication is all about the radiation of electromagnetic
waves, and the optical waveguide transmits signals at the speed of light.
The aspiration of this work is to introduce the vertexbased residual distribution(RD) schemes for Maxwell’s equations, which is timeexplicit and still secondorderaccurate. The computational electromagnetics (CEM) works do not havea standard mesh topology for unstructured grid, which might inhibit their computationaldevelopment. The most eminent residual distribution scheme which
vouches for the secondorderaccuracy is the LaxWendroff residual distribution
(RDLW) scheme. The RD schemes are transcendent for upwind schemes that
stay compact, such as the RDLDA (low diffusion A) scheme, but appears to be
timeimplicit for timedependent fluid problems. The first innovation in this work is to procure a timeexplicit updating scheme for RDLDA scheme while still retaining the orderofaccuracy. Besides, the RDGalerkin method is propounded
in this work, which is rare in RD framework. Secondly, the weak Galerkin FEM is
adapted for timedependent secondorder Maxwell’s equation, and also devising a
gradient flux residual approach which is tantamount to the RDscheme for secondorder Maxwell’s equation. These two effective solvers reduce firstorder Maxwell’s equations to secondorder Maxwell’s equation in scalar form. The weak Galerkin finiteelement method (FEM) is indisputably more accurate in replicating nuxxiv merical results, but it is somehow deficient upon handling certain boundaries,unlike the gradient flux residual approach. The novelty of this work comes from introducing the RD schemes to firstorder Maxwell’s equations, while devising a new RD scheme for the secondorder Maxwell’s equation. The test cases in this work comprised of three main electrodynamics phenomena, they are waveguide propagation, radiation mechanism and scattering problem. Threedimensional problems are also studied to ascertain the extension of these schemes for realtime applications. The numerical results manifest no instability issues for all the constructed numerical schemes. The lumped RDLDA scheme trims off the
computational cost by approximately 50 times, as compared to its timeimplicit
consistent massmatrix approach, although this is still 4 to 6 times higher than
the RDLW scheme’s. In general, the spacecentered schemes of RDLW, RDGalerkin,
weak Galerkin FEM and gradient flux residual in this work promise an
orderofaccuracy between 1:4212 and 2:43871. In contradistinction to the spacecentered schemes, the upwind RDLDA schemes only have an orderofaccuracy
ranging from 0:7825 to 0:9335.
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