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 vertex-based residual distribution(RD) schemes for Maxwell’s equations, which is time-explicit and still secondorder-accurate. 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 second-order-accuracy is the Lax-Wendroff residual distribution
(RD-LW) scheme. The RD schemes are transcendent for upwind schemes that
stay compact, such as the RD-LDA (low diffusion A) scheme, but appears to be
time-implicit for time-dependent fluid problems. The first innovation in this work is to procure a time-explicit updating scheme for RD-LDA scheme while still retaining the order-of-accuracy. Besides, the RD-Galerkin method is propounded
in this work, which is rare in RD framework. Secondly, the weak Galerkin FEM is
adapted for time-dependent second-order Maxwell’s equation, and also devising a
gradient flux residual approach which is tantamount to the RD-scheme for secondorder Maxwell’s equation. These two effective solvers reduce first-order Maxwell’s equations to second-order Maxwell’s equation in scalar form. The weak Galerkin finite-element 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 first-order Maxwell’s equations, while devising a new RD scheme for the second-order Maxwell’s equation. The test cases in this work comprised of three main electrodynamics phenomena, they are waveguide propagation, radiation mechanism and scattering problem. Three-dimensional 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 RD-LDA scheme trims off the
computational cost by approximately 50 times, as compared to its time-implicit
consistent mass-matrix approach, although this is still 4 to 6 times higher than
the RD-LW scheme’s. In general, the space-centered schemes of RD-LW, RDGalerkin,
weak Galerkin FEM and gradient flux residual in this work promise an
order-of-accuracy between 1:4212 and 2:43871. In contradistinction to the spacecentered schemes, the upwind RD-LDA schemes only have an order-of-accuracy
ranging from 0:7825 to 0:9335.
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