Efficient absorbing boundary condition for UWB simulation in frequency dependent ADI-FDTD

Abstract

fIhe FmiteDifference Tie-,Domain (FDTD) method has become intng for electromagnetic simulations since the wide availability ofcomputerresource. Its key feaures are its simplicity both in le tn and in the simulation Space. One of its teetdhng problems, togh, is that h e needs to be terminated. Ihis is not an issue when the mulation space is sonded by physical boundaries, like in a cavity, butproblems ariseforfree space simulaion. Thatiswhere Absrbing Boundary Conditions (ABCs) come into play; They aim at absolbng the outgoing wave as if it was still travelling outward. Dffeent echniques to absorb the outgoing wave have been devised. Mur used Maxwell-Gauss' equations to cancel the outgoing wave, reslang in Mur's ABC [1]. It is easy to implement and is c uonaly efficient although it only absorbs accurately orthogonal waves, so comers are a problem and tus it cannot be plaed close to the scaterers Anodter cniqle alled liao's ABC [2] comes fiom wave tery. It only uses wave tieorytoabsorb the outgoing wave and altmugh itis more compl than afirt order Mur's ABC and is also only efficient at absorbing orthogonal waves, another formulation makes use of a damping parameter which can absorb non-orthogonal incident waves [3,41. The last technique, which has received a lot of attention, consists in surrounding the computation space by an artificial anisotpic media. It wes first intrxduced by Brenger and it is called the Perfecdy Matched Layer (PML) ABC [5]. It is th most veatile of the ABCs, effectively absorbing any outgoing waves, from any direction and any fiequency. Because PML emulates a media, it increases the size of the conputatidl space by the size of the absorbing media and moreover the PML media is updated like the computational space and requies some computation. That makes the PML ABC the most memory and computatonally de g ABC.The oiginal PML as proposed by Bdrenger had some problems. The first one was dtat the PML media paamets proposed were not general enough to fit some simulations. As exposed in [6], the oiginal PML does not absorb evanescent waves efficiently, so the PML has to be placed furhr away from the scantrs for the waves to have enough time to decay. This problem has been taken care of by Gribbons et aL [7] by intrucing a stretched coordinates system inside the PML media so that evannt waves spend enough time in the PML to get absorbed. Another shortcoming of the original PML is tht when simulations involve long grids or signals with long tme signature, which means that the simulation is run long after the initial excitation decayed, late time refiections can show up [8]. This is due to the weak causal nature of the original PML fulaon. Kuzuoglu et al. [9] increased the causal naure of the scheme by shifing the frequency dependent pole of the PML media parameters off the real axis into the negative-imaginary half of the complex plane. This is the most general PML formulation, as all the othr can be expressed as special cases of this one. The problem in this approach is that it requires three auxilia...