Domain Decomposition FDTD Algorithm for the Analysis of Electromagnetic
Fields and Microwave Structures
Feng Xu
1
, and Ke Wu
*2
1
School of Electronic Science & Engineering, Nanjing University of Posts and Telecommunications,
66 Xin Mofen Road, Nanjing, 210003, China, feng.xu@njupt.edu.cn
2
Département de Génie Électrique, École Polytechnique (Université de Montréal), 2500, Chemin de Polytechnique,
Montréal, H3T 1J4, QC, Canada, ke.wu@polymtl.ca
Abstract
In this paper, a universal and efficient algorithm of domain decomposition finite difference time domain (DD-FDTD)
is presented for the analysis of electromagnetic fields and microwave structures. The proposed algorithm can not
only be used to analyze very complicated microwave structures but also be used to analyze sparse multi-domain
electromagnetic fields. The algorithm can greatly increase the accuracy of numerical simulations and save
computation time and memory space. Moreover, by combining the DD-FDTD method with a numerical thru-line
(TL) calibration technique, an efficient hybrid algorithm is developed for the accurate parameter extraction of
microwave circuits and structures, such as substrate integrated circuits (SICs). The SICs that are studied in this work
are based on substrate integrated waveguides (SIW) which are useful for the design of millimeter-wave planar
circuits such as filters, resonators and antennas.
1. Introduction
The finite difference time domain (FDTD) method, first introduced by Yee [1], is a powerful, robust, and popular
modeling algorithm based on the direct numerical solution of Maxwell’s equations in the differential, time domain
form. The most important feature of the FDTD method is that broad-band frequency information can be provided in
a single-pass simulation. It has been extensively used in the parameter extraction of waveguides [2-7], microstrip
circuits [8-10] and multiple coupled lines [11, 12].
In the researches and applications, three main drawbacks of the FDTD method have been discovered. The first one
is that a suitable meshes scheme is very difficult to be obtained when the simulated structures of antennas, circuits or
systems are very complicated. In this case, a locally conformed scheme relying on the integral form of the
Maxwell’s equation [13, 14] or an additional local coordinate system near the complicated structures combined with
an interpolation technique in the overlapping region [15] can be used. The second is related to the sparse multi-
object simulation in which the distances among these objects are very large. A considerable amount of meshes have
to be arranged between objects to finish the transfer of EM information. In this case, multiple-region FDTD
(MR/FDTD) method
[16, 17] and a discrete wavelet transform (DWT) based on compression technique
[18, 19] can
be used to decrease the cost of near-field to near-field transform. The third is how to set up a suitable excitation
source on a complicated structure port and how to extract the parameters of these circuits and components, for
example, a circuit based on the substrate integrated waveguide (SIW) which has been widely discussed and
developed recently.
By combining the idea of domain decomposition with the FDTD method, one can find that the three drawbacks can
be easily overcome. In the first case, by decomposing the complicated structure into some simple sub-domains and
using different local coordinate meshes according to each sub-domain structure, the simulation will be simplified
significantly if a suitable interpolation technique is used [20]. For the second case, the idea of domain decomposition
is introduced to divide the sparse problem domain into several sub-domains. The DD-FDTD method is based on
near-field to far-field transform and equivalent incident field [21, 22]. The time-domain Green’s function is used to
fulfil the fields transfer. As a result, a large amount of meshes between the sub-domains are removed. In the third
case, a numerical thru-line (TL) calibration procedure, which allows for a very accurate extraction of dynamic
circuit parameters, will be combined into the DD-FDTD method [23].
2. DD-FDTD Algorithm