Open Access
Kwon, Soon Jae
Graduate Program:
Electrical Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
October 22, 2004
Committee Members:
  • Raj Mittra, Committee Chair/Co-Chair
  • Douglas Henry Werner, Committee Member
  • Lynn A Carpenter, Committee Member
  • Michael T Lanagan, Committee Member
  • Method of Moments
  • Layered structure
  • Full-wave electromagnetic field analysis
The method of moments (MoM) has been widely used for the full-wave electromagnetic analysis of layered structures. It has been gaining in popularity because the conventional equivalent circuit based simulation techniques have difficulty in producing accurate results for circuits with complex geometry and high operating frequency. However, the MoM is a computationally intensive process and requires considerable computer resources to perform the analysis. This thesis proposes and validates several techniques to speed up different stages of the MoM process. We first consider the computation of impedance matrix for layered structures. It is time-consuming since each element requires the evaluation of quadruple integrals. To increase the efficiency, we propose a technique, referred to as the Fast Matrix Generation (FMG). In this method, conventional and rigorous numerical methods are still used for generating the impedance matrix elements that are associated with the near-field interactions, while a more efficient scheme is employed where the separation distance between basis and testing functions exceeds a threshold value. A significant saving in computation time, sometimes over 90%, can be achieved via the application of this approach, as is demonstrated by numerical results for a number of typical microwave circuits. The frequency response of microwave passive structures often involves one or more resonances, and this, in turn, requires the use of small frequency steps for their analysis. This imposes an enormous computational burden when computing their frequency response via the MoM process. We introduce an impedance matrix interpolation technique that serves to reduce the computation time for the impedance matrix quite considerably, especially if the frequency band of interest is wide. In this approach, the frequency variation of the matrix element is expressed in term of interpolating polynomials with or without extracting the phase factor exp(-jkr), depending on the separation distance between the source and field points. Although the concept of matrix interpolation is not entirely new, the accuracy has been improved in this work over those published previously. Furthermore, our algorithm has the added advantage that it can be readily incorporated into existing codes. The efficiency of this approach is validated by considering a variety of layered structure problems. Next, the Characteristic Basis Function Method (CBFM) is proposed to reduce the matrix solution time for MoM analysis of large and/or complex geometries. The CBFs are special types of high-level basis functions, defined over domains that encompass a relatively large number of conventional subdomain bases, e.g., triangular patches or rooftops. In this approach, we define two kinds of CBFs that represent different kinds of interactions between the conventional subdomain bases contained in the CBFs. The primary CBF for a particular block is associated with the solution for the isolated block, while the secondary ones account for the mutual coupling effects between this block and others. Efficiency of the CBFM is demonstrated with several numerical examples Finally, we present an iterative process for solving the matrix equation by using an extrapolated initial guess in conjunction with the Conjugate Gradient (CG) method. The initial guess is computed from the orthonormalized version of the solutions at previous frequencies. The number of iterations needed to make the residual error smaller than a tolerance is reduced via the application of the extrapolated initial guess. The effectiveness of this approach is illustrated via several numerical examples.