A Study of Techniques to Solve the Disparate Mesh Size Problem With an Application to Sinuous Antennas

132 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1999.The disparate mesh size problem has only recently been recognized as a major impediment to solving large-scale electromagnetic radiation and scattering problems. This problem first came to the author's attention when trying to apply the fast multipole method (FMM) to a particular wideband antenna, the sinuous antenna. The essence of the problem is that a triangular patch mesh containing a wide range in patch sizes produces an ill-conditioned method of moments impedance matrix. Since the FMM algorithm relies on iterative solvers to solve the matrix equation, the fast in FMM becomes a misnomer if the iterative solver converges very slowly or not at all. The sinuous antenna embodies the disparate mesh size problem, so if any of the recent fast algorithms in electromagnetic scattering are to be applied, this problem must be dealt with. This dissertation is divided into two parts. One part describes several approaches that were explored to ameliorate the disparate mesh size problem. These include expansion functions, integral equations, iterative methods, and preconditioning. The main result is that preconditioning is the only viable avenue available to treat the disparate mesh size problem for a wide variety of scatterers. This dissertation describes a preconditioner that effectively removes the problem. It can reduce the overall cost of iteratively solving the matrix equation, and its complexity ranges from O( N1.3) to O(N 2.2) depending on the scatterer. The other part describes a particular wideband antenna, the sinuous antenna. Its mode of operation and its design are still not very well understood though it was patented in 1987. The sinuous antenna can belong to the class of self-complementary, self-scaling antennas and is thus a good candidate for frequency-independent operation. However, the patent allows for sinuous designs which axe not self-scaling, and such a design is most nearly independent of frequency. The sinuous antenna is geometrically related to the logarithmic spiral antenna, but its mode of operation is fundamentally different. The logarithmic spiral antenna is a traveling wave antenna, while the sinuous antenna is more like a resonant antenna.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD