Iterative On-Surface Discretized Boundary Equation Method And Its Applications

Based on the existing on-surface discretized boundary equation (OS-DBE) method, an approach, called iterative OS-DBE (IT-OS-DBE), is proposed and applied to the analysis of two-dimensional (2D) and three-dimensional (3D) problems of scattering by perfect electric conducting (PEC) objects and3D electrostatic problems.For the above2D problems, the original OS-DBE method allows independent determination of the electric surface current at arbitrary given point on the scatterer surface with subdomain basis functions and field points (matching points) covering just a part of the entire cylinder surface and centering around that given point. Hence, the method is very suitable for parallel computing. Furthermore, it has low memory requirement because a matrix of smaller order than that in the method of moments is used and the larger the problem is, the smaller the matrix order ratio is. The fast multipole algorithm (FMA) or the multilevel FMA (MLFMA) can be incorporated into the method to diminish the computational complexity. However, a matrix equation is solved repeatedly at each current calculation point in order to generate the whole current distribution and this is the efficiency bottleneck of the method. The present IT-OS-DBE method comprises a series of alternate OS-DBE solution and revision processes. Formally, an OS-DBE solution process seems to be the same as the original OS-DBE method. Within the present iterative scheme, however, it significantly decreases the OS-DBE matrix order by one to two orders of magnitude. The solution count of the matrix equation in obtaining the whole current distribution in the OS-DBE solution process can be reduced to just one for2D scattering problems and3D electrostatic problems using the proposed one matrix inversion technique, such that the computational burden for the OS-DBE solution process can be diminished to a minimum degree. For the2D problem of scattering by a PEC cylinder, the one matrix inversion technique utilizes the vector composed of coupling coefficients between the scattered tangential magnetic field at a rather arbitrarily chosen point on the cylinder surface and the incident tangential electric fields at the related field points all around the surface to produce the whole current distribution as if it were location independent. For3D electrostatic problems, the corresponding coupling coefficient vector obtained at one point on the surface of a conductor or dielectric can also be employed to determine the whole surface charge or surface bound charge density. The FMA/MLFMA can be implemented into the revision processes of the present IT-OS-DBE method as well to reduce the computational cost for concerned matrix vector multiplications. As the present method may converge fast and complete the solution in just a few iterations, independent of the problem scale, there are several optional forms regarding the memory usage in connection with the FMA/MLFMA adopted in the revision processes.A new spatial sweep technique for the original OS-DBE is also proposed in this dissertation and applied to the analysis of scattering by2D PEC cylinders. It uses the aforementioned coupling coefficient vector generated at a given point to calculate the current distribution in its nearby area to reduce the solution count of the matrix equation in the original OS-DBE. The complex frequency hopping is employed for the automatic control of sweep calculations. Compared with the available spatial sweep technique based on the asymptotic waveform evaluation, the new technique has the advantages of lower computational complexity, wider sweep range, easier implementation of the FMA/MLFMA, and no necessity of recalculating coupling coefficient vectors when incident waves or exciting sources alter. The method has low memory requirement and is very suitable for parallel computing as the original OS-DBE method.For2D scattering problems.efforts have also been made in this dissertation to improve the traditional FMA/MLFMA in both accuracy and efficiency. The higher order analytical approximations to far interactions in the FMA/MLFMA are derived. In addition.a scheme with more efficient memory usage is proposed for computing the far interactions related to the electric field integral equation and the combined field integral equation for the case of a TE wave incidence. The filling time of translation matrices and its portion within the total computation time are significantly diminished by the discrete Fourier transform and its inverse. These enhancements benefit the method of moments, the OS-DBE method.and the IT-OS-DBE method all in conjunction with the FMA/MLFMA in both accuracy and efficiency.