An “add-on” analysis of large open circular-cylindrical cavities

The add-on method utilizes previously acquired solutions for sub-problems, comprising portions of a scatterer, as a part of the analysis. The process of adding the remainder of the solution is a relatively efficient one, assuming that the initial stage of the sub-problem has been performed. The “add on” method is based on two basic principles: A. Superposition is used to break up the unknown current into two components, the first one being a readily computable solution to a simple short circuited problem, and the second one is excited by a current source over the aperture area, and is the only one requiring computation. B. A gradual algorithm is used for the computation of the second current component for many sub-problems. Principle A leads to a purely algebraic algorithm of principle B, with no integral operators. In this work, this formulation is extended to the cylindrical case. In this ease, the aperture region is a portion of a circle complementing the circular conducting shell, thus it shrinks as the conductor increases in size and no truncation is needed. The short circuit current for the closed circular cylinder is computed rapidly using the FFT. The cylindrical problem is solved for large cylinders in three ways: (1) a direct Moment Method solution, (2) a direct spatial decomposition solution based on the MoM matrix and invoking the matrix partitioning technique, and (3) the cylindrical add-on scheme. All solutions are identical, however, the computational advantage of the add-on technique is quite apparent, as seen from the analysis of the operation count as well as from numerical examples