OBTAINING SCATTERING SOLUTIONS FOR PERTURBED GEOMETRIES AND MATERIALS FROM MOMENT METHOD SOLUTIONS

Abstract

In this paper, we present an efficient method for computing the solution to scattering problems using a perturbation scheme based on the solution of related original problems. Assuming the radar cross section has been computed for a particular scatterer associated with a moment method matrix B, we call the computation of the radar cross section of a slightly perturbed scatterer a "perturbed problem of B". If the original problem has n unknowns, and the perturbed problem is formed by changing p cells of the original problem, then our method requires an operation count of O(n2p + p3) while a direct moment method solutions requires an operation count of O(n3). Our method involves application of the Sherman-Morrison-Woodbury formula for inverses of perturbed matrices. We show that the method can be easily implemented in any moment method code, and the user does not have to learn a new input procedure. Further, the modified code can provide a basis for a non-linear optimization procedure which minimizes the radar cross section of an obstacle by varying the surface impedance's. An appropriate objective function in this problem depends on the radar cross section at the angles and frequencies of interest. Let n be the number of cells in the obstacle and let p be the number of cells with variable impedance, with n>>p. Then application of the Sherman-Morrison-Woodbury formula results in objective function evaluations requiring an O(np+p3) operation count. In contrast, application of the classical moment method results in objective function evaluations requiring an O(n3) operation count. Numerical results from large practical problems demonstrate the efficiency and stability of the new method. [Vol. 3, No. 2, pp. 95-118 (1988)]