Analysis of Partial Geometry Modification Problems Using the Partitioned-Inverse Formula and Sherman–Morrison–Woodbury Formula-Based Method

Abstract

In this paper, we present an efficient method for accelerated analysis of the partial geometry modification problem involving an original structure with small modifications. The conventional method of moments can be very time consuming for this type of problem because the impedance matrix equation has to be solved anew each time the original structure is modified. However, the proposed method only requires the solution of the impedance matrix equation of the original structure. Any small modification of the original object is handled into two steps: first by subtracting a small part from the original structure and then by adding a small part to the rest-structure. Both of these steps can be efficiently computed by using the partitioned-inverse and Sherman–Morrison–Woodbury formulas with the solution of the original structure. When the structure is modified, the proposed method only requires additional operations whose computational burden is $O(N^{2})$ , as opposed to $O(N^{3})$ , where ${N}$ is the number of unknowns in the original structure. Furthermore, the presented method is purely algebraic and rigorous rather than based on approximations. Numerical results for electromagnetic scattering are included in this paper to demonstrate the efficiency and accuracy of this method.