PRECONDITIONED ITERATIVE SOLUTION OF IML MOMENT METHOD PROBLEMS

The Impedance Matrix Localization (IML) method replaces the usual Method of Moments matrix Z by a sparse matrix T. For example, when both Z and T are N x N, T generally has about 50N nonzero elements. Although this allows each iteration of an iterative method to take only 50N operations (rather than N2), the number of iterations still must be decreased to truly have a ''fast'' method. For example, often more than N iterations are necessary for standard methods. Several standard and fast iterative methods are compared. These methods all converge to the exact solution of the matrix equation involving T, and the fast ones do so by using an approximate solution to this matrix equation. This approximate solution is derived from a sparse, approximate factorization of T. The approximate factorization is accurate enough to allow a solution for general problems in five iterations.