INTERACTION MATRIX LOCALIZATION (IML) PERMITS SOLUTION OF LARGER SCATTERING PROBLEMS

The Interaction Matrix Localization Method (IML) replaces the usual N by N moment method matrix having N2 nonzero elements by a sparse N by N matrix having roughly 100N nonzero elements. It gives a similar reduction in the number of operations required per iteration for iterative solution methods. While these savings alone are quite significant, this paper shows how additional reductions are possible by using the structure of the sparse matrix to develop preconditioners which allow a solution in fewer iterative steps. The method considered here is preconditioning by Incomplete LU (ILU) decomposition. A problem is solved with N = 15,000, using less memory than that required for N = 1,500 problems using standard methods. Furthermore, the number of operations necessary to iteratively solve for each incidence angle (i.e., right hand side of the matrix problem) is approximately equal to the number of operations needed by standard methods to solve for each right hand side even after the inverse of the moment method matrix has been calculated! Saving orders of magnitude in the storage needed and in the execution time needed extends the range of applicability of the moment method to very significantly larger bodies.