Interaction matrix localization (IML) permits solution of larger scattering problems

The interaction matrix localization (IML) replaces the usual N-by-N moment method matrix, with N² nonzero elements, by a sparse N-by-N matrix with roughly 100 N nonzero elements. It gives a similar reduction in the number of operations required per iteration for iterative solution methods. While these savings are significant, 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 is preconditioning by incomplete LU (ILU) decomposition. A problem is solved with N=15000 using less memory than that required for N=1500 problems using standard methods. The number of operations necessary to iteratively solve for each incidence angle (i.e., the 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 significantly larger bodies.