The impedance matrix localization (IML) method for moment-method calculations

Abstract

The impedance matrix localization (IML) method, a modification of the standard method of moments that can be implemented as a modification to existing computer programs, is examined. This modification greatly eases the excessive storage requirements and long computation times of moment-method approaches by using novel bases and testing function that localize the important interactions to only a small number of elements within the impedance matrix elements can be made so small (typically 10/sup -4/ to 10/sup -6/ in relative magnitude) that they may be approximated by zero. In the case of a two-dimensional body with unknowns on its surface, both analytical arguments and numerical calculations suggest that, for an N*N matrix, about 100N matrix elements will need to be kept, even for very large N. The resulting sparse matrix requires storage for only 100N complex numbers rather than for N/sup 2/ numbers. Similar results are expected in three dimensions. The structure of the resulting matrix problem allows the use of highly efficient solution methods. Results are given for one such possibility: iteration preconditioned by incomplete LU decomposition.