A diagonal factorization for integral equation matrices

This paper reports on an improved factorization strategy for integral equation matrices based on source and field transformations that have localizing radiation and reception properties. In addition to the use of localizing functions, the method incorporates orthogonally matched receivers. It is shown that this yields a controllably diagonal multilevel matrix factorization. To simplify the presentation, the algorithm is described for symmetric systems. Numerical results are presented for both symmetric and non-symmetric matrices.