Sparse Factorization of the Impedance Matrix in an Overlapped Localizing Basis: TMz Case

It has been observed that localizing current modes provide sparse factorizations of discrete integral equations at low frequencies. This paper extends these results by incorporating overlapping localized modes. For TMz scattering, it is observed that the computational complexity of the resulting factorization algorithm approaches O(NlogN). The memory complexity of the factored representation scales approximately as O(N) for electrically small arrays. Results from the 3-D implementation of these algorithms will be presented separately at this meeting