Single level dual rank SVD algorithm for volume integral equations of electromagnetic scattering

Electromagnetic scattering from arbitrarily shaped inhomogeneous dielectric bodies has been an interesting topic due to its importance in problems that include propagation through inhomogeneities. This paper presents a novel single level dual rank SVD algorithm that efficiently compresses the system matrix to reduce the memory requirement and CPU time for both matrix assembly and matrix-vector multiplication to O(N/sup N2/). The dual rank SVD algorithm is based on the rank deficiency feature of the integral equation for well-separated groups of basis functions. The algorithm forms the Q-R factorization of rank deficient local matrices due to non-self group interactions by ranking the most linearly independent basis functions in the transmitting (source) group and the most significant ones in the receiving (observation) group.