A low-rank IE-QR algorithm for matrix compression in volume integral equations

A single-level matrix compression algorithm based on pivoted QR factorization with partial matrix assembling, which exploits the rank deficiency of matrix blocks for physically separated groups of basis functions, is presented for the volume integral equation solution of electromagnetic scattering from arbitrarily shaped dielectric bodies. For a system of N equations, an amount of work of the order O(N²) has traditionally been required by the method of moments (MoM). The algorithm of the present paper reduces both computational complexity and storage requirement to O(N^1.5) with relatively less dependence on the integral equation kernel. Hence, the proposed algorithm is more practical for large-scale problems and can be implemented in a wide range of applications with few or no modifications.