A butterfly‐based direct solver using hierarchical LU factorization for Poggio‐Miller‐Chang‐Harrington‐Wu‐Tsai equations

A butterfly-based hierarchical LU factorization scheme for solving the PMCHWT equations for analyzing scattering from homogenous dielectric objects is presented. The proposed solver judiciously re-orders the discretized integral operator and butterfly-compresses blocks in the operator and its LU factors. The observed memory and CPU complexities scale as O(N log(2)N) and O(N-1.5 log N), respectively. The proposed solver is applied to the analyses of scattering several large-scale dielectric objects.