Iterative On-Surface Discretized Boundary Equation Method for 2-D Scattering Problems

The recently developed on-surface discretized boundary equation (OS-DBE) method has low memory requirement and is very suitable for parallel computing because the current at each point can be independently evaluated with a matrix of much smaller order than that in the method of moments (MoM) for electrically large objects. However, repeated solutions of the matrix equation in generating the whole current distribution are still the major computational burden when the scatterer size becomes large. In this paper, an iterative OS-DBE (IT-OS-DBE) method is presented for 2-D scattering problems. It further reduces the OS-DBE matrix order significantly and solves the matrix equation only once. The fast multipole algorithm (FMA) or multilevel FMA (MLFMA) can be incorporated into the present method to reduce the computational cost for concerned matrix vector multiplications. Three optional forms regarding memory usage of the IT-OS-DBE method are given. All the three options have advantage of less CPU time consumption than the MoM-based MLFMA. Two of the three options prevail not only in CPU time consumed but also in memory cost.