Numerical calculation of scattering from N conducting circular cylinders by using Greengard-Rokhlin´s fast multipole algorithm

We considered EM scattering from N conducting circular cylinders as a simple example of many body and large body scattering, and discussed the efficiency of Greengard-Rokhlin´s fast multipole algorithm (GRFMA) for the two cases in the range of NM < 1,100,000. GRFMA has the floating point operation of O(NM) theoretically. We confirmed that the floating point operation is O(NM) both for the many body case and for the large one body case as M→∞, and showed that the amount of used memory is O((NM)²3/) for the many body case and O(NM) for the large body case as M→∞. However, both the net computation time and the net amount of used memory are larger for the many body case than for the large one body case.