Engheta, NaderMurphy, William D.Rokhlin, VladimirVassiliou, Marius S.2023-05-222023-05-221992-06-012006-06-30https://repository.upenn.edu/handle/20.500.14332/33380The fast multipole method (FMM) was developed by Rokhlin to solve acoustic scattering problems very efficiently. We have modified and adapted it to the second-kind-integral-equation formulation of electromagnetic scattering problems in two dimensions. The present implementation treats the exterior Dirichlet (TM) problem for two-dimensional closed conducting objects of arbitrary geometry. The FMM reduces the operation count for solving the second-kind integral equation (SKIE) from O(n3) for Gaussian elimination to O(n4/3) per conjugated-gradient iteration, where n is the number of sample points on the boundary of the scatterer. We also present a simple technique for accelerating convergence of the iterative method: "complexifying" k, the wavenumber. This has the effect of bounding the condition number of the discrete system; consequently, the operation count of the entire FMM (all iterations) becomes O(n4/3). We present computational results for moderate values of ka, where a is the characteristic size of the scatterer.Article