A combined finite element-boundary integral formulation for solution of two-dimensional scattering problems via CGFFT

A novel technique is presented for computing the scattering by two-dimensional structures of arbitrary inhomogeneity. The proposed approach combines the usual finite-element (FE) method with the boundary-integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are then convolutions and can be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach presented here offers the principal advantage of having O(N) memory demand and employs a one-dimensional FFT, as against the two-dimensional FFT required in a traditional implementation of the proposed CG-FFT algorithm. The speed of the proposed solution method is compared with that of the traditional CG-FFT algorithm. Results are presented for several rectangular composite cylinders and one perfectly conducting cylinder. These are shown to be in excellent agreement with the moment method