Circulant preconditioners for domain integral equations in electromagnetics

In this paper, we present an optimal circulant preconditioner for domain integral equations in electromagnetics. The preconditioner is the best circulant fit to the discretized domain integral operator as measured by the Frobenius norm. We show that the discretized integral operators exhibit a Toeplitz-like structure for inhomogeneous objects and present an explicit expression for the elements of the optimal circulant. The circulant matrix can be used as an effective preconditioner in iterative solvers, since its action on a vector can be computed using the Fast Fourier Transform. Numerical experiments illustrate the performance of the preconditioner.