A fast integral-equation solver for electromagnetic scattering problems

We describe a new fast integral-equation solver applicable to large-scale electromagnetic scattering problems. In our approach, the field generated by a given current distribution M decomposed into near and far field components. The near field is computed using the conventional method of moments technique with the Galerkin discretization. The far field is calculated by approximating the original current distribution by an equivalent current distribution on a regular Cartesian grid, such that the two currents have identical multipole moments up to a required order m. As the result of this discretization, the original full impedance matrix is decomposed into a sum of a sparse matrix (corresponding to the near field component) and a product of sparse and Toeplitz matrices (corresponding to the far field component). Because of the convolution nature of the Toeplitz kernel, the field generated by the equivalent current distribution can be then obtained by means of discrete fast Fourier transforms. The single computational domain solver based on our formulation requires both memory and computation time of order O(N log N) (in volume problems) or O(N/sup 3/2/) (in surface problems), where N is the number of unknown current elements. In the domain-decomposed parallelized version of the solver, with the number P of processors equal to the number of domains, the total memory required in surface problems is reduced to O(N/sup 3/2//P/sup 1/2/). The corresponding speedup factor is equal to the number of processors P. During the talk, applications of the solver to 2- and 3-dimensional electromagnetic volumetric and boundary-value problems will be presented.<
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