Development of Fast Integral Solver in Time and Frequency Domains

摘要

We constructed a new time domain algorithm which is particularly well suited to general dispersive media with penetrable and impenetrable surface and bulk volumetric properties. The algorithm complexity does not depend on the degree of dispersion. The algorithm small computational cost (O(Nt Ns logNt logNs) and O(Nt Ns**4/3 logNt logNs) for volume and surface problems respectively, where Nt and Ns denote the number of temporal and spatial samples) is achieved through the simultaneous application of Fast Fourier Transforms in space and time. The algorithm is based on a new formulation of integral equations: instead of using the customary integral equations involving the Green function and its derivatives, we constructed supplemental integral equation operators equal to the Fourier transform of the dispersive medium Green function, to the Fourier transform of the product of the dispersive medium Green function with the frequency dependent dielectric permittivity, and to the Fourier transform of the product of the dispersive medium Green function with the inverse of the dielectric permittivity. The algorithm does not require analytical representation of the (dispersive) medium Green function and, in particular, it can be used with a medium Green function given in a tabular form. The algorithm is already being successfully used for the simulation of SAR imaging and in the context of electronic packaging.