An efficient preconditioning scheme for eigenanalysis of inhomogeneously loaded rectangular cavities

An efficient preconditioning scheme for the eigenanalysis of inhomogeneously loaded rectangular cavities is presented. Such structures are modeled with the finite-difference frequency-domain (FDFD) method, while the desired interior eigen-spectra are sought for by Arnoldi iterations with the shift-and-invert operation. In large scale problems, the inversion can only be performed iteratively. A preconditioner is constructed in order to accelerate the inversion. It can effectively shrink the spectrum of the governing matrix, and can be solved for by using fast discrete sine and cosine transforms (DST's and DCT's). The efficiency of this scheme is demonstrated by several numerical examples.