An Efficiently Preconditioned Eigenanalysis of Inhomogeneously Loaded Rectangular Cavities

In this letter, we demonstrate an efficient preconditioning scheme for the eigenanalysis of inhomogeneously loaded rectangular cavities. Modeling the entire structure with the finite-difference frequency-domain (FDFD) method yields a large sparse eigenvalue problem. The desired interior eigen-spectrum is sought for by Arnoldi iterations with the shift-and-invert operation, where the inversion can only be performed iteratively in large-scale applications. A preconditioner is constructed to speed up 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 (DSTs and DCTs). Several numerical examples are included to illustrate the efficiency of the preconditioned eigenanalysis.