In this paper, we propose a finite element method together with a constraint Lanczos algorithm for analysing arbitrarily-shaped microwave cavities. The proposed methodology is based on the use of (curl) tangential vector finite elements. Moreover, in order to solve for the generalized eigenmatrix equation efficiently, we have also developed a constrained Lanczos algorithm. Specifically, in the constrained Lanczos algorithm, we orthogonalize each new Krylov vector with respect to the spurious DC modes. Consequently, the iterative process can be used to solve for the physical resonant modes, including physical static fields, without the occurrences of any spurious DC modes.

Anisotropic material characteristics can be exploited to construct absorbers that provide reflectionless interfaces for waves at arbitrary incident angles. Since their computer implementation requires the specification of appropriate material characteristics only, these Perfectly Matched Layers (PMLs) allow for simple but accurate mesh truncation schemes for the finite element method. The present paper extends the concept of PMLs to waveguides of inhomogeneous cross-sections and layered media. We describe the use of generalized PMLs in a software package for (M)MIC devices and demonstrate the benefits of the suggested approach by two numerical examples.