Solving Nonlinear Eigenvalue Problems for Waveguide-Coupled Cavities Using an Integral Solver With Subspace Projection

The standard curl-curl eigenvalue problem (EVP) in discrete electromagnetic formulations becomes non-linear if the system matrix contains additional expressions that depend on frequency, i.e., the searched eigenvalue. This is the case, e.g., for models based on the finite-integration technique (FIT) and special radiating boundary conditions for waveguide-coupled cavities. Such non-linear EVPs are a special challenge to modern solvers. In this article, an improvement of a nonlinear eigenvalue solver based on Beyn's contour integration technique is presented. Since the main computational effort arises from the solution of a number of large linear systems along the integration contour, a method using reduced-order modeling is presented. The validation example is the calculation of a number of eigenfrequencies in a rectangular waveguide filter.