A Finite-Element-Based Fast Frequency Sweep Framework Including Excitation by Frequency-Dependent Waveguide Mode Patterns

Abstract

This paper presents a frequency-sweep technique based on model-order reduction and finite elements, for the broadband analysis of structures fed by waveguides (WGs) possessing frequency-dependent modal field patterns. Standard order reduction requires the matrices and right-hand sides (RHSs) to exhibit affine frequency parameterization. This precondition is violated when the transverse fields of the WG modes vary with frequency. The proposed solution involves two steps. First, a reduced-order model (ROM) for the WG is constructed. It enables the accurate yet inexpensive computation of propagation characteristics. Second, order reduction is applied to the driven problem, wherein the reduced WG model is utilized to construct affine approximations to the matrices and RHSs. Since this process requires operations on reduced-order matrices only, it is computationally cheap and enables offline/online decomposition. Both impedance and scattering formulations are considered. For the latter, an alternative to the transfinite element method is proposed, which does not employ modal field patterns as shape functions. It avoids interior resonances and computes scattering parameters more efficiently when only a limited set of excitations is of interest. The resulting algebraic system is of somewhat larger dimension but easier to assemble. Its simple structure greatly facilitates the construction of the ROM.