An efficient model order reduction method for three-dimensional Finite Element Method (FEM) analysis of waveguide structures is proposed. The method is based on the Efficient Nodal Order Reduction (ENOR) algorithm for creating macro-elements in cascaded subdomains. The resulting macro-elements are represented by very compact submatrices, leading to significant reduction of the overall number of unknowns. The efficiency of the model order reduction is enhanced by projecting fields at the boundaries of macro-elements onto a subspace spanned by a few low-order waveguide modes. The combination of these two techniques results in considerable saving in overall computational time and memory requirement. An additional advantage of the presented method is that the reduced-order system matrix remains frequency-independent, which allows for very fast frequency sweeping and efficient calculation of resonant frequencies. Several numerical examples for driven and eigenvalue problems demonstrate the performance of the proposed methodology in terms of accuracy, memory usage and simulation time.
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