Abstract-An efficient model order reduction method for threedimensional Finite Element Method (FEM) analysis of waveguide structures is proposed. The method is based on the Efficient Modal 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 macroelements 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 reducedorder 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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Abstract-This paper presents a multilevel Model Order Reduction technique for a 3-D electromagnetic Finite Element Method analysis. The reduction process is carried out in a hierarchical way and involves several steps which are repeated at each level. This approach brings about versatility and allows one to efficiently analyze complex electromagnetic structures. In the proposed multilevel reduction the entire computational domain is covered with macro-elements which are subsequently nested, in such a way that size of the problem which has to be reduced at each level is relatively small. In order to increase the speed of the reduction at each level, the electric field at the macro-elements' boundaries is projected onto the subspace spanned by Legendre polynomials and trigonometric functions. The results of the numerical experiments confirm the validity and efficiency of the presented approach.

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