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Single-point methods of moment-matching type provide a most effective means for realizing fast frequency sweeps. The impedance formulation of the finite element method is very well-suited for such techniques, but it is susceptible to interior resonances, especially in the case of lossless microwave structures. This deficiency can be resolved by imposing transparent boundary conditions at the waveguide ports, but the resulting matrices exhibit nonpolynomial frequency-dependency unless all waveguide modes are of the transverse electric and magnetic type. In consequence, single-point methods cannot be applied without approximations. This article proposes a fast frequency sweep technique that handles not only transverse electric and magnetic modes but also transverse electric and transverse magnetic modes without any approximations. Moreover, it retains the efficiency of the impedance formulation but prevents interior resonances from occurring. The theoretical background of and numerical evidence for the failure of the impedance formulation is given, and a mathematical proof for the validity of the new method is presented. Computational results demonstrate the reliability and low error of the suggested approach.

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