A method for compact modeling linear time-invariant structures of high frequency engineering on the level of electromagnetic fields

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Numerical methods of electromagnetic fields simulation in the frequency domain -- such as the finite-element (FE) method -- enable the analysis of linear time-invariant systems of high-frequency engineering at low levels of error and provide high flexibility in modeling dispersive material properties. However, they lead to algebraic systems of large scale and high computational cost. Methods of model-order reduction (MOR) provide a systematic approach to transforming FE systems into low-dimensional models that stand out for moderate memory requirements, short solution times, and controllable error.The MOR methods developed in the first phase of the project exhibit stable behavior in the low-frequency regime and are capable of handling systems that are excited by waveguide modes of frequency-dependent transversal field patterns. Neglecting losses in the waveguide feeds, the methods succeed in formulating the distributed-parameter system, its FE discretization, and the resulting reduced-order system (ROM) in such a way that essential system properties are provably preserved throughout the entire modeling chain; this includes passivity, causality, stability, reciprocity, and energy.This renewal proposal extends the suggested methodology in the following aspects:1. Since many applications require time-domain simulations, the first goal is to transform the ROM, which is originally residing in the frequency-domain. Thanks to its preservation properties, the a-posteriori passivation required by competing methods may be omitted. Moreover, the well-defined structure of the ROM enables the realization of a descriptor or state-space model in the time-domain under non-restrictive assumptions and, in consequence, the use of fast recursive methods of convolution.2. The inclusion of losses in the waveguide feeds extends the range of application of the methodology and completes its theoretical foundations. One extra difficulty compared to the lossless case is that the waveguide modes are no longer energetically decoupled. The plan is to generalize the modeling within the theoretical framework of port-Hamiltonian systems, to extend the numerical methods for waveguides by frequency-dependent dissipative material models, and to update the time-domain transformation.3. Real-world applications require ROMs of known error limits. Likewise, it is desirable to minimize the ROM dimension for a given error tolerance. For these purposes, a self-adaptive MOR method is required which chooses appropriate expansion frequencies and adjusts the ROM order according to the requirements. As part of the project, an existing method for the non-dispersive case shall be extended to the case of frequency-dependent mode patterns.