The Finite-Difference Time-Domain (FDTD) method, the Finite-Integration Technique (FIT) and the Transmission Line Matrix (TLM) method provide for discrete approximations of electromagnetic boundary value problems cast in state-space forms. The dimension of the generated state-space models is usually very large. In general terms, Model Order Reduction (MOR) enhances computational efficiency. Application of the reduced-order modeling to the FDTD, FIT and TLM methods yields considerable reduction in the computational effort necessary for the solution of the discrete models. Furthermore, MOR can be used to generate compact, broadband discrete models of the original electromagnetic systems. Such compact broadband macro-modeling enables the abstraction of the discretized electromagnetic system in terms of a frequency-dependent transfer function matrix representation, which, in turn, provides for efficient implementation of the model in both general-purpose network-analysis oriented simulators, and full-wave, time- and frequency-domain electromagnetic field solvers aimed at system-level electromagnetic modeling. Reduced-order modeling in TLM is an approximation of the discrete model of electromagnetic field obtained through the application of the TLM method, in terms of a model of considerable lower dimension. The development of such a reduced-order model (ROM) can be achieved using two classes of methods, namely, singular value decomposition (SVD) methods and moment matching methods. A representative member of the former class of methods is the so-called balanced model reduction, which is aimed at removing from the original system those eigenstates that are difficult to observe and control. SVD-based MOR-techniques have the attractive attribute that bounds for the approximation error in the reduced model can be established. One disadvantage is that they tend to be computationally more expensive than moment matching methods. The main focus of this work is on moment matching methods. While techniques for MOR based on moment matching have been studied extensively in the case of FDTD and FIT methods, they have not yet been considered in detail in the context of TLM approximations of electromagnetic systems. The application of moment matching MOR-techniques to TLM is presented, with emphasis placed on Krylov subspace methods that utilize the Lanczos and Arnoldi processes. The attributes of such methods, both in terms of computational efficiency and solution accuracy, are examined through their application to the analysis of several electromagnetic structures. For this purpose the implicit time evolution TLM-scheme is utilized. Also, a comparison is provided between FDTD, FIT and TLM with regards to the computational efficiency of MOR-methods for expediting their numerical integration.     «

The Finite-Difference Time-Domain (FDTD) method, the Finite-Integration Technique (FIT) and the Transmission Line Matrix (TLM) method provide for discrete approximations of electromagnetic boundary value problems cast in state-space forms. The dimension of the generated state-space models is usually very large. In general terms, Model Order Reduction (MOR) enhances computational efficiency. Application of the reduced-order modeling to the FDTD, FIT and TLM methods yields considerable reduction i...     »

Die Transmission Line Matrix (TLM)-Methode ist eine raum- und zeitdiskrete Methode zur Vollwellenanalyse elektromagnetischer Felder. Auf Grund der hohen Ordnung des zu lösenden Gleichungssystems, ist der numerische Aufwand bei der Anwendung der TLM-Methode sehr groß. Verfahren der Ordnungsreduktion zielen darauf ab, ein zu lösendes Gleichungssystem durch ein Gleichungssystem wesentlich niedrigerer Ordnung zu ersetzen. Die Anwendung der Modell-Ordnungsreduktion auf die TLM-Methode führt zu einer erheblichen Reduzierung des Rechenaufwandes und erlaubt, ein kompaktes breitbandiges Model des originalen Systems zu extrahieren. In der Arbeit wird eine auf der Momentenanpassung basierte Ordnungsreduktion auf das implizite TLM-Schema angewendet. Dabei werden schwerpunktmäßig Krylov-Unterraum-Projektionsmethoden verwendet. Die Eigenschaften dieser Methoden, insbesondere ihre numerische Effizienz und ihre Genauigkeit, wurden durch Analyse verschiedener elektromagnetischer Strukturen untersucht.     «

Die Transmission Line Matrix (TLM)-Methode ist eine raum- und zeitdiskrete Methode zur Vollwellenanalyse elektromagnetischer Felder. Auf Grund der hohen Ordnung des zu lösenden Gleichungssystems, ist der numerische Aufwand bei der Anwendung der TLM-Methode sehr groß. Verfahren der Ordnungsreduktion zielen darauf ab, ein zu lösendes Gleichungssystem durch ein Gleichungssystem wesentlich niedrigerer Ordnung zu ersetzen. Die Anwendung der Modell-Ordnungsreduktion auf die TLM-Methode führt zu einer...     »