Advanced Model-Order Reduction Techniques for Large Scale Dynamical Systems

Model Order Reduction (MOR) has proven to be a powerful and necessary tool for various applications such as circuit simulation. In the context of MOR, there are some unaddressed issues that prevent its efficient application, such as “reduction of multiport networks” and “optimal order estimation” for both linear and nonlinear circuits. This thesis presents the solutions for these obstacles to ensure successful model reduction of large-scale linear and nonlinear systems. This thesis proposes a novel algorithm for creating efficient reduced-order macromodels from multiport linear systems (e.g. massively coupled interconnect structures). The new algorithm addresses the difficulties associated with the reduction of networks with large numbers of input/output terminals, that often result in large and dense reduced-order models. The application of the proposed reduction algorithm leads to reduced-order models that are sparse and block-diagonal in nature. It does not assume any correlation between the responses at ports; and thereby overcomes the accuracy degradation that is normally associated with the existing (Singular Value Decomposition based) terminal reduction techniques. Estimating an optimal order for the reduced linear models is of crucial importance to ensure accurate and efficient transient behavior. Order determination is known to be a challenging task and is often based on heuristics. Guided by geometrical considerations, a novel and efficient algorithm is presented to determine the minimum sufficient order that ensures the accuracy and efficiency of the reduced linear models. The optimum order estimation for nonlinear MOR is extremely important. This is mainly due to the fact that, the nonlinear functions in circuit equations should be computed in the original size within the iterations of the transient analysis. As a result, ensuring both accuracy and efficiency becomes a cumbersome task. In response to this reality, an efficient algorithm for nonlinear order determination is presented. This is achieved by adopting the geometrical approach to nonlinear systems, to ensure the accuracy and efficiency in transient analysis. Both linear and nonlinear optimal order estimation methods are not dependent on any specific order reduction algorithm and can work in conjunction with any intended reduced modeling technique.