Forschungsbericht 2007
Model reduction combined with hierarchical substructuring
The modelling of time-invariant linear systems often yields state space models with a very large state space dimension, e.g. due to discretizations of partial differential equations. This is a problem for efficient simulation purposes or the design of real time controllers. The idea of model reduction is to approximate such systems by systems with significantly smaller order. A very popular class of reduction techniques are the SVD-based methods. The advantages of those methods are the preservation of system characteristics (e.g. stability, minimality) and easily computable global error bounds. But the high computational effort of SVD-based methods restricts the applicability to relatively small systems. Hierarchical substructuring like it is used in AMLS is a possibility to reduce large systems by SVD-based reduction techniques. The original problem is recursively divided into smaller substructures on several levels and the reduction methods are applied to LTI-systems corresponding to these substructures. Furthermore there are approaches to combine SVD-based and Krylov-based methods to improve the quality of the approximation. Another goal is to use the combination of substructuring and model reduction for the solution of rational eigenvalue problems which result from a rational low-rank perturbation of linear eigenvalue problems. Publikationen
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