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CivilComp Proceedings
ISSN 17593433 CCP: 89
PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: M. Papadrakakis and B.H.V. Topping
Paper 125
Order Reduction of Linear TimeInvariant FiniteIntegrationTechnique Discretized Structures with Length and Frequency Parameterization K.S. Stavrakakis^{1}, T. Wittig^{2}, W. Ackermann^{1} and T. Weiland^{1}
^{1}Institute for Electromagnetic Field Theory, TU Darmstadt, Germany
K.S. Stavrakakis, T. Wittig, W. Ackermann, T. Weiland, "Order Reduction of Linear TimeInvariant FiniteIntegrationTechnique Discretized Structures with Length and Frequency Parameterization", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", CivilComp Press, Stirlingshire, UK, Paper 125, 2008. doi:10.4203/ccp.89.125
Keywords: model order reduction, multivariate Krylov subspace methods, parameterized systems, finite integration technique.
Summary
In this paper we consider large linear time invariant
systems which depend on several parameters s_{1},s_{2},...,s_{n}.
These may be the frequency, material or geometric parameters. It is
presented how they arise from the FITdiscretized [1,2] Maxwell
equations. In order to solve such systems in a reasonable time,
model order reduction is used which aims to reduce the
n dimensional system to an m<<n dimensional system which
preserves some qualities of the original system. Especially model
order reduction via projection on Krylovsubspaces has proven to be
very effective and its characteristics for oneparameter linear
systems are briefly highlighted here.
In the single parameter case [3,4] the order reduction is carried out via projection on a subspace with dimension m<<n. The solution vector x of the original system is restricted on a space V spanned by orthonormal trial vectors v_{1}...v_{2}. By projection with a test matrix W in C^{l*m} the dimension of the system matrix is reduced from n*n to m*m. The matrices V and W are chosen so that the resulting reduced order model is a partial realization, Padé approximation or rational interpolant of the transfer function of the original system. Details concerning the relation of the approximations and the projection matrices are found in [5] as well as in [3,4]. It is a common characteristic of all these cases, that colsp(V) and colsp(W) must contain unions of Krylov subspaces of the system matrices and vectors [5]. An analogous method exists for multivariate linear systems (see also [6,7,8]) and is presented also in this paper. Unfortunately it cannot be used for FITsystems directly as they are nonlinear with respect to line length. This work shows a linearization method. We consider the mesh being stretched according to the length variation, so that the mesh topology is maintained and expresses all matrices according to this mesh variation. The procedure presented here is demonstrated on a numerical example. References
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