Abstract
Model order reduction of a linear time-invariant system consists in approximating its p ×m rational transfer function H(s) of high degree by another p ×m rational transfer function \(\widehat{H}(s)\) of much smaller degree. Minimizing the \(\mathcal{H}_{2}\)-norm of the approximation error can be achieved iteratively. The convergence behavior of the algorithm depends on the choice of the initial condition. If a large scale dynamical system is obtained by discretizing a partial differential equation on a fine mesh, the efficiency can be improved by taking advantage of several discretizations on coarser meshes. This idea is illustrated on the advection–diffusion equation.
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References
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Acknowledgements
Samuel Melchior is Research fellow with the Belgian National Fund for Scientific Research (FNRS). The present study was carried out within the scope of the project “A second-generation model of the ocean system”, which is funded by the Communauté Française de Belgique, as Actions de Recherche Concertées, under Contract ARC 04/09-316. This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with its author(s).
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Melchior, S.A., Legat, V., Van Dooren, P. (2013). Multimesh ℋ2-Optimal Model Reduction for Discretized PDEs. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_24
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DOI: https://doi.org/10.1007/978-3-642-33134-3_24
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