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Published in:
2013 | OriginalPaper | Chapter
Multimesh ℋ2-Optimal Model Reduction for Discretized PDEs
Authors : S. A. Melchior, V. Legat, P. Van Dooren
Published in: Numerical Mathematics and Advanced Applications 2011
Publisher: Springer Berlin Heidelberg
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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.