Multimesh ℋ2-Optimal Model Reduction for Discretized PDEs

S. A. Melchior (), V. Legat () and P. Van Dooren ()
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S. A. Melchior: Université catholique de Louvain (UCL)
V. Legat: Université catholique de Louvain (UCL)
P. Van Dooren: Université catholique de Louvain (UCL)

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 219-226 from Springer

Abstract: 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.

Keywords: Fine Mesh; Coarse Mesh; Reduce Order Model; SISO System; Balance Truncation (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-3-642-33134-3_24

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