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Multimesh ℋ2-Optimal Model Reduction for Discretized PDEs

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • S. A. Melchior

    (Université catholique de Louvain (UCL))

  • V. Legat

    (Université catholique de Louvain (UCL))

  • P. Van Dooren

    (Université catholique de Louvain (UCL))

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.

Suggested Citation

  • S. A. Melchior & V. Legat & P. Van Dooren, 2013. "Multimesh ℋ2-Optimal Model Reduction for Discretized PDEs," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 219-226, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_24
    DOI: 10.1007/978-3-642-33134-3_24
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