Intervenant:  Zhaojun Bai
-------------    
 Department of Computer Science and
        Department of Mathematics 
        University of California
        Davis, CA 95616, USA  
      email: bai@cs.ucdavis.edu

Titre:
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 Krylov Subspace Techniques for Reduced-Order Modeling 
       of Large-Scale Dynamical Systems

Resume
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The goal of reduced-order modeling of a large scale dynamical system is
to
replace such a system by an approximate small system, namely,
with much smaller state-space dimension. An accurate and effective 
reduced-order model can be applied for steady state analysis, transient 
analysis and sensitivity analysis. As a result, it can significantly 
reduce design time and allow for aggressive design strategies. Such a 
computational prototyping tool would let designers try ``what-if'' 
experiments in minutes and hours, not days.

In recent years, a great deal of attention has been devoted to Krylov 
subspace based reduced-order modeling techniques.  The surge of interest 
was triggered by the needs of numerical techniques for simulations
of extremely large scale dynamical systems, such as VLSI circuit
simulation.  In this talk, we will begin with a review of successful 
Krylov subspace based techniques for linear dynamical systems, and 
present the recent progress in quadratic dynamical systems.
We will conclude with the needs and challenges of reduced-order modeling 
techniques for nonlinear dynamical systems. Numerical simulation results
for
dynamical systems arising in circuit simulation, structural dynamics,
and microelectromechanical systems (MEMS) will be presented.