A Survey on Model Order Reduction of Linear Dynamical Systems

The text is written in August 2008 for the http://groups.google.com/group/mor4ansys group.

I have just browsed a recent presentation of Rudy Eid

A Survey on Model Order Reduction,of Linear Dynamical Systems
http://www.rt.mw.tum.de/eid/Eid-GACM07.pdf

It is a short presentation (21 slide) but it gives concise introduction in MOR and comparison of TBR and Krylov subspace methods. It should be very useful as good introduction to the topic.

Two comments. At the end it is written

Krylov subspace methods – stability is not preserved

I would not completely agree. For one-sided methods the stability is preserved, at least in the case when the original matrices are positive definite.

Then it is written

Main features of Krylov subspaces:
2.Applicability to very large-scale systems (order > 500,000)

With modern hardware and modern direct solvers one can go further. MOR for ANSYS with the MUMPS solver allows us to go to a few millions DoFs on a system with 16 Gb RAM.


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