On symbolic model order reduction

The text is written in March 2009 for the http://groups.google.com/group/mor4ansys group.

 A few comments to the paper

G. Shi, B. Hu, and C.-J. R. Shi, “On symbolic model order reduction”, IEEE Trans. on Computer-Aided Design, vol. 25, no. 7, pp. 1257-1272, July 2006.




that I have recently read.

This is an interesting paper. In my view the goal is basically the same as for parametric model reduction. The authors have considered several approaches to do it.

1) Symbol isolation.

Here the idea to split the network to pieces and then reduces pieces without symbols to be preserved. It seems to be similar to a way in

R. W. Freund, Krylov-subspace methods for reduced-order modeling in circuit simulation, Journal of Computational and Applied Mathematics, Vol. 123, pp. 395-421, 2000. Beginning of section 2.2.

where a network is split to linear and nonlinear parts.

2) Nominal project method

Here is the idea to compute a projection for some values of parameters and then use this projection also for the cases when the parameters change.

3) First order approximation method

In order to escape an inverse of a symbolic matrix, the authors have suggested to use an approximation for the inverse (see Eq 22). This way one needs the inverse of a numeric matrix only. It is interesting but then there are problems with orthonormalization. Anyway this is a very interesting idea.

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