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

I have read an interesting paper in TCAD on parametric model reduction

Yung-Ta Li, Zhaojun Bai, Yangfeng Su, Xuan Zeng

Model Order Reduction of Parameterized Interconnect Networks via a Two-Directional Arnoldi Process

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, v. 27, N 9, p. 1571-1582, 2008

http://dx.doi.org/10.1109/TCAD.2008.927768

The authors have suggested a new very interesting algorithm to find a projection subspace for multimoment matching in a numerically robust way. Really interesting.

Well, the problem with parametric model reduction that still remains is the mixed moments. There are so many of them and as a result the dimension of the reduced model grows too fast.

Once I have tried a natural solution to ignore them in the case of several film coefficients:

http://modelreduction.com/doc/papers/rudnyi05therminic.pdf

It worked but it is unclear how general the results were.

So, on one hand the theory of parametric model reduction is developed and now we have a robust algorithm to compute the subspace but how to use it in practice is still an open question due to a huge number of mixed moments.

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