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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