International Conference «Mathematical and Informational Technologies, MIT-2013»
(X Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, September, 5–8, 2013

Budva, Montenegro, September, 9-14, 2013

Gourary M.M.   Rusakov S.G.   Stempkovsky A.L.   Ulyanov S.L.   Zharov M.M.  

The Elimination Techniques to Solve Computational Problems of Model Order Reduction for Large Multi-terminal Circuits

Reporter: Rusakov S.G.

The goal of model order reduction (MOR) in VLSI CAD is to generate automatically an electrical model of essentially lower dimension than original one saving good approximation of its behavior. The recent significant achievements were obtained in two main research directions of MOR algorithms development: SVD- based methods and Krylov-based methods. But today actual problem in practical simulation is MOR of systems with large number of inputs and outputs or in other words MOR of multi-terminal circuits. The simulation of interconnects or substrate networks are the examples of such actual simulation tasks. It can be mentioned that SVD-based methods and Kry-lov-based methods are inefficient in the multi-terminal cases and essential research energies are directed for its im-provements.
The alternative MOR approach is discussed in this paper that is more suitable to large number of ports. The approach is based on elimination of internal nodal variables and partitioning techniques. Firstly this approach is directed to reducing RC networks. Some results were obtained while development of this approach. Among them:
- it was shown that developed numerical MOR procedure on the base of perturbation technique provides the generation of the reduced models of first order of accuracy, provides correct computation of first moments and coincides with elimination based MOR with accuracy of first order:
- the passivity of generated models was shown.
The limitation of this approach was connected with account of the inductances since initial order of ODE is growing in this case due to involving additional current variables. To take into account inductances the special procedure was suggested and the elimination approach was extended for MOR of RLC networks. In comparison with other ap-proaches the first order of accuracy is saved. Moreover the stability and passivity are saved.

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