Joint work with Tong Zhang.

Maxwell's equations can be discretized in such a way that a circuit solution results [1]. The resultant circuit model is called Partial Element Equivalent Circuits (PEEC). Applications of PEEC models are of interest in both the time as well as the spectral domain. These models result in a large set of neutral DDEs in the form

C y' = G₀ y + _i G_i y(t-_i) + _i H_i y'(t-_i) + _i u_i(t-_i). (1)

Due to the large size, the solution of this system is required to be efficient. A further issue is the stability of the time solution. Suitable numerical integration methods have been studied in [2]. Some results and insights will be give in the fast solution of very large systems of PEEC equations in the time domain. Further, we look at solution of these systems using Model Order Reduction (MOR) techniques. Some MOR results have been obtained in [3]. In this paper, we will give further insights into the solution using MOR techniques and we use eigenvalue techniques to investigate the stability of these large systems.

References

[1] A. E. Ruehli. Equivalent circuit models for three dimensional multiconductor systems. IEEE Transactions on Microwave Theory and Techniques, MTT-22(3):216-221, March 1974.

[2] A. Bellen, N. Guglielmi, A. Ruehli. Methods for linear systems of circuit delay differential equations of neutral type. IEEE Transactions on Circuits and Systems, 46:212-216, January 1999.

[3] J. Cullum, A. Ruehli, T. Zhang. Model reduction for PEEC models including retardation. In Digest of Electr. Perf. Electronic Packaging, number 7, pages 287-290, West Point, NY, October 1998.

MINISIMPOSIUM SESSION: 3. Numerical methods for delay equations (2 sessions)