Robust, stable time-domain methods for solving MPDEs of fast/slow systems

Authors:
Ting Mei;Jaijeet Roychowdhury;Todd S. Coffey;Scott A. Hutchinson;David M. Day
Affiliations:
University of Minnesota, Minneapolis, MN;University of Minnesota, Minneapolis, MN;Sandia National Laboratories, Albuquerque, NM;Sandia National Laboratories, Albuquerque, NM;Sandia National Laboratories, Albuquerque, NM
Venue:
Proceedings of the 41st annual Design Automation Conference
Year:
2004

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Abstract

In this paper, we explore in detail the stability properties of time-domain numerical methods for multi-time partial differential equations (MPDEs). We demonstrate that simple techniques for numerical discretization can lead easily to instability. By investigating the underlying eigenstructure of several discretization techniques along different artificial time scales, we show that not all combinations of techniques are stable. We identify choices of discretization method and of step size along slow time scales that lead to robust, stable time-domain integration methods for the MPDE. One of our results is that applying overstable methods along one time-scale can compensate for unstable discretization along others. Our novel integration schemes bring robustness to time-domain MPDE solution methods, as we demonstrate with examples.