Abstract-In this paper we show that the two-sided Lanczos procedure combined with implicit restarts, offers significant advantages over Pad6 approximations used typically for model reduction in circuit simulation.

In this preliminary report we describe an optimization-based approach for reduction of the number of reactions in chemical kinetics models. Numerical results for several reaction mechanisms are given, and future plans are outlined. 1 Introduction The kinetics of a detailed chemically reacting system can potentially be very complex. Although the chemist may be interested in only a few species, the reaction model almost always involves a much larger number of species. Some of those species are referred to as radicals. These are very reactive species (usually of low concentration) which can be important intermediaries in the reaction scheme. A large number of elementary reactions can occur among the species; some of these reactions are fast and some are slow. The aim of simplified kinetics modeling is to derive the simplest reaction system which retains the essential features of the full system. The conventional technique [26, 20, 21] is to systematically apply the so-called steady-state...

One of the outstanding problems in the numerical simulation of mechanical systems is the development of efficient methods for dealing with highly oscillatory systems. These types of systems arise for example in vehicle simulation in modeling the suspension system or tires, in models for contact and impact, in flexible body simulation from vibrations in the structural model, and in molecular dynamics. Simulations involving high frequency vibration can take a huge number of time steps, often as a consequence of oscillations which are not physically important. The components causing the oscillations cannot usually be eliminated from the model because in some situations they are critical to the simulation. The equations of motion of a multibody mechanical system are described by a system of differential-algebraic equations (DAEs). In this paper, we will explore two types of methods. The first class of methods damps out the oscillation via highly stable implicit methods. Even in this relati...