Estimating the critical time-step in explicit dynamics using the Lanczos method

The goal of our paper is to demonstrate the cost-effective use of the Lanczos method for estimating the critical time step in an explicit, transient dynamics code. The Lanczos method can provide a significantly larger estimate for the critical time-step than an element-based method (the typical scheme). However, the Lanczos method represents a more expensive method for calculating a critical time-step than elementbased methods. Our paper shows how the additional cost of the Lanczos method can be amortized over a number of time steps and lead to an overall decrease in run-time for an explicit, transient dynamics code. We present an adaptive hybrid scheme that synthesizes the Lanczos-based and element-based estimates and allows us to run near the critical time-step estimate provided by the Lanczos method. Copyright q 2006 John Wiley & Sons, Ltd.