Premium
Estimating the critical time‐step in explicit dynamics using the Lanczos method
Author(s) -
Koteras J. R.,
Lehoucq R. B.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1865
Subject(s) - lanczos resampling , lanczos algorithm , computer science , transient (computer programming) , algorithm , mathematics , generalized minimal residual method , element (criminal law) , mathematical optimization , iterative method , physics , eigenvalues and eigenvectors , quantum mechanics , political science , law , operating system
Abstract 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 element‐based 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 © 2006 John Wiley & Sons, Ltd.