Analysis of a New Method for Finding Eigenmodesof Very Large Lattice Systems

Abstract

This paper analyses a new numerical method, based on mechanical resonance to extract pure vibrational eigenmodes for very large systems. This method can be used for systems containing as many as ∼10 ⁶ particles, which are too large to be treated by conventional numerical methods. In addition, this algorithm can easily be vectorized for implementation on an array-processing supercomputer. A formula is given to judge the accuracy of the eigenmodes and eigenfrequencies that are found. In addition a discussion is given of how to make the most efficient choice for two key parameters entering into the algorithm, namely the driving time interval t and the number of iterations p .