Solving Large Scale Eigenvalue Problems in Amorphous Materials

Abstract

Amorphous solids, like metallic glasses exhibit an excess of states in the low frequency regime very close to the Boson peak, and the precise nature of these low frequency vibrations remains unclear. The purpose of this thesis is to investigate the use of a polynomial filtered eigensolver for the computation and study of low frequency eigenmodes of a Hessian matrix located in a specific interval close to the Boson peak regime. A distributed-memory parallel implementation of a polynomial filtered eigensolver is presented. Our implementation is then applied to Hessian matrices of different atomistic bulk metallic glass structures derived from molecular dynamics simulations for the computation of low frequency eigenmodes close to the Boson peak region. In addition, we demonstrate the parallel scalability of our implementation on multicore nodes. Our resulting calculations successfully concur with previous results, and anomalous behavior of the particles in the region close to the Boson peak can be observed from the data.