Solving large-scale interior eigenvalue problems to investigate the vibrational properties of the boson peak regime in amorphous materials

Amorphous solids, like metallic glasses, exhibit an excess of low frequency vibrational states reflecting the break-up of sound due to the strong structural disorder inherent to these materials. Referred to as the boson peak regime of frequencies, how the corresponding eigenmodes relate to the underlying atomic-scale disorder remains an active research topic. In this paper we 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, based on the Trilinos framework, is then applied to Hessian matrices of different atomistic bulk metallic glass structures derived from molecular dynamics simulations for the computation of eigenmodes close to the boson peak. In addition, we demonstrate the parallel scalability of our implementation on multicore nodes. Our resulting calculations successfully concur with previous atomistic results, and additionally demonstrate a broad cross-over of boson peak frequencies within which sound is seen to break-up.