GPU accelerated variational methods for fast phononic eigenvalue solutions

Abstract

In this paper we present a Graphical Processing Unit (GPU) accelerated variational formulation for fast phononic band-structure calculations. The thousands of parallel threads available on GPUs massively reduce the time taken to assemble the phononic eigenvalue problem for arbitrarily complex unit cells. The computation times then become bounded by the eigenvalue solution and if only a few eigenvalues are desired then the computation becomes linear in complexity. Since most of the current applications of phononic crystals require the calculation of only the first few eigenvalues, the GPU acceleration scheme presented in this paper promises to facilitate the solutions to currently tough phononic problems such as 3-D optimization and inverse solutions. The parallelization scheme and GPU application presented in this paper are not limited to the variational scheme used but can be easily extended to other phononic algorithms such as the Plane Wave Expansion method and also to the general eigenvalue solutions of elastodynamics.