Stacked-Bloch-wave electron diffraction simulations using GPU acceleration

In this paper, we discuss the advantages for Bloch-wave simulations performed using graphics processing units (GPUs), based on approximating the matrix exponential directly instead of performing a matrix diagonalization. Our direct matrix-exponential algorithm yields a functionally identical electron scattering matrix to that generated with matrix diagonalization. Using the matrix-exponential scalingand-squaring method with a Pade approximation, direct GPU-based matrix-exponential doubleprecision calculations are up to 20 x faster than CPU-based calculations and up to approximately 70 x faster than matrix cliagonalization. We compare precision and runtime of scaling and squaring methods with either the Pade approximation or a Taylor expansion. We also discuss the stacked-Blochwave method, and show that our stacked-Bloch-wave implementation yields the same electron scattering matrix as traditional Bloch-wave matrix cliagonalization. (C) 2014 Elsevier B.V. All rights reserved.