Stacked-Bloch-wave electron diffraction simulations using GPU acceleration.

Area of Science:

• Computational physics
• Materials science
• Solid-state physics

Background:

• Bloch-wave simulations are crucial for understanding electron behavior in materials.
• Traditional methods often rely on matrix diagonalization, which can be computationally intensive.
• Graphics processing units (GPUs) offer parallel processing capabilities that can accelerate complex calculations.

Purpose of the Study:

• To investigate the advantages of using graphics processing units (GPUs) for Bloch-wave simulations.
• To develop and evaluate a direct matrix-exponential approximation method for these simulations.
• To compare the performance and accuracy of GPU-based methods against traditional CPU-based approaches.

Main Methods:

• Implemented a direct matrix-exponential approximation using the scaling-and-squaring method with Padé approximation on GPUs.
• Compared the precision and runtime of this method with matrix diagonalization and Taylor expansion-based approaches.
• Utilized the stacked-Bloch-wave method for implementation and comparison.

Main Results:

• The GPU-based direct matrix-exponential algorithm produces an electron scattering matrix functionally identical to matrix diagonalization.
• GPU calculations are up to 20x faster than CPU-based calculations and up to 70x faster than matrix diagonalization.
• The stacked-Bloch-wave implementation using this method yields the same electron scattering matrix as traditional methods.

Conclusions:

• Direct matrix-exponential approximation on GPUs is a highly efficient and accurate method for Bloch-wave simulations.
• This approach significantly reduces computation time without compromising the integrity of the electron scattering matrix.
• The findings pave the way for faster and more scalable simulations in condensed matter physics and materials science.