Simulating electron wave dynamics in graphene superlattices exploiting parallel processing advantages

This work introduces a parallel computing framework to characterize the propagation of electron waves in graphene-based nanostructures. The electron wave dynamics is modeled using both “microscopic” and effective medium formalisms and the numerical solution of the two-dimensional massless Dirac equation is determined using a Finite-Difference Time-Domain scheme. The propagation of electron waves in graphene superlattices with localized scattering centers is studied, and the role of the symmetry of the microscopic potential in the electron velocity is discussed. The computational methodologies target the parallel capabilities of heterogeneous multi-core CPU and multi-GPU environments and are built with the OpenCL parallel programming framework which provides a portable, vendor agnostic and high throughput-performance solution. The proposed heterogeneous multi-GPU implementation achieves speedup ratios up to 75x when compared to multi-thread and multi-core CPU execution, reducing simulation times from several hours to a couple of minutes.

本研究引入了一种并行计算框架，用以表征基于石墨烯的纳米结构中电子波的传播特性。电子波动力学模型采用“微观”与有效介质形式进行建模，并通过有限差分时域法求解二维无质量狄拉克方程。本研究探讨了具有局域散射中心的石墨烯超晶格中电子波的传播，并讨论了微观势对称性对电子速度的影响。计算方法针对异构多核CPU和多GPU环境中的并行能力进行优化，并基于OpenCL并行编程框架构建，该框架提供了一种便携、供应商无关且高性能的解决方案。所提出的异构多GPU实现方案，相较于多线程和多核CPU执行，实现了高达75倍的加速比，将仿真时间从数小时缩短至数分钟。