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GPU accelerated variational methods for fast phononic eigenvalue solutions

机译：GPU加速变分方法用于快速声子特征值解决方案

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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 paralleliza-tion 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.
机译：在本文中，我们提出了用于快速声子带结构计算的图形处理单元（GPU）加速变分公式。 GPU上可用的数千个并行线程极大地减少了组装任意复杂单位单元的声子本征值问题所需的时间。然后，计算时间就受到特征值解的限制，如果仅需要几个特征值，则计算的复杂度将变为线性。由于当前大多数声子晶体应用仅需要计算前几个特征值，因此本文提出的GPU加速方案有望促进解决当前棘手的声子问题，例如3-D优化和逆解。本文提出的并行化方案和GPU应用不限于所使用的变分方案，还可以轻松扩展到其他声子算法，例如平面波扩展方法，以及弹性力学的一般特征值解。

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