通过GPU加速混合变分公式快速计算分布式声子能带结构
Fast distributed phononic band-structure calculations through a GPU accelerated mixed-variational formulation
摘要：
在本文中，我们提出了一个图形处理单元加速混合变分制定快速声子能带结构计算的任意复杂的单位细胞和报告的速度增益了100倍的未优化的串行CPU计算。据作者所知，这是GPU计算的非FE/FDTD带结构算法的第一个应用程序。该制剂是在一种形式，这是适用于1-，2-和3-D的情况下。然而，在本文中，我们专注于优化的GPU计算的范例内的配方，提出了2-D单位细胞的结果。我们描述了应用的制定与长期的观点，对高效和大规模分布式能带结构算法，适合于解决优化和逆问题。我们报告，准确的能带结构的边界上的不可约布里渊区（IBZ）的前18个声子分支的复杂的2-D晶胞（1132个不同的相位）的评估可以在不到20秒的时间内实现在一个普通的桌面上。对于一个简单的晶胞，前几个声子分支在同一系统上计算不到2.5秒。因此，本文提出的方案，代表了相当大的节省声子带结构的计算成本。
英文摘要：
In this paper we present a Graphical Processing Unit accelerated mixed variational formulation for fast phononic band-structure calculation of arbitrarily complex unit cells and report speed gains of a hundred fold over unoptimized serial cpu computations. To the author's knowledge this is the first application of gpu computing to a non-FE/FDTD bandstructure algorithm. The formulation is presented in a form which is applicable to 1-, 2-, and 3-D cases. However, in this paper we concentrate on optimizing the formulation within the paradigm of gpu computing, presenting results for 2-D unit cells. We describe the application of the formulation with a long term view towards highly efficient and massively distributed band-structure algorithms suitable for tackling optimization and inverse problems. We report that the accurate band-structure evaluation over the boundary of the Irreducible Brillouin Zone (IBZ) for the first 18 phononic branches of a complex 2-D unit cell (with 1132 different phases) can be achieved in less than 20 seconds on a regular desktop. For a simpler unit cell, the first few phononic branches are calculated in less than 2.5 seconds on the same system. The scheme presented in this paper, therefore, represents considerable savings in the computational costs of phononic band-structures.
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