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首页> 外文期刊>RSC Advances >New scaling relations to compute atom-in-material polarizabilities and dispersion coefficients: part 2. Linear-scaling computational algorithms and parallelization
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New scaling relations to compute atom-in-material polarizabilities and dispersion coefficients: part 2. Linear-scaling computational algorithms and parallelization

机译：新的缩放关系，计算原子态偏振力和色散系数：第2部分。线性缩放计算算法和并行化

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We present two algorithms to compute system-specific polarizabilities and dispersion coefficients such that required memory and computational time scale linearly with increasing number of atoms in the unit cell for large systems. The first algorithm computes the atom-in-material (AIM) static polarizability tensors, force-field polarizabilities, and C-6, C-8, C-9, C-10 dispersion coefficients using the MCLF method. The second algorithm computes the AIM polarizability tensors and C-6 coefficients using the TS-SCS method. Linear-scaling computational cost is achieved using a dipole interaction cutoff length function combined with iterative methods that avoid large dense matrix multiplies and large matrix inversions. For MCLF, Richardson extrapolation of the screening increments is used. For TS-SCS, a failproof conjugate residual (FCR) algorithm is introduced that solves any linear equation system having Hermitian coefficients matrix. These algorithms have mathematically provable stable convergence that resists round-off errors. We parallelized these methods to provide rapid computation on multi-core computers. Excellent parallelization efficiencies were obtained, and adding parallel processors does not significantly increase memory requirements. This enables system-specific polarizabilities and dispersion coefficients to be readily computed for materials containing millions of atoms in the unit cell. The largest example studied herein is an ice crystal containing >2 million atoms in the unit cell. For this material, the FCR algorithm solved a linear equation system containing >6 million rows, 7.57 billion interacting atom pairs, 45.4 billion stored non-negligible matrix components used in each large matrix-vector multiplication, and similar to 19 million unknowns per frequency point (>300 million total unknowns).
机译：我们呈现了两种算法来计算特定于系统特定的偏振性和色散系数，使得随着用于大型系统的单位小区中的原子数量而线性地线性地线性地线性地进行了线性的存储器和计算时间。第一算法计算使用MCLF方法计算原子内型（AIM）静态极化性张力，力场偏振性和C-6，C-8，C-8，C-10色散系数。第二种算法使用TS-SCS方法计算目标极化性张量和C-6系数。使用偶极交互切断长度函数与迭代方法结合实现线性缩放计算成本，避免了大密集矩阵倍增和大矩阵逆势。对于MCLF，利用Richardson的筛选增量外推。对于TS-SCS，引入了失败的缀合物残差（FCR）算法，其解决了具有Hermitian系数矩阵的任何线性方程系统。这些算法已经数学上提供了稳定的收敛性，抵抗圆偏移误差。我们并行化这些方法可在多核计算机上提供快速计算。获得了优异的并行化效率，并添加了并行处理器不会显着提高内存要求。这使得能够容易地计算特定于系统的偏振性和分散系数，以用于在单元电池中包含数百万原子的材料。研究的最大示例是在单元电池中含有> 200万原子的冰晶。对于这种材料，FCR算法解决了含有> 600万行，75.7亿个互动原子对的线性方程系统，每个大矩阵矢量乘法中使用的454亿件存储的不可忽略的矩阵组件，并且与每个频率点的类似1900万未知数（> 3亿个全部未知数）。

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    《RSC Advances》 |2019年第57期|共27页
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  • 正文语种 eng
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