论文标题
朝向高阶数值随机扰动计算应用于扭曲的Eguchi-Kawai模型
Towards higher order numerical stochastic perturbation computation applied to the twisted Eguchi-Kawai model
论文作者
论文摘要
我们已经评估了Wilson循环的扰动系数（g^8）$用于使用Arxiv中的数值随机扰动理论（NSPT）的四维扭曲eguchi-kawai模型：1902.09847。在本次演讲中，我们介绍了高阶计算的进度报告，最高$ O（g^{63}）$，为此我们将基于快速的傅立叶变换（FFT）卷积算法应用于NSPT中多项式矩阵的乘法，以实现高阶计算。我们将两个实现与仅CPU版本和基于FFT的GPU版本和基于FFT的GPU版本进行了比较，并在$ O（g^{31}）$ o（g^{31}）$的NSPT算法的计算速度上找到了一个因子9改进。计算时间的扰动顺序依赖性，我们将其调查至$ o（g^{63}）$，显示了截断顺序上的轻度缩放行为。
We have evaluated perturbation coefficients of Wilson loops up to $O(g^8)$ for the four-dimensional twisted Eguchi-Kawai model using the numerical stochastic perturbation theory (NSPT) in arXiv:1902.09847. In this talk we present a progress report on the higher order calculation up to $O(g^{63})$, for which we apply a fast Fourier transformation (FFT) based convolution algorithm to the multiplication of polynomial matrices in the NSPT aiming for higher order calculation. We compare two implementations with the CPU-only version and the GPU version of the FFT based convolution algorithm, and find a factor 9 improvement on the computational speed of the NSPT algorithm with SU($N=225$) at $O(g^{31})$. The perturbation order dependence of the computational time, we investigate it up to $O(g^{63})$, shows a mild scaling behavior on the truncation order.
