论文标题

使用现代GPU的水动力相互作用的高度分辨率聚合物链的Petascale Brownian动力学模拟

Petascale Brownian dynamics simulations of highly resolved polymer chains with hydrodynamic interactions using modern GPUs

论文作者

Krishna, Venkata Siva, Kumar, Praphul, Sharma, Bharatkumar, Dalal, Indranil Saha

论文摘要

在单一库恩步骤的分辨率下,即使在现代处理器上,在单一库恩步骤的分辨率下,对相当长,高度详细的聚合物链的布朗动力学模拟也仍然具有计算性的性能。当链上的珠子体验流体动力相互作用(HI)时,这尤其如此,这需要在每个时间步中使用大型矩阵等方法。在这项研究中,我们在现代GPU上进行了相当长且高度分辨的聚合物链的HI进行Petascale BD模拟。我们的结果清楚地表明,使用弹簧连接的珠子的典型模型不足。首先,在本手稿中,我们介绍了在GPU上实现的高度可扩展的并行混合代码的详细信息,用于解决单个Kuhn步骤的链条模拟。在使用CUDA和MPI的此混合代码中,我们使用Cholesky分解方法将HI合并。接下来,我们对GPU实施进行了广泛的验证,其对聚合物链的理论期望是平衡和流动的,并在没有HI的情况下导致结果。此外,相对于常规的珠子弹簧模型,在启动延伸和剪切流中,我们在HI流量的结果显示了拉伸的时间变化显着不同。在所有调查的情况下,整体平均链伸展远低于珠子弹簧预测。另外,非常值得注意的是,我们的GPU实现显示了$ \ sim $$ n^{1.2} $和$ \ sim $$ $$ n^{2.2} $的计算时间,分别是最现代现代的GPU中的较短且更长的链条,这比理论上预期的$ \ sim $ $ $ $ $ n^} $明显低。我们期望我们的方法和结果为通过长期且高度详细的链模型在流场中进一步分析聚合物物理学铺平道路。

Brownian dynamics simulations of fairly long, highly detailed polymer chains, at the resolution of a single Kuhn step, remains computationally prohibitive even on the modern processors. This is especially true when the beads on the chain experience hydrodynamic interactions (HI), which requires the usage of methods like Cholesky decomposition of large matrices at every timestep. In this study, we perform Petascale BD simulations, with HI, of fairly long and highly resolved polymer chains on modern GPUs. Our results clearly highlight the inadequacies of the typical models that use beads connected by springs. In this manuscript, firstly, we present the details of a highly scalable, parallel hybrid code implemented on a GPU for BD simulations of chains resolved to a single Kuhn step. In this hybrid code using CUDA and MPI, we have incorporated HI using the Cholesky decomposition method. Next, we validate the GPU implementation extensively with theoretical expectations for polymer chains at equilibrium and in flow with results in the absence of HI. Further, our results in flow with HI show significantly different temporal variations of stretch, in both startup extensional and shear flows, relative to the conventional bead-spring models. In all cases investigated, the ensemble averaged chain stretch is much lower than bead-spring predictions. Also, quite remarkably, our GPU implementation shows a scaling of $\sim$$N^{1.2}$ and $\sim$$N^{2.2}$ of the computational times for shorter and longer chains in the most modern available GPU, respectively, which is significantly lower than the theoretically expected $\sim$$N^{3}$. We expect our methods and results to pave the way for further analysis of polymer physics in flow fields, with long and highly detailed chain models.

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