Methods to model and simulate super carbon nanotubes of higher order
Methods to model and simulate super carbon nanotubes of higher order
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DOI：
10.1002/cpe.3872
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发表时间：
2017-04
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通讯作者：
Michael Burger;C. Bischof;Christian Schröppel;J. Wackerfuß
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作者：
Michael Burger;C. Bischof;Christian Schröppel;J. Wackerfuß
超碳纳米管(SCNTs)由于其强度和重量特性，在材料设计中引起了人们的兴趣。在本文中，我们提出了一种基于图代数的方法来建模和构造任意阶的SCNT。以Y结点为基本建模元素，用有向图表示SCNT。提出了一种新的数据结构来存储这些图，该结构充分利用了SCNT中的层次结构，并允许高效地查询节点和边。对SCNT的对称性进行了考虑，并与基于图代数的建模有关。我们提出了一个扩展和改进的算法来模拟碳纳米管的力学行为。与我们之前在Level 0 SCNTs上所做的工作相比，在16核对称多处理系统上，串口运行时性能提高了2倍以上，并行运行时性能提高了4.4倍。新的利用结构对称性的预处理步骤和改进的邻近性感知矩阵向量乘法例程使得这种性能改进成为可能，而只消耗很少的额外内存。我们现在还考虑了1阶和2阶SCNTs。实验结果表明，在有和没有变形的情况下，我们的新求解器比基于压缩行存储的0、1和2阶SCNTs的参考求解器快1.4倍，而只需要一半的内存。由于记忆是此类模拟可行性的限制因素，我们的新方法极大地扩展了此类模拟的可行性领域。版权所有©2016 John Wiley&Sons，Ltd.
Super carbon nanotubes (SCNTs) are of interest in material design because of their strength and weight characteristics. In this paper, we present a graph algebra‐based approach to model and construct SCNTs of arbitrary order. The SCNTs are represented by directed graphs with Y junctions as basic modeling element. A new data structure to store these graphs is proposed that capitalizes on the hierarchy within SCNTs and allows efficient queries for nodes and edges. Symmetry considerations for SCNTs are conducted and related to the graph algebra‐based modeling. We present an extended and improved algorithm for simulating the mechanical behavior of SCNTs. Compared with our previous work on level 0 SCNTs, the performance is improved by a factor higher than 2 when running in serial and a factor up to 4.4 when running in parallel on a 16‐core symmetric multiprocessing system. A new pre‐processing step exploiting structural symmetry and an improved proximity‐aware matrix‐vector‐multiplication routine make this performance improvement possible while only consuming little additional memory. We also now consider SCNTs of order 1 and 2. Experimental results show that our new solver is up to 1.4 times faster than a compressed‐row‐storage based reference solver, on order 0, 1, and 2 SCNTs, with and without deformations, while requiring only half the memory. Because memory is the limiting factor for the feasibility of such simulations, our new approach significantly expands the realm of feasibility for such simulations. Copyright © 2016 John Wiley & Sons, Ltd.