Scalability and locality of extrapolation methods on large parallel systems
Scalability and locality of extrapolation methods on large parallel systems
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DOI：
10.1002/cpe.1765
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发表时间：
2011-10
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通讯作者：
Matthias Korch;T. Rauber;C. Scholtes
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作者：
Matthias Korch;T. Rauber;C. Scholtes
时变过程通常可以用常微分方程（ODE）系统来建模。求解这种系统的详细模型可能是高度计算密集型的。我们研究了显式外推方法，用于在具有共享或分布式内存架构的当前高度并行超级计算机系统上有效地解决此类系统。我们分析和比较几种并行化变体的可扩展性，其中一些使用多级并行化。对于一大类ODE系统，通过利用ODE系统的特殊结构，可以大大降低数据访问开销。此外，通过采用类似流水线的循环结构，对于这样的系统增加了存储器引用的局部性，从而更好地利用了该高速缓存层级。仿真实验表明，优化后的实现具有较高的可扩展性。版权所有© 2011约翰威利父子有限公司.
Time‐dependent processes can often be modeled by systems of ordinary differential equations (ODEs). Solving such a system for a detailed model can be highly computationally intensive. We investigate explicit extrapolation methods for solving such systems efficiently on current highly parallel supercomputer systems with shared‐or distributed‐memory architecture. We analyze and compare the scalability of several parallelization variants, some of them using multiple levels of parallelization. For a large class of ODE systems, data access costs are reduced considerably by exploiting the special structure of the ODE system. Furthermore, by employing a pipeline‐like loop structure, the locality of memory references is increased for such systems resulting in a better utilization of the cache hierarchy. Runtime experiments show that the optimized implementations can deliver a high scalability. Copyright © 2011 John Wiley & Sons, Ltd.