基于阿里云的四维弹簧模型并行运算性能

四维弹簧模型（Four-Dimensional Lattice Spring Model，4D-LSM）是一种考虑额外维相互作用的新型离散数值计算方法。该方法用于岩石破坏分析需要消耗大量计算资源，不适合在普通个人电脑上运行。基于多核并行技术，在阿里云和多核工作站等多种硬件环境下对4D-LSM的计算极限性能及瓶颈进行详细分析，主要研究了求解规模、求解类型、线程数、硬件配置等对4D-LSM求解效能的影响。研究发现，内存容量决定可计算的模型规模，弹性问题的计算时间与模型规模成正比，并行计算效率受CPU性能和内存带宽的共同影响。在不考虑经济因素的情况下，云计算在多核匹配和内存分配方面的灵活性特别适合于四维弹簧模型的并行计算分析。结果表明：基于阿里云的4D-LSM最大运算规模可以达到十亿单元，由于目前的瓶颈在于前后处理，4D-LSM目前的可分析规模仍然限制在两千万单元。最后，展示了采用极限规模的并行四维弹簧模型求解三维币形裂纹扩展的实际应用案例。

Performance of the parallel four-dimensional lattice spring model using Alibaba cloud

Four-dimensional Lattice Spring Model (4D-LSM) is a newly developed discrete numerical method considering the extra-dimensional interaction. The method needs large amounts of computing resources in three-dimensional rock failure analysis and therefore is not suitable for the conventional personal computer (PC). In this work, based on the multi-core parallel technology, the computational performance and bottleneck of 4D-LSM were analyzed in details. A variety of hardware environments, such as Alibaba cloud, multi-core PC, and multi-core workstation, were selected to investigate effects of the model size, problem type, thread number and hardware configuration on the parallel computing performance. It is found that the memory capacity determines the limit size of the computable model, and the computational time of the elastic problem is proportional to the model size. The parallel computing efficiency is affected by both the CPU performance and memory bandwidth. The flexibility of cloud computing in multi-core matching and memory allocation is especially suitable for parallel computing of 4D-LSM without considering the economic factor. Through analysis, it is found that the maximum size of 4D-LSM based on Alibaba cloud can reach 1 billion particles. However, due to the bottleneck lies on the pre-processing and post-processing, the current maximum capacity of 4D-LSM is still limited to 20 million particles. Finally, as an example, 4D-LSM was used to solve a three-dimensional coin-shaped crack propagation problem.