Abstract As a newly developed computational method, the four-dimensional lattice spring model (4D-LSM) is computationally intensive due to the introduction of extra-dimensional interactions. In this work, the 4D-LSM is parallelized to fully utilize the available computational resources of modern computers, namely, the multi-core CPU and the GPU. To utilize computing power of the multi-core CPU, OpenMP with a fork-join scheme is used to assign computational tasks to different CPU threads, whereas CUDA, with a granular computing scheme, is adopted to assign computations to thousands of GPU threads. A domain decomposition with a data communication scheme is proposed to utilize both the multi-core CPU and the GPU. The influence of digital precision and hardware on the parallel computing performance of the 4D-LSM are investigated through a number of numerical examples including elastic deformation, elastic bulking and dynamic fracturing. Finally, the multi-core CPU 4D-LSM is used to solve a crack propagation problem and is compared with existing experimental and numerical results.

中文翻译：

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四维点阵弹簧模型在异构 CPU-GPU 系统上的并行实现

摘要 四维晶格弹簧模型（4D-LSM）作为一种新兴的计算方法，由于引入了超维相互作用，计算量大。在这项工作中，4D-LSM 被并行化以充分利用现代计算机的可用计算资源，即多核 CPU 和 GPU。为了利用多核 CPU 的计算能力，OpenMP 采用 fork-join 方案将计算任务分配给不同的 CPU 线程，而采用粒度计算方案的 CUDA 将计算分配给数千个 GPU 线程。提出了一种具有数据通信方案的域分解，以利用多核 CPU 和 GPU。通过弹性变形、弹性膨胀和动态压裂等数值算例，研究了数字精度和硬件对4D-LSM并行计算性能的影响。最后，使用多核 CPU 4D-LSM 解决裂纹扩展问题，并与现有的实验和数值结果进行比较。