Lattice H-Matrices for Massively Parallel Micromagnetic Simulations of Current-Induced Domain Wall Motion
Lattice H-Matrices for Massively Parallel Micromagnetic Simulations of Current-Induced Domain Wall Motion
复制标题
DOI：
10.1109/tmag.2019.2959349
复制
发表时间：
2020-04
影响因子：
2.1
通讯作者：
Akihiro Ida;T. Ataka;A. Furuya
中科院分区：
文献类型：
--
作者：
Akihiro Ida;T. Ataka;A. Furuya
本文讨论了计算退磁场的并行层次矩阵（$\mathcal {H}$ -矩阵），这是电流感应畴壁运动（CDWM）微磁模拟中最耗时的部分。虽然普通的$\mathcal {H}$ -矩阵对于少量的消息传递接口（MPI）进程表现出高效率，但随着进程数量的增加，由于负载不平衡和MPI通信成本，性能会迅速下降。当使用大量进程时，我们引入格$\mathcal {H}$ -矩阵来提高并行可扩展性。证实了格$\mathcal {H}$ -矩阵在CDWM模拟中的适用性，并利用实际数据集研究了格$\mathcal {H}$ -矩阵向量积（hmvp）的格块大小和过程网格形状。在适当的设置下，晶格$\mathcal {H}$ -矩阵在内存使用和计算时间上表现出几乎线性的复杂性。我们的实现继续加速至少大约3600个MPI进程，即使是在一个有数万个未知数的小问题中。
This article discusses parallel hierarchical-matrices ( $\mathcal {H}$ -matrices) to compute a demagnetizing field, which is the most time-consuming part in the micromagnetic simulation of current-induced domain wall motion (CDWM). Although normal $\mathcal {H}$ -matrices exhibit high efficiencies for small numbers of message passing interface (MPI) processes, the performance rapidly decays due to load imbalance and the MPI communication costs as the number of processes increases. We introduce lattice $\mathcal {H}$ -matrices to improve the parallel scalability, when using a large number of processes. The applicability of lattice $\mathcal {H}$ -matrices to CDWM simulations is confirmed and proper lattice block sizes and process grid shapes of the lattice $\mathcal {H}$ -matrices for $\mathcal {H}$ -matrix-vector products (HMVPs) are investigated using practical data sets. Under appropriate settings, the lattice $\mathcal {H}$ -matrices exhibit almost linear complexity in memory usage and calculation time of HMVPs. Our implementation continues to accelerate at least up to about 3600 MPI processes, even in a small problem with several tens of thousands of unknowns.