New version of hex-ecs, the B-spline implementation of exterior complex scaling method for solution of electron–hydrogen scattering

We provide an updated version of the program hex-ecs originally presented in Comput. Phys. Commun. 185 (2014) 2903–2912. The original version used an iterative method preconditioned by the incomplete LU factorization (ILU), which–though very stable and predictable–requires a large amount of working memory. In the new version we implemented a “separated electrons” (or “Kronecker product approximation”, KPA) preconditioner as suggested by Bar-On et al., Appl. Num. Math. 33 (2000) 95–104. This preconditioner has much lower memory requirements, though in return it requires more iterations to reach converged results. By careful choice between ILU and KPA preconditioners one is able to extend the computational feasibility to larger calculations. Secondly, we added the option to run the KPA preconditioner on an OpenCL device (e.g. GPU). GPUs have generally better memory access times, which speeds up particularly the sparse matrix multiplication. The original version of this program (AETI_v1_0) may be found at dx.doi.org/10.1016/j.cpc.2014.05.021.

本团队提供了程序hex-ecs的更新版本，该程序最初发表于《计算机物理通讯（Computer Physics Communications）》185卷（2014年）第2903–2912页。原始版本采用了以不完全LU分解（incomplete LU factorization, ILU）为预处理手段的迭代方法，该方法虽稳定性与可预测性俱佳，但需占用大量工作内存。在新版本中，我们实现了由Bar-On等人在《应用数值数学（Applied Numerical Mathematics）》33卷（2000年）第95–104页中提出的“分离电子”预处理器（亦称“克罗内克积近似（Kronecker product approximation, KPA）”）。该预处理器的内存占用需求显著更低，但相应地，达到收敛结果所需的迭代次数更多。通过在ILU与KPA预处理器间谨慎选择，可将计算可行性拓展至更大规模的计算任务。其次，新版本新增了在OpenCL设备（如图形处理器GPU）上运行KPA预处理器的功能。GPU通常具备更优的内存访问时延，可显著加速稀疏矩阵乘法运算。该程序的原始版本（AETI_v1_0）可通过dx.doi.org/10.1016/j.cpc.2014.05.021获取。