A Submatrix-Based Method for Approximate Matrix Function Evaluation in the Quantum Chemistry Code CP2K
A Submatrix-Based Method for Approximate Matrix Function Evaluation in the Quantum Chemistry Code CP2K
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DOI：
10.1109/sc41405.2020.00084
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发表时间：
2020-04
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通讯作者：
Michael Lass;Robert Schade;T. Kuhne;Christian Plessl
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作者：
Michael Lass;Robert Schade;T. Kuhne;Christian Plessl
基于密度泛函理论 (DFT) 的电子结构计算代表了当今 HPC 工作负载的重要组成部分，并对高性能计算资源提出了很高的要求。为了在复杂的大规模系统上执行这些量子力学 DFT 计算，需要使用所谓的线性标度方法而不是传统的立方标度方法。在这项工作中，我们采用了子矩阵方法的思想，并将其应用于软件包 CP2K 中的 DFT 计算。为此，我们将分布式、大型、稀疏矩阵上的底层数值运算转换为局部、小得多且近乎稠密的矩阵上的计算。这使我们能够充分利用现代 CPU 的浮点性能，并利用专用加速器硬件，而以前的性能一直受到内存带宽的限制。我们展示了我们实现的功能和性能，并展示了如何使用 GPU 和 FPGA 对其进行加速。
Electronic structure calculations based on density-functional theory (DFT) represent a significant part of today’s HPC workloads and pose high demands on high-performance computing resources. To perform these quantum-mechanical DFT calculations on complex large-scale systems, so-called linear scaling methods instead of conventional cubic scaling methods are required. In this work, we take up the idea of the submatrix method and apply it to the DFT computations in the software package CP2K. For that purpose, we transform the underlying numeric operations on distributed, large, sparse matrices into computations on local, much smaller and nearly dense matrices. This allows us to exploit the full floating-point performance of modern CPUs and to make use of dedicated accelerator hardware, where performance has been limited by memory bandwidth before. We demonstrate both functionality and performance of our implementation and show how it can be accelerated with GPUs and FPGAs.