量子化学代码CP2K中基于子矩阵的近似矩阵函数求值方法
A Submatrix-Based Method for Approximate Matrix Function Evaluation in the Quantum Chemistry Code CP2K
AI总结：
本研究将子矩阵方法应用于量子化学软件CP2K的DFT计算，通过将大稀疏矩阵运算转化为局部小近密矩阵运算，突破内存带宽限制，实现了CPU、GPU及FPGA上的性能提升。
摘要：
基于密度泛函理论（DFT）的电子结构计算是当今高性能计算（HPC）工作负载的重要组成部分，对高性能计算资源提出了很高要求。要在复杂的大规模体系上开展这类量子力学DFT计算，需要采用所谓的线性标度方法，而非传统的立方标度方法。本研究借鉴子矩阵方法的思路，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基础数值运算转化为局部的、尺寸小得多且近乎稠密的矩阵上的计算。这使得我们能够发挥现代CPU的全部浮点性能，并利用专用加速器硬件——此前这类硬件的性能一直受限于内存带宽。我们验证了所实现方案的功能与性能，并展示了如何借助GPU和FPGA对其进行加速。
英文摘要：
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.
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