标题： 大规模电子结构理论的求解器：ELPA 和 ELSI 显示英文标题

标题： Solvers for Large-Scale Electronic Structure Theory: ELPA and ELSI

摘要： 在本次贡献中，我们概述了ELPA库和ELSI接口，它们是FHI-aims中大规模电子结构计算的关键要素。 ELPA是一个关键的求解器库，为标准和广义特征值问题提供高效的解决方案，这些问题是密度泛函理论（DFT）中Kohn-Sham形式主义的核心。 它支持CPU和GPU架构，全面支持NVIDIA和AMD GPU，并正在开发对Intel GPU的支持。 这里我们还报告了最近的优化结果，导致广义特征值问题的GPU性能显著提升。 ELSI是一个开源软件接口层，它在“用户”电子结构代码和“求解器”库之间创建了一个明确的连接，用于Kohn-Sham问题，抽象了从哈密顿矩阵和重叠矩阵（作为ELSI和相应求解器的输入）到特征值和特征向量或密度矩阵解（作为输出返回给“用户”电子结构代码）之间的步骤。 除了ELPA之外，ELSI还支持包括LAPACK和MAGMA、PEXSI和NTPoly库（这些库绕过了显式的特征值求解）以及其他几个求解器。 显示英文摘要

摘要： In this contribution, we give an overview of the ELPA library and ELSI interface, which are crucial elements for large-scale electronic structure calculations in FHI-aims. ELPA is a key solver library that provides efficient solutions for both standard and generalized eigenproblems, which are central to the Kohn-Sham formalism in density functional theory (DFT). It supports CPU and GPU architectures, with full support for NVIDIA and AMD GPUs, and ongoing development for Intel GPUs. Here we also report the results of recent optimizations, leading to significant improvements in GPU performance for the generalized eigenproblem. ELSI is an open-source software interface layer that creates a well-defined connection between "user" electronic structure codes and "solver" libraries for the Kohn-Sham problem, abstracting the step between Hamilton and overlap matrices (as input to ELSI and the respective solvers) and eigenvalues and eigenvectors or density matrix solutions (as output to be passed back to the "user" electronic structure code). In addition to ELPA, ELSI supports solvers including LAPACK and MAGMA, the PEXSI and NTPoly libraries (which bypass an explicit eigenvalue solution), and several others.