Elements: libkrylov, a Modular Open-Source Software Library for Extremely Large Eigenvalue and Linear Problems

强耦合线性方程组或具有极大未知量的特征值问题是科学和工程中许多重大挑战的计算解决的关键瓶颈。例如，根据第一性原理进行发光或光伏材料的计算设计，需要在几分钟内解出数千万个强耦合的线性方程才能实用。这个项目的目标是开发、实现、测试和部署libkrylov，这是一个健壮、高效和通用的“即时”Krylov空间方法库，适用于解决这种非常大、密集的问题。Libkrylov将通过提供统一的、可重复的和用户友好的软件标准，为科学界和工程界提供Krylov空间方法的最新创新。与电子结构代码相结合，该库将能够大规模模拟有机金属和生物-无机体系的分子随时间变化的X射线吸收光谱。这个项目将通过加州大学欧文分校和圣地亚哥州立大学的学生培训和劳动力教育来促进计算素养，并通过与弗吉尼亚州布莱克斯堡的NSF资助的分子科学软件研究所(MolSSI)的合作来增强国家软件基础设施。Pi和他的团队最近开发了非正交化的Krylov空间方法来解决极大的稠密本征值和线性问题，即不需要显式存储或访问系数矩阵，具有良好的效率和稳定性。该项目旨在将这一方法转变为健壮、高效和可持续的软件基础设施，供公众免费访问。主要特征包括：(I)解决极大问题的独特能力；(Ii)高度灵活的矩阵-向量乘法“引擎”接口；(Iii)通过最小化矩阵-向量乘法的数量和成本而实现的超高效率；(Iv)通过动态控制误差和条件以及稳定方法而实现的卓越稳健性；(V)通过利用对称性和特殊结构、实数和复数算术实现的多功能性；(Vi)可配置的精度、收敛控制、预调节、存储器和磁盘使用；(Vii)可移植到广泛的平台、环境和语言；(Viii)灵活且用户友好的通用接口、文档、和测试能力，(9)面向对象和模块化的可扩展性，(X)通过专用测试套件的可重复性，(11)社区参与和可持续发展，通过与MolSSI合作和部署公共问题和特征请求跟踪器。该项目由计算机和安全部高级数字基础设施办公室支持；这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Strongly coupled linear equation systems or eigenvalue problems with extremely large numbers of unknowns are a critical bottleneck for computational solutions to many grand challenges in science and engineering. For example, computational design of light emitting or photovoltaic materials from first principles requires the solution of tens of millions of strongly coupled linear equations within minutes to be practical. This project aims to develop, implement, test, and deploy libkrylov, a robust, efficient, and general open-source library of "on-the-fly" Krylov space methods suitable for solving such extremely large, dense problems. libkrylov will deliver the latest innovations in Krylov-space methods to the scientific and engineering communities by providing a uniform, reproducible, and user-friendly software standard. Coupled with electronic structure codes, the library will enable large-scale simulations of molecular time-dependent X-ray absorption spectra of organometallic and bio-inorganic systems. This project will promote computational literacy through student training and workforce education at University of California, Irvine and San Diego State University, and enhance national software infrastructure through collaboration with the NSF-funded Molecular Sciences Software Institute (MolSSI) in Blacksburg, VA.The PI and his group have recently developed nonorthonormal Krylov space methods for solving extremely large dense eigenvalue and linear problems "on-the-fly", i.e., without explicit storage or access of coefficient matrices, with demonstrated efficiency and stability. This project aims to transform this methodology into robust, efficient, and sustainable software infrastructure freely accessible to the public. Key features include (i) unique capability to solve extremely large problems, (ii) a highly flexible interface to matrix-vector multiplication "engines" (iii) ultrahigh efficiency by minimizing the number and cost of matrix-vector multiplications, (iv) outstanding robustness by dynamic control of errors and condition, and stabilization methods, (v) versatility by exploiting symmetry and special structure, real and complex arithmetic, (vi) configurable precision, convergence control, preconditioning, memory and disk usage, (vii) portability to broad range of platforms, environments, and languages, (viii) flexible and user-friendly generic interfaces, documentation, and testing capabilities, (ix) extensibility through object orientation and modularity, (x) reproducibility through a dedicated test suite, (xi) community involvement and sustainability by collaboration with MolSSI and deployment of a public issue and feature request tracker.This project is supported by the Office of Advanced Cyberinfrastructure in the Directorate for Computer & Information Science & Engineering and the Division of Chemistry in the Directorate of Mathematical and Physical Sciences.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.