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

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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.