CAREER: Acceleration Methods, Iterative Solvers and Heterogeneous Architectures: The New Landscape of Large-Scale Scientific Simulations

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The rapidly changing landscape of traditional high-performance computing and the emerging technology of edge computing, used in smart grids, unmanned autonomous vehicles, and wearable healthcare devices, bring new challenges to modern scientific simulations. This project aims to enable new algorithmic and software advancements, particularly in the field of numerical linear algebra, to fully utilize these new heterogeneous architectures. The primary goal of this project is to provide computational building blocks for scalable implementation of numerical linear algebra, which is an essential and often indispensable component of simulation software. Methods developed as a part of this project will help computational physicists and chemists to efficiently identify and study promising novel materials and enable high fidelity numerical simulations to address the challenges at the frontiers of science and engineering. The research program is integrated with education and outreach activities that aim to build the future science and engineering workforce and stimulate public engagement with mathematics. The project provides undergraduate and graduate students with advanced training in critical science and technology skills as well as opportunities for interdisciplinary research on applications of global importance. The investigator also aims to increase local engagement and participation through STEM-promoting public events, provide K-12 students with hands-on computational mathematics education, as well as include members of underrepresented groups and enable their professional success.The overarching goal of this research is to further the understanding of a broad class of extrapolation and nonlinear convergence acceleration techniques and explore their ability to enhance and extend existing solvers to fully utilize distributed and heterogeneous computing environments. Convergence acceleration methods have been successfully used in science and engineering for decades, but their rigorous mathematical underpinnings are still not fully understood. Moreover, iterative methods for computations in eigenvalue problems and general nonlinear systems are one of the most important research areas in computational mathematics. The project has the following research objectives: (1) provide a systematic mathematical study of nonlinear acceleration techniques; (2) develop accelerated, possibly asynchronous, iterative algorithms to solve linear systems with potential similar to the well-established Krylov subspace methods; (3) enable efficient and reliable eigenvalue computations by developing accelerated (block) iterative (non)linear eigenvalue/eigenvector solvers; (4) develop and validate new numerical linear algebra tools to support algorithmic developments in computational physics and chemistry. All the methods under development are intended for application to a wide range of complex science and engineering simulations in exascale and distributed computing environments.This project is jointly funded by Computational Mathematics and the Established Program to Stimulate Competitive Research (EPSCoR).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.