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

传统高性能计算的快速变化和边缘计算的新兴技术，用于智能电网，无人驾驶汽车和可穿戴医疗设备，为现代科学模拟带来了新的挑战。该项目旨在实现新的算法和软件进步，特别是在数值线性代数领域，以充分利用这些新的异构体系结构。该项目的主要目标是为数值线性代数的可扩展实现提供计算构建块，这是仿真软件的基本且通常不可或缺的组成部分。作为该项目的一部分开发的方法将帮助计算物理学家和化学家有效地识别和研究有前途的新材料，并实现高保真数值模拟，以应对科学和工程前沿的挑战。该研究计划与教育和推广活动相结合，旨在建立未来的科学和工程劳动力，并刺激公众参与数学。该项目为本科生和研究生提供关键科学和技术技能方面的高级培训，以及对全球重要应用进行跨学科研究的机会。调查人员还旨在通过促进STEM的公共活动增加当地的参与和参与，为K-12学生提供动手计算数学教育，以及包括代表性不足的群体的成员，使他们的专业成功。这项研究的首要目标是进一步了解广泛的外推和非线性收敛加速技术，并探讨他们的能力，以提高和扩展现有求解器以充分利用分布式和异构计算环境。收敛加速方法已经成功地应用于科学和工程领域几十年，但其严格的数学基础仍然没有完全理解。此外，特征值问题和一般非线性系统的迭代计算方法是计算数学中最重要的研究领域之一。该项目有以下研究目标：（1）对非线性加速技术进行系统的数学研究;（2）开发加速的、可能异步的迭代算法，以求解具有类似于成熟的Krylov子空间方法的势能的线性系统;（3）通过开发加速的（块）迭代（非）线性特征值/特征向量求解器，实现有效和可靠的特征值计算;（4）开发和验证新的数值线性代数工具，以支持计算物理和化学的算法开发。所有正在开发的方法都是为了应用于在exascale和分布式计算环境中的广泛的复杂科学和工程模拟。该项目由计算数学和刺激竞争研究的既定计划（EPSCoR）共同资助。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响进行评估，被认为值得支持审查标准。

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.