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

智能电网、无人驾驶汽车和可穿戴医疗设备中使用的传统高性能计算和新兴边缘计算技术的快速变化，给现代科学模拟带来了新的挑战。该项目旨在使新的算法和软件的进步，特别是在数值线性代数领域，充分利用这些新的异构架构。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，这是仿真软件必不可少的组成部分。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，并使高保真的数值模拟能够解决科学和工程前沿的挑战。该研究项目与教育和推广活动相结合，旨在培养未来的科学和工程劳动力，并激发公众对数学的参与。该项目为本科生和研究生提供关键科学技术技能的高级培训，并为具有全球重要性的应用进行跨学科研究提供机会。研究者还旨在通过促进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成员并使他们取得专业成功。本研究的首要目标是进一步理解外推和非线性收敛加速技术，并探索它们增强和扩展现有求解器的能力，以充分利用分布式和异构计算环境。收敛加速方法已经在科学和工程中成功地应用了几十年，但其严格的数学基础仍然没有完全理解。而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方向之一。本项目的研究目标如下：(1)对非线性加速度技术进行系统的数学研究；(2)开发加速（可能是异步的）迭代算法来求解具有类似于已建立的Krylov子空间方法的潜在线性系统；(3)通过开发加速（块）迭代（非线性）特征值/特征向量求解器，实现高效可靠的特征值计算；(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发展。所有正在开发的方法都是为了在百亿亿次和分布式计算环境中应用广泛的复杂科学和工程模拟。该项目是由计算数学和建立计划，以刺激竞争研究（EPSCoR）共同资助。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.