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

职业：加速方法、迭代求解器和异构架构：大规模科学模拟的新景观

• 批准号: 2144181
• 负责人: Agnieszka Miedlar
• 金额: $ 43.06万
• 依托单位: University of Kansas Center for Research Inc
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-09-01 至 2023-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2144181&HistoricalAwards=false
• 关键词: CAREER; Acceleration; Methods; Iterative; Solvers

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.

传统高性能计算的快速变化以及应用于智能电网、无人驾驶汽车和可穿戴医疗设备的新兴边缘计算技术给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，数值线性代数是仿真软件的基本且通常不可或缺的组件。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型材料，并实现高保真度数值模​​拟，以应对科学和工程前沿的挑战。该研究计划与教育和外展活动相结合，旨在培养未来的科学和工程劳动力并刺激公众对数学的参与。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，以及对具有全球重要性的应用进行跨学科研究的机会。研究人员还旨在通过促进 STEM 的公共活动来提高当地的参与度和参与度，为 K-12 学生提供实践计算数学教育，并吸纳代表性不足群体的成员并帮助他们取得职业成功。 这项研究的总体目标旨在进一步了解广泛的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以充分利用分布式和异构计算环境的能力。收敛加速方法已在科学和工程中成功使用了数十年，但其严格的数学基础仍未被完全理解。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）提供非线性加速技术的系统数学研究； (2) 开发加速的、可能异步的迭代算法来求解线性系统，其潜力类似于成熟的 Krylov 子空间方法； (3) 通过开发加速（块）迭代（非线性）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开发。所有正在开发的方法都旨在应用于百亿亿次和分布式计算环境中的各种复杂科学和工程模拟。该项目由计算数学和刺激竞争性研究既定计划（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智力价值和更广泛的影响审查标准进行评估，被认为值得支持。