Design and Analysis of Algorithms for High-Performance Scientific Computing

高性能科学计算算法的设计与分析

• 批准号: RGPIN-2019-05692
• 负责人: MacLachlan, Scott
• 金额: $ 3.5万
• 依托单位: Memorial University of Newfoundland
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=715746
• 关键词: Design; Analysis; Algorithms; Performance; Scientific; Design; Analysis; Algorithms; Performance; Scientific

Computational simulation of physical systems is a significant scientific and industrial tool. Recent improvements in simulation have come from the development of efficient parallel algorithms for heterogeneous systems, simulating problems with multiple materials, with varying material properties, and/or coupling to additional physical laws. Mathematically, these systems are modeled as coupled systems of partial differential equations (PDEs) representing physical conservation and energy laws, with variable and nonlinear coefficients reflecting the heterogeneity. Finite-element discretizations transform these continuum equations into finite-dimensional linear and non-linear systems; the solution of these systems is the core resource-intensive computational task in many simulation algorithms. My long-term research program focuses on the development and analysis of efficient parallel algorithms for solving the linear, linearized, and non-linear systems that result from these discretizations. My approach follows the multigrid methodology, where a hierarchical decomposition is used to ensure optimal complexity of the iterative solution process. In recent years, this has included a strong focus on structured-grid multigrid methods, which can naturally achieve high parallel efficiency. Of note, my research group has developed state-of-the-art simulation tools for flows of charged fluids (magnetohydrodynamics) and nematic and chiral liquid crystals. Concurrent with this work, I have undertaken the development of predictive algorithmic analysis tools, to help design and optimize solvers in this setting. Furthermore, I have contributed fundamental algorithms and analysis tools to the rapidly growing field of parallel-in-time simulation. The research goals of this proposal are the development of improved methodologies for high-performance scientific computing in these areas. A challenging physical system, smectic liquid crystals, will drive this research, providing new challenges from the dependence of free energy on an auxiliary variable. Concurrently, we will develop a robust optimization viewpoint on local Fourier analysis, the best-practices tool for optimizing algorithmic parameters for monolithic multigrid methods. This will allow us to design and analyse systems of increasing complexity, freed from the traditional high CPU times required for brute-force analysis of monolithic algorithms for coupled finite-element discretizations. Finally, I will continue to develop both algorithms and analysis tools for space-time systems, with a focus on the multigrid reduction-in-time algorithm and corresponding semi-algebraic mode analysis tool. At all stages of this project, the training of HQP in algorithmic design and analysis, as well as programming in high-performance computing environments, will be a central theme, providing key skills in computational science and engineering that can be applied in both academia and industry.

物理系统的计算模拟是一种重要的科学和工业工具。 模拟的最新改进来自于为异构系统的有效平行算法的开发，模拟多种材料的问题，具有变化的材料特性以及/或与其他物理定律耦合。 从数学上讲，这些系统被建模为代表物理保护和能量定律的部分微分方程（PDE）的耦合系统，其可变和非线性系数反映了异质性。 有限元离散化将这些连续方程转换为有限维线性和非线性系统。这些系统的解决方案是许多模拟算法中核心资源密集型计算任务。 我的长期研究计划着重于用于解决这些离散化导致的线性，线性和非线性系统的有效平行算法的开发和分析。 我的方法遵循了多方方法，其中使用层次分解来确保迭代溶液过程的最佳复杂性。 近年来，这包括对结构性网格多族方法的强烈关注，这些方法自然可以实现高平行效率。 值得注意的是，我的研究小组开发了最新的模拟工具，用于用于电荷流体（磁流失动力学）以及夜间和手性液体晶体。同时，我进行了预测算法分析工具的开发，以帮助在此环境中设计和优化求解器。 此外，我为快速增长的平行仿真领域贡献了基本算法和分析工具。 该提案的研究目标是开发这些领域高性能科学计算方法的改进方法。 具有挑战性的物理系统，即近晶液晶，将推动这项研究，从而从自由能对辅助变量的依赖方面带来了新的挑战。 同时，我们将在局部傅立叶分析上开发出强大的优化视点，这是用于优化单片多机方法算法参数的最佳实践工具。 这将使我们能够设计和分析增加复杂性的系统，这是从传统的高力分析中，用于对耦合有限元离散化的单片算法所需的传统高CPU时间。 最后，我将继续开发用于时空系统的算法和分析工具，重点是多机还原时算法和相应的半代数模式分析工具。 在该项目的所有阶段，HQP在算法设计和分析中的培训以及高性能计算环境中的编程将是一个中心主题，可以在学术界和行业中应用计算科学和工程的关键技能。