A New Multiscale Framework for Hyperbolic Problems

双曲线问题的新多尺度框架

• 批准号: 1913209
• 负责人: Bjorn Engquist
• 金额: $ 44.49万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-06-15 至 2022-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1913209&HistoricalAwards=false
• 关键词: New; Multiscale; Framework; Hyperbolic; Problems

In this project, the PIs will develop a novel computational framework for building numerical algorithms that are capable of fully utilizing the power of the next generation super computers. By fully using the large scale computing power, these algorithms will be able to perform highly accurate simulations of important physical phenomena involving propagation of different types of waves. These simulations provide important data and information for further decision making.In many physical applications, one typically is interested in computing certain observables and effective properties from the given systems that involve many temporal and length scales. However, the computational complexity required to numerically resolve all the scales in the given system is unfeasible. Multiscale algorithms have been developed to compute the effective properties of systems that have sufficiently wide separation of scales, and certain homogeneity and ergodic properties. As multiscale computation for these classical settings have reached a relatively mature stage, it is now necessary to develop new strategies addressing some of the core problems of scientific computing for the coming era. This project will involve multiscale hyperbolic problems. Hyperbolic problems characteristically support oscillations in the solutions, and phase errors typically dominate the numerical solutions and do not dissipate in time. These properties make accurate long time simulations very difficult. The project will further tackle a harder class of hyperbolic problems in which a wide spectrum of non-negligible scales is present. With the stagnation of processor core performance, parallel computation for these more challenging multiscale problems becomes inevitable. On the other hand, computations of hyperbolic problems will not benefit from the available exa-scale computing power unless parallelization-in-time can be performed, as the speed-up from spatial domain decomposition has saturated. It is widely recognized that robust and convergent numerical computation using such parallel-in-time algorithms still remains a main challenge for hyperbolic problems. The investigators will leverage success of earlier NSF supported research and develop a new multiscale framework that enables stable parallel-in-time computation for multiscale hyperbolic problems. An essential component of the framework involves making up the deficiencies of the typical multiscale models by judiciously utilizing data collected from suitable ensembles of the parallel computations.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.

在这个项目中，PI将开发一个新的计算框架，用于构建能够充分利用下一代超级计算机的能力的数值算法。通过充分利用大规模计算能力，这些算法将能够对涉及不同类型波传播的重要物理现象进行高度精确的模拟。这些模拟为进一步的决策提供了重要的数据和信息。在许多物理应用中，人们通常对从给定的涉及许多时间和长度尺度的系统中计算某些可观测量和有效性质感兴趣。然而，在给定的系统中，数值解决所有尺度所需的计算复杂性是不可行的。多尺度算法已经被开发用于计算具有足够宽的尺度分离以及一定的齐次性和遍历性的系统的有效性质。由于这些经典环境的多尺度计算已经达到了一个相对成熟的阶段，现在有必要开发新的策略来解决未来时代科学计算的一些核心问题。这个项目将涉及多尺度双曲问题。双曲问题的特点是支持振荡的解决方案，相位误差通常占主导地位的数值解，并不消散的时间。这些特性使得精确的长时间模拟非常困难。该项目将进一步解决一类更难的双曲问题，其中存在广泛的不可忽略的尺度。随着处理器核性能的停滞，这些更具挑战性的多尺度问题的并行计算变得不可避免。另一方面，双曲问题的计算将不会受益于可用的exa规模的计算能力，除非可以执行时间上的并行化，因为空间区域分解的加速已经饱和。人们普遍认为，使用这种时间并行算法的鲁棒和收敛的数值计算仍然是双曲问题的主要挑战。研究人员将利用早期NSF支持的研究的成功，并开发一个新的多尺度框架，为多尺度双曲问题提供稳定的时间并行计算。该框架的一个重要组成部分是通过明智地利用从并行计算的合适集合中收集的数据来弥补典型多尺度模型的不足。该奖项反映了NSF的法定使命，并被认为值得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来支持。

项目成果

Near-wall patch representation of wall-bounded turbulence

• DOI: 10.1017/jfm.2020.658
• 发表时间: 2018-11
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: S. Carney;B. Engquist;R. Moser

Optimal Transport Based Seismic Inversion:Beyond Cycle Skipping

• DOI: 10.1002/cpa.21990
• 发表时间: 2020-01
• 期刊: Communications on Pure and Applied Mathematics
• 影响因子: 3
• 作者: Bjorn Engquist;Yunan Yang

Effects of resolution inhomogeneity in large-eddy simulation

大涡模拟中分辨率不均匀性的影响

• DOI: 10.1103/physrevfluids.6.074604
• 发表时间: 2021
• 期刊: Physical Review Fluids
• 影响因子: 2.7
• 作者: Yalla, Gopal R.;Oliver, Todd A.;Haering, Sigfried W.;Engquist, Björn;Moser, Robert D.
• 通讯作者: Moser, Robert D.

Corrected trapezoidal rules for singular implicit boundary integrals

奇异隐式边界积分的修正梯形规则

• DOI: 10.1016/j.jcp.2022.111193
• 发表时间: 2022
• 期刊: Journal of Computational Physics
• 影响因子: 4.1
• 作者: Izzo, Federico;Runborg, Olof;Tsai, Richard
• 通讯作者: Tsai, Richard

A stable parareal-like method for the second order wave equation

• DOI: 10.1016/j.jcp.2019.109156
• 发表时间: 2019-05
• 期刊: J. Comput. Phys.
• 作者: Hieu Nguyen;R. Tsai