A New Multiscale Framework for Hyperbolic Problems

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，人们通常对计算涉及许多时间和长度尺度的给定系统的某些可观察性和有效特性感兴趣。然而，在给定系统中对所有尺度进行数值解析所需的计算复杂性是不可行的。多尺度算法被用来计算具有足够宽的尺度间隔和一定的均匀性和遍历性的系统的有效性质。由于这些经典环境下的多尺度计算已经达到了相对成熟的阶段，现在有必要制定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。双曲型问题的特点是在解中支持振荡，相位误差通常在数值解中占主导地位，并且不会随时间消散。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尺度。随着处理器核心性能的停滞不前，这些更具挑战性的多尺度问题的并行计算成为必然。另一方面，由于空间域分解的加速已经饱和，除非可以执行实时并行化，否则双曲问题的计算将无法从可用的超大规模计算能力中受益。人们普遍认为，使用这种实时并行算法进行鲁棒性和收敛性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支持的研究成果，开发一种新的多尺度框架，为多尺度双曲问题提供稳定的并行计算。该框架的一个重要组成部分是通过明智地利用从适当的并行计算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。

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.