Parallel Multiscale Algorithms for Dynamical Systems

所提出的研究将为未来大规模并行计算机体系结构的真实计算机模拟开辟重要的问题类。目标区域是具有强烈时间变化的动态现象。典型的过程将受益于这种改进的模拟能力，例如，化学和生物系统的分子动力学，振动机械系统，系统生物现象，大气流动和地震波传播。新的计算方法和理论理解将为具有挑战性的动力系统的数值解引入新的范式，并具有许多未来实际应用的潜力。培养这些领域的学生也非常重要，因为他们将塑造学术界和工业界多尺度建模和高性能计算发展的未来。具有高振荡解的时相关系统在许多重要的科学和工程领域中都可以找到，它们在分析和科学计算中都提出了巨大的挑战。研究活动的一个主要焦点是这些系统的多尺度方法的发展，这些方法侧重于这些系统的有效行为，而不解决所有细节。PIs建议在未来几年开发一个新的框架来解决科学计算的一些核心问题。这将在两个方向上完成。在第一章中，早期的技术将推广到无限维振荡系统，并应用于地震波传播。另一个方向是开发下一代大规模并行计算机系统。有效行为的多尺度模型将被用作粗解器，以解决具有挑战性的并行或平行计算中的重要障碍。研究结果将进一步促进多尺度建模领域的协同发展。

The proposed research will open important problem classes for realistic computer simulation on future massively parallel computer architectures. The targeted areas are dynamical phenomena with strong variations in time. Typical processes that will benefit from this improved simulation capability are, for example, molecular dynamics for chemical and biological systems, vibrating mechanical systems, systems biological phenomena, atmospheric flow and seismic wave propagation. The novel computational methods and theoretical understanding will introduce new paradigms in the numerical solutions of challenging dynamical systems with a potential for many future realistic applications. The training of students in these fields is also very important, as they will shape the future of the development of multiscale modeling and high performance computing in academia and industry.Time dependent systems that have highly oscillatory solutions can be found in many important fields of science and engineering, and they present great challenges both in analysis and in scientific computation. A major focus of research activities has been on the development of multiscale methods for such systems that focus on the effective behavior of these systems without resolution of all details. The PIs propose to develop a new framework addressing some of the core problems of scientific computing for the coming years. This will be done in two directions. In one the earlier techniques will be generalized to infinite dimensional oscillatory systems with application to seismic wave propagation. The other direction will exploit next generation massively parallel computer systems. The multiscale models for effective behavior will be used as coarse solvers to resolve important obstacles in the challenging parallel-in-time or parareal computation. The results will facilitate further synergistic advancement in the field of multiscale modeling in general.