Parallel Multiscale Algorithms for Dynamical Systems

拟议的研究将打开现实的计算机模拟未来的大规模并行计算机体系结构的重要问题类。目标区域是具有强烈时间变化的动态现象。将受益于这种改进的模拟能力的典型过程例如是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认识将引入新的范式在具有挑战性的动力系统的数值解与许多未来的现实应用的潜力。在这些领域的学生的培训也是非常重要的，因为他们将塑造未来的多尺度建模和高性能计算在学术界和工业界的发展。时间依赖系统，具有高振荡的解决方案，可以在许多重要的科学和工程领域，他们提出了巨大的挑战，无论是在分析和科学计算。研究活动的一个主要重点是发展多尺度方法，这些系统的重点是这些系统的有效行为，而没有解决所有的细节。PI建议开发一个新的框架，解决未来几年科学计算的一些核心问题。这将在两个方向进行。其中，早期的技术将被推广到无限维振动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略求解器，以解决具有挑战性的时间并行或并行计算中的重要障碍。研究结果将促进多尺度建模领域的进一步协同进步。

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.