Parallel Multiscale Algorithms for Dynamical Systems

University Of Texas At Austin, Austin TX

Investigators

Abstract

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.