Qiqi Wang
MIT

Towards Scalable Parallel Long Time Integration of Chaotic Dynamical Systems

Simulations of chaotic dynamical systems, e.g., turbulent fluid flows, often require hundreds of thousands of time steps in order to obtain converged statistics. For applications that requires fast turnaround time, scalable parallel time integration is needed to break the bottle neck of spatial-only parallelization in current-generation simulations. This talk first summarizes existing parallel time integration methods, and analyze the scalability problem encountered in chaotic dynamical systems.  We then outlines a new method that can potentially achieve perfect scalability. This new method is based on a least squares problem of the governing equation, instead of an initial value problem. In contrast to many existing time decomposition methods, the number of iterations required by our method is insensitive to the length of the time integration, making our method scalable.