Parareal methods for highly oscillatory ordinary differential equations

Series: 
Applied and Computational Mathematics Seminar
Monday, April 13, 2015 - 14:00
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Georgia Tech
,  
We introduce a new parallel in time (parareal) algorithm which couples multiscale integrators with fully resolved fine scale integration and computes highly oscillatory solutions for a class of ordinary differential equations in parallel. The algorithm computes a low-cost approximation of all slow variables in the system. Then, fast phase-like variables are obtained using the parareal iterative methodology and an alignment algorithm. The method may be used either to enhance the accuracy and range of applicability of the multiscale method in approximating only the slow variables, or to resolve all the state variables. The numerical scheme does not require that the system is split into slow and fast coordinates. Moreover, the dynamics may involve hidden slow variables, for example, due to resonances.