IMEX Parareal Integrators

Parareal is a widely studied parallel-in-time method that can achieve meaningful speedup on certain problems. However, it is well known that the method typically performs poorly on dispersive equations. This paper analyzes linear stability and convergence for IMEX Runge-Kutta parareal methods on dispersive equations. By combining standard linear stability analysis with a simple convergence analysis, we find that certain parareal configurations can achieve parallel speedup on dispersive equations. These stable configurations all posses low iteration counts, large block sizes, and a large number of processors.