An asymptotic parallel-in-time method for highly oscillatory PDEs
For computational scientists solving highly oscillatory PDEs, this method offers a way to overcome the inefficiency of parallel-in-time methods for such problems.
The paper presents a hybrid time-stepping algorithm combining asymptotic methods with parallel-in-time techniques for nonlinear PDEs with temporal scale separation, achieving significant parallel speedup and high accuracy on rotating shallow water equations.
We present a new time-stepping algorithm for nonlinear PDEs that exhibit scale separation in time. Our scheme combines asymptotic techniques (which are inexpensive but can have insufficient accuracy) with parallel-in-time methods (which, alone, can be inefficient for equations that exhibit rapid temporal oscillations). In particular, we use an asymptotic numerical method for computing, in serial, a solution with low accuracy, and a more expensive fine solver for iteratively refining the solutions in parallel. We present examples on the rotating shallow water equations that demonstrate that significant parallel speedup and high accuracy are achievable.