An asymptotic parallel-in-time method for highly oscillatory PDEs

2013/03/26 by Terry Haut, Haut, Terry, Beth Wingate +1 · 1 citation
Earth and Planetary Sciences · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1303.6615

openalex publication_date 2013/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants

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