The time-parallel solution of parabolic partial differential equations using the frequency-filtering method

Abstract

We consider the parallel solution of time-dependent partial differential equations. Due to the fact that time is a one-way dimension, traditional methods attack this type of equation by solving the resulting sequence of problems in a sequential manner. Parallel solution methods retain this sequential process, obtaining their parallelism by distributing the problem at each discrete time-step. It has been recently shown that a new approach called time-parallelism, which assigns successive time-steps to different processors can also lead to high efficiencies. In this paper we describe such a time-parallel algorithm based on the frequency-filtering scheme of Wittum.