A direct solver for the heat equation with domain decomposition in space and time

Abstract

In this paper we generalize the Aitken-like acceleration method of the additive Schwarz algorithm for elliptic problems to the additive Schwarz waveform relaxation for the heat equation. The domain decomposition is in space and time. The standard Schwarz waveform relaxation algorithm has a linear rate of convergence and low numerical efficiency. This algorithm is, however, friendly to cache use and scales with the memory in parallel environments. We show that our new acceleration procedure of the waveform acceleration algorithm results in a fast direct solver.