Pipeline Implementations of Neumann-Neumann and Dirichlet-Neumann Waveform Relaxation Methods

Abstract

This paper is concerned with the reformulation of Neumann-Neumann Waveform Relaxation (NNWR) methods and Dirichlet-Neumann Waveform Relaxation (DNWR) methods, a family of parallel space-time approaches to solving time-dependent PDEs. By changing the order of the operations, pipeline-parallel computation of the waveform iterates are possible without changing the final solution. The parallel efficiency and the increased communication cost of the pipeline implementation is presented, along with weak scaling studies to show the effectiveness of the pipeline NNWR and DNWR algorithms.