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

TL;DR

This paper reformulates Neumann-Neumann and Dirichlet-Neumann waveform relaxation methods to enable pipeline-parallel computation, improving efficiency for solving time-dependent PDEs while analyzing communication costs and scalability.

Contribution

It introduces a pipeline implementation of NNWR and DNWR methods, enhancing parallel efficiency without altering the final solution.

Findings

Pipeline implementation improves parallel efficiency

Weak scaling studies demonstrate effectiveness

Communication costs are analyzed

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.