Reliable performance prediction for multigrid software on distributed memory systems

We propose a model for describing and predicting the parallel performance of a broad class of parallel numerical software on distributed memory architectures. The purpose of this model is to allow reliable predictions to be made for the performance of the software on large numbers of processors of a given parallel system, by only benchmarking the code on small numbers of processors. Having described the methods used, and emphasized the simplicity of their implementation, the approach is tested on a range of engineering software applications that are built upon the use of multigrid algorithms. Despite their simplicity, the models are demonstrated to provide both accurate and robust predictions across a range of different parallel architectures, partitioning strategies and multigrid codes. In particular, the effectiveness of the predictive methodology is shown for a practical engineering software implementation of an elastohydrodynamic lubrication solver.