Optimisation of a Parallel Multigrid Solver for HPC Simulations

The book starts with an introduction to equation solvers and how computational work can be distributed on High Performance Computers. In the following chapters a state-of-the-art Multigrid Solver is investigated and possible improvements are discussed. This solver is designed to solve the Navier-Stokes equation in two steps. In this solver, an intermediate velocity is computed via the Chorins projection using pressure values from a previous step. Secondly a pressure correction is made by using a pressure Poisson equation. The improved solver is tested against the original version in several scenarios that demonstrate an increase of speed up to a factor of 65. The final chapter provides the reader with some ideas on how the performance of a Multigrid Solver could be further improved.