Fast elliptic solver for incompressible Navier Stokes Flow and Heat Transfer problems on the grid

The objective of this work is to present a fast parallel elliptic solver that improves efficiently the run of incompressible Navier-Stokes Flow code or Heat Transfer code on a grid of parallel computers. We focus on the design of the elliptic solver because the pressure solver in an incompressible Navier-Stokes code , is the one that is most time consuming, and demanding on communications between processors. We describe a domain decomposition method that is numerically efficient, scales well on a parallel computer and is tolerant to the high latency and low bandwidth of a slow network. The main feature of our method is to keep the framework of additive Schwarz algorithm that is easy to code, to parallelize, and to make it numerically efficient with an acceleration procedure. We discuss also a model to handle the automatic performance tuning of the linear solver for each subdomain, each processor architecture and each applications with surface response modeling. Results are shown with performance on grid of heterogeneous parallel computers.