Parallelism in the Matrix Construction Routines and the Linear System Solver forthe ISNaS Program

摘要

The purpose of the incompressible solver of the Information System for the Navier-Stokes equation (ISNaS) software is to provide a flexible and portable solver for the incompressible Navier-Stokes equations. To guarantee this flexibility the software uses curvilinear grids to allow for curved domain boundaries and domain decomposition to allow for irregular domains or domains that contain one or more holes. Because in this code domain decomposition is intended to resolve problems caused by the geometry of the domain, using it purely as a parallelization tool may not be very efficient, especially on massively parallel machines. This led to a study of ways to parallelize the matrix construction and problem solution process for the separate sub-domains. Ideally this would allow for parallelism at two levels: parallelism over the sub-domains, with large amounts of work per processor, but a complicated interaction between processors, and parallelism within sub-domains, with smaller amounts of work per processor but very simple interaction between processors. It is the construction of the matrices for a single sub-domain and the solution of the resulting linear system that will concern us in the report.