A parallel ILU strategy for solving Navier-Stokes equations on an unstructured 3D mesh

An iterative algorithm for solving a mixed finite element formulation of Navier-Stokes equations on a distributed memory computer is presented. The solver is a Krylov subspace method with a parallel preconditioner suitable for high latency clusters. Nodes are pivoted to minimize the number of synchronization points in each solver iteration. An unstructured mesh is decomposed into non-overlapping subdomains. Each node is given a category depending on which subdomains it is a member of and on the subdomains of its neighboring nodes in the mesh. Based on these categories, an a priori pivoting suited for parallel solution is constructed. The solver requires approximately the same number of iterations as good serial solvers with a similar preconditioner. The incomplete LU (ILU) preconditioning and subsequent solve is performed on a global matrix implicitly formed as a sum of all subdomain matrices. Communication overhead is kept low by generating a schedule to send information to neighboring subdomains as soon as dependencies in the matrix are resolved. Results will be shown to indicate that this is a viable strategy on computer clusters built with cheap off the shelf components.