Chapter 40 - The efficiency of a parallel ILU preconditioner for finite element solutions of the Navier-Stokes equations

Abstract

This chapter presents an efficient parallel preconditioner suitable for solving the incompressible Navier–Stokes equations. The domain is modeled by an unstructured tetrahedral mesh split into nonoverlapping subdomains. Each subdomain is adaptively refined independently based on local Reynolds number estimates. Computational load is balanced by transferring element-octrees between subdomains. The preconditioner is an incomplete LU factorization where the fill-in criterion is to keep the structure of the finite element matrix. A parallel conjugate gradient solver is achieved by resolving node dependencies based on mesh structure. Each node is sorted by category giving an a priori pivoting suited for parallel solution. Through a priori node pivoting, serial dependencies between interface nodes can be minimized to allow parallel synchronization of subdomains. All decisions to construct the pivot are based on locally available information. The parallel solver has convergence ratios comparable to the best serial solvers with similar ILU strategies. It constructs dependencies for any subdomain partitioning. It is therefore well suited for adaptive mesh generators with parallel refinement. Mesh generation and load balancing can function without any additional constraints imposed by the equation solver.