A Parallel ILU Strategy For Solving
Navier-Stokes Equations On An
Unstructured 3D Mesh
Author(s)
Ø. Staff & S. Ø. Wille
Abstract
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.
Keywords: ILU, preconditioning, parallel, unstructuredmesh, CFD, Navier-Stokes.
1 Introduction
Simulations on single processors are often limited by CPU speed and available
central memory. Even fairly modest three dimensional problems can surpass what
Keywords
ILU, preconditioning, parallel, unstructuredmesh, CFD, Navier-Stokes.
Related Book
Other papers in this volume
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