Reordering and incomplete preconditioning in serial and parallel adaptive mesh refinement and coarsening flow solutions
Article first published online: 29 JUN 2011
Copyright © 2011 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids
Volume 69, Issue 4, pages 802–823, 10 June 2012
How to Cite
Camata, J.J., Rossa, A.L., Valli, A.M.P., Catabriga, L., Carey, G.F. and Coutinho, A.L.G.A. (2012), Reordering and incomplete preconditioning in serial and parallel adaptive mesh refinement and coarsening flow solutions. Int. J. Numer. Meth. Fluids, 69: 802–823. doi: 10.1002/fld.2614
- Issue published online: 19 APR 2012
- Article first published online: 29 JUN 2011
- Manuscript Revised: 13 FEB 2011
- Manuscript Received: 15 FEB 2010
- ILU preconditioning;
- adaptive mesh refinement;
- Krylov subspace solvers;
- parallel implementation
The effects of reordering the unknowns on the convergence of incomplete factorization preconditioned Krylov subspace methods are investigated. Of particular interest is the resulting preconditioned iterative solver behavior when adaptive mesh refinement and coarsening (AMR/C) are utilized for serial or distributed parallel simulations. As representative schemes, we consider the familiar reverse Cuthill–McKee and quotient minimum degree algorithms applied with incomplete factorization preconditioners to CG and GMRES solvers. In the parallel distributed case, reordering is applied to local subdomains for block ILU preconditioning, and subdomains are repartitioned dynamically as mesh adaptation proceeds. Numerical studies for representative applications are conducted using the object-oriented AMR/C software system libMesh linked to the PETSc solver library. Serial tests demonstrate that global unknown reordering and incomplete factorization preconditioning can reduce the number of iterations and improve serial CPU time in AMR/C computations. Parallel experiments indicate that local reordering for subdomain block preconditioning associated with dynamic repartitioning because of AMR/C leads to an overall reduction in processing time. Copyright © 2011 John Wiley & Sons, Ltd.