Reordering and incomplete preconditioning in serial and parallel adaptive mesh refinement and coarsening flow solutions

SUMMARY 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 fo...

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Veröffentlicht in:International journal for numerical methods in fluids 2012-06, Vol.69 (4), p.802-823
Hauptverfasser: Camata, J.J., Rossa, A.L., Valli, A.M.P., Catabriga, L., Carey, G.F., Coutinho, A.L.G.A.
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container_end_page 823
container_issue 4
container_start_page 802
container_title International journal for numerical methods in fluids
container_volume 69
creator Camata, J.J.
Rossa, A.L.
Valli, A.M.P.
Catabriga, L.
Carey, G.F.
Coutinho, A.L.G.A.
description SUMMARY 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.
doi_str_mv 10.1002/fld.2614
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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. 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subjects adaptive mesh refinement
Computational methods in fluid dynamics
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
ILU preconditioning
Krylov subspace solvers
parallel implementation
Physics
reordering
title Reordering and incomplete preconditioning in serial and parallel adaptive mesh refinement and coarsening flow solutions
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