255 IGPM255.pdf        March 2006
TITLE Numbering Techniques for Preconditioners in Iterative Solvers for Compressible Flows
AUTHORS Bernhard Pollul, Arnold Reusken
ABSTRACT We consider Newton-Krylov methods for solving discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is crucial for the efficiency of the solver. In this paper we consider a point-block Gauss-Seidel method as preconditioner. We describe and compare renumbering strategies that aim at improving the quality of this preconditioner. A variant of reordering methods known from multigrid for convection-dominated elliptic problems is introduced. This reordering algorithm is essentially black-box and significantly improves the robustness and efficiency of the point-block Gauss-Seidel preconditioner. Results of numerical experiments using the QUADFLOW solver and the PETSc library are given.
KEYWORDS Euler equations, Krylov subspace methods, preconditioning, ordering algorithms
DOI 10.1002/fld.1450
PUBLICATION International journal for numerical methods in fluids
55(3), 241-261 (2007)