REORDERING EFFECTS ON PRECONDITIONED KRYLOV METHODS IN AMR SOLUTIONS OF FLOW AND TRANSPORT

This paper evaluates the effects of reordering the unknowns on the convergence of preconditioned Krylov subspace methods for the solution of nonsymmetric linear sys- tems that arise from the finite element discretization of flow and transport. Of particular interest is the iterative solver behavior when adaptive mesh refinement (AMR) is utilized. Numerical studies are conducted using the object oriented AMR software system LibMesh with the PETSc Library. Using incomplete factorization preconditioners with several lev- els of fill-in, we investigate the effects of the Reverse Cuthill-McKee algorithm on GMRES, LCD and BICGSTAB methods. It is shown that the reordering applied in this finite ele- ment implementation with adaptive mesh refinement can reduce the number of iterations and, consequently, improve CPU time for some incomplete factorization preconditioners.