Convergence of Line Iterative Methods for Cyclically Reduced Non-SymmetrizableLinear Systems

摘要

We derive analytic bounds on the convergence factors associated with blockrelaxation methods for solving the discrete two-dimensional convection-diffusion equation. The analysis applies to the reduced systems derived when one step of block Gaussian elimination is performed on red-black ordered two-cyclic discretizations. We consider the case where centered finite difference discretization is used and one cell Reynolds number is less than one in absolute value and the other is greater than one. It is shown that line ordered relaxation exhibits very fast rates of convergence. (AN).