Sixth order compact multi-phase block-AGE iteration methods for computing 2D Helmholtz equation

We discuss sixth order accurate 9-point compact 2- and 3-phase block alternating group explicit (block-AGE) iteration methods for computing 2D Helmholtz equation. We use Dirichlet boundary conditions and no fictitious points are involved outside the solution region for computation. The proposed 2- and 3-phase block-AGE methods require only two and three sweeps for computation and the error analysis of the suggested approximation is analyzed. We have compared the 2- and 3-phase block-AGE iteration methods with the corresponding block successive over relaxation (block-SOR) method in three experiments, in regard to number of iterations required for convergence and cpu time, where the importance of the role performed by optimal relaxation parameters of the proposed block-AGE iteration methods become evident in stipulating the convergence and precision of the calculated results. In all cases we use the tridiagonal solver and obtain the optimal relaxation parameters through computation.