A data driven heuristic for rapid convergence of general Scheduled Relaxation Jacobi (SRJ) schemes
The Scheduled Relaxation Jacobi (SRJ) method is a viable candidate as a high performance linear solver for elliptic PDEs. The method greatly improves the convergence of standard Jacobi iteration by applying a sequence of $M$ overrelaxation and underrelaxation steps in each cycle of the algorithm. In previous work, the relaxation factors associated with each of the $M$ steps (which characterize an SRJ scheme) were derived to be specific to the problem of interest and its discretization. In this work we develop a class of SRJ schemes which could be applied to solve any linear system as long as the original Jacobi iterative method would converge. Furthermore, we use data to train an algorithm to select which scheme to use at each cycle of the SRJ method for rapid convergence. Specifically, the algorithm is trained using convergence data obtained from randomly applying SRJ schemes to the 1D Poisson problem. The automatic selection heuristic that is developed based on this limited data is found to provide good convergence for a wide range of problems.