  The Scheduled Relaxation Jacobi (SRJ) method is a viable candidate as a high
performance linear solver for elliptic partial differential equations (PDEs).
The method greatly improves the convergence of the standard Jacobi iteration by
applying a sequence of $M$ well-chosen overrelaxation and underrelaxation
factors in each cycle of the algorithm to effectively attenuate the solution
error. In previous work, optimal SRJ schemes (sets of relaxation factors) have
been derived to accelerate convergence for specific discretizations of elliptic
PDEs. In this work, we develop a family of SRJ schemes which can be applied to
solve elliptic PDEs regardless of the specific discretization employed. To
achieve favorable convergence, we train an algorithm to select which scheme in
this family to apply at each cycle of the linear solve process, based on
convergence data collected from applying these schemes to the one-dimensional
Poisson equation. The automatic selection heuristic that is developed based on
this limited data is found to provide good convergence for a wide range of
problems.
