Performance of the Scheduled Relaxation Jacobi method in a geometric multilevel setting. I. Linear case

Abstract

I investigate the suitability of the Scheduled-Relaxation-Jacobi method as a smoother within a geometric multilevel (ML) solver. Its performance in the solution of a linear elliptic equation is measured, based on two metrics: absolute performance (measured by the residual reduction in a fixed number of iterations), and parallel scalability. I discuss the theoretical expectations on the effect of this hybrid scheme on the solution iterate and, especially, the solution error, and confirm them numerically.