Inexact hierarchical scale separation: A two-scale approach for linear systems from discontinuous Galerkin discretizations

We propose a modified HSS scheme (“inexact HSS”, “IHSS”) that exploits the highly parallel fine-scale solver more extensively and only approximates the coarse-scale solution in every iteration, thus resulting in a significant speedup. The tolerance of the coarse-scale solver is adapted in every IHSS cycle, controlled by the residual norm of the fine-scale system. Anderson acceleration is employed in the repeated solving of the fine-scale system to stabilize the scheme. We investigate the applicability of IHSS to systems stemming from the nonsymmetric interior penalty DG discretization of the Cahn-Hilliard equation, discuss its hybrid parallel implementation for large-scale simulations, and compare the performance of a widely used iterative solver with and without IHSS.