In this chapter, we present efficient fine-grained parallelization techniques for robust
multigrid solvers, in particular for numerically strong, inherently sequential smoothing
operators. We apply them to sparse ill-conditioned linear systems of equations that arise
from grid-based discretization techniques like finite differences, volumes and elements. Our
exemplary results demonstrate both the numerical and runtime performance of these
techniques, as well as significant speedups over conventional CPUs. We implement the …

… Employ mixed precision approach … Combined with ADI, this is the best general
smoother (we know) for this matrix structure … Test problem: Generalised Poisson with
anisotropic diffusion Total efficiency: Time per unknown per digit (µs) Mixed precision
iterative refinement multigrid solver …