Speaker
Description
We report on the current status of the renormalization-group preconditioned conjugate gradient (RGPCG) for domain wall fermions (DWF), an algorithm that leverages the correspondence between low modes of the Dirac operator on ensembles related by RG-blocking to produce a preconditioner with small setup overhead. We have studied this approach for Möbius DWFs on a fine $a^{-1} = 2$ GeV lattice, with a preconditioner that uses low modes of an RG-blocked coarse $a^{-1} = 1$ GeV lattice, which are much cheaper to compute. While preconditioning with an approximate coarse-lattice solution effectively deflates the low mode space, the prolongation introduces unwanted noise in the higher modes, limiting the preconditioner's utility. Motivated by the equivalence of physical observables on the RG-related fine and coarse lattices, and the exponential localization of chiral low modes of the DWF operator on the boundaries of the fifth dimension, we find that restricting the preconditioner to these physical chiral components reduces noise contamination from higher modes while also lowering the deflation cost by a factor of $L_s$. Our preliminary results indicate that the improvement in convergence rate exceeds the preconditioner cost, making this a candidate for use in ensemble generation.