Speaker
Description
Aggregation-based, adaptive algebraic multigrid has established itself as the most efficient linear solver for QCD lattice discretizations such as the (clover improved) Wilson discretization or the twisted mass discretizationn. As we are now able to simulate at the physical point, the resulting systems are severely ill-conditioned, and the multigrid approach shifts this ill-conditioning to the coarsest level in the multigrid hierarchy. This is why now often the by far largest amount of time is spent in the coarse level solves, where standard multigrid implementations for lattice QCD rely just on (restarted) GMRES as a solver.
In this talk we present three ways of accelerating the coarsest level solves, namely (1) polynomial preconditioning, (2) deflation and (3) using an (incomplete) LU-factorization. We will explain the heuristics underlying all three improvements and present numerical results on large lattices. It turns out that the twisted mass calculations profit the most of these improvements and that a technique called agglomeration is particularly beneficial in case (3). Agglomeration means that we reduce the number of cores used on the coarsest level to reduce communication.
