A first look at Structured-Multiscale Algebraic Multigrid for Lattice Field Theory

Abstract

State-of-the-art solvers for the Dirac equation in Lattice QCD are based on adaptive multigrid methods. These require fine-tuning of many algorithmic parameters to achieve optimal performance. We apply a new multigrid approach to Lattice Field Theory adapted from oil-reservoir simulations: Structured-Multiscale Algebraic Multigrid (SM-AMG). This method builds compact aggregates with overlapping borders to coarsen the grid and yields accurate interpolation. A key advantage is that aggregate size is the primary tunable parameter. For our results, we used SM-AMG in an algebraic approach, called Aggregative-Multiscale AMG (AM-AMG). We benchmark the efficiency of AM-AMG against that of DD$\alpha$AMG, a successful adaptive multigrid solver which alleviates critical slowing down. The two solvers are compared within the framework of the two-flavor Schwinger model using the Wilson discretization. On fine lattices, the operation count of both methods is similar near the critical point and for large volumes, reflecting a comparable computational cost. However, the number of fine-grid iterations is larger for AM-AMG. On coarse lattices, AM-AMG encounters difficulties to remove the low modes close to the critical mass.