Accelerating multigrid with streaming chiral SVD for Wilson fermions in lattice QCD

• A new setup method using a singular value decomposition for the multigrid preconditioner of Wilson type fermions in lattice QCD is presented • The use of the singular value decomposition decreases the overall solve time of the preconditioned system of linear equations arising from Wilson clover discretization • To address the cost of storage, we implement a streaming singular value decomposition of the multigrid basis • The number of fine grid iterations is demonstrated to decrease by a factor of 1.7 for m q ≈ m crit . A modification to the setup algorithm for the multigrid preconditioner of Wilson fermions in lattice QCD is presented. A larger basis of test vectors than that used in regular multigrid is calculated by the smoother and truncated by singular value decomposition on the chiral components of the test vectors. The truncated basis is used to form the prolongation and restriction matrices of the multigrid hierarchy. This modification of the setup method is demonstrated to increase the convergence of linear solvers on an anisotropic lattice with m π ≈ 239 MeV from the Hadron Spectrum Collaboration and an isotropic lattice with m π ≈ 220 MeV from the MILC Collaboration. The lattice volume dependence of the method is also examined. Increasing the number of test vectors improves speedup up to a point, but storing these vectors becomes impossible in limited memory resources such as GPUs. To address storage cost, we implement a streaming singular value decomposition of the basis of test vectors on the chiral components and demonstrate a decrease in the number of fine level iterations by a factor of 1.7 for m q ≈ m crit .