Multigrid approach in shifted linear systems for the non-degenerated twisted mass operator

Abstract

Application of multigrid solvers in shifted linear systems is studied. We focus on accelerating the rational approximation needed for simulating single flavor operators. This is particularly useful, in the case of twisted mass fermions for mass non-degenerate quarks and can be employed to accelerate the N f = 1 + 1 sector of N f = 2 + 1 + 1 twisted mass fermion simulations. The multigrid solver is accelerated by employing suitable initial guesses. We propose a novel strategy for proposing initial guesses for shifted linear systems based on the Lagrangian interpolation of the previous solutions. arXiv:1805.09584v1 [hep-lat]

Complete flavor decomposition of the spin and momentum fraction of the proton using lattice QCD simulations at physical pion mass

“…The average momentum fraction hxi is extracted directly from the nucleon matrix element at zero momentum transfer from Eqs. (24) and (25). In the case of the connected contribution, since we only have access to three-point functions with ⃗p 0 ¼ ⃗ 0, we are restricted to using Eq.…”

“…A subset of simulations also includes a dynamical charm quark with mass fixed to approximately its physical value. This progress was made possible using efficient algorithms and in particular multigrid solvers [23] that were developed for twisted mass fermions [24].…”

“…In summary, we perform in total 12,690,000 inversions for the connected and 16,272,000 for the disconnected contributions by employing the DD-αAMG solver and its QUDA version [24,68,69] to accelerate the inversions. Using GPUs and the DD-αAMG solver are essential to obtain the required statistics.…”

“…The grey band is the predicted time dependence of the ratio using the parameters extracted from the two-state fit when t low contribution one can use a boosted nucleon without the need of additional inversions, one can extract it both from the diagonal part of the EMT as in Eq. (24) and from the nondiagonal as in Eq. (25).…”

Recent progress on the study of nucleon structure from lattice QCD and future perspectives

“…Left: Time to solution for the computation of D −1 using the conjugate gradient (red points) and the 3-level Adaptive Aggregation-based Domain Decomposition Multigrid (DD-αAMG) for twisted mass fermion[4,5]. Right: A summary of zero-temperature simulations by various collaborations that include Clover, Twisted Mass, Staggered and Domain Wall fermions.…”