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Register a new user(Approximate) Low-Mode Averaging with a new Multigrid Eigensolver
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We present a multigrid based eigensolver for computing low-modes of the Hermitian Wilson Dirac operator. For the non-Hermitian case multigrid methods have already replaced conventional Krylov subspace solvers in many lattice QCD computations. Since the $gamma_5$-preserving aggregation based interpolation used in our multigrid method is valid for both, the Hermitian and the non-Hermitian case,
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We study the performance of all-mode-averaging (AMA) when used in conjunction with a locally deflated SAP-preconditioned solver, determining how to optimize the local block sizes and number of deflation fields in order to minimize the computational cost for a given level of overall statistical accuracy. We find that AMA enables a reduction of the statistical error on nucleon charges by a factor of around two at the same cost when compared to the standard method. As a demonstration, we compute the axial, scalar and tensor charges of the nucleon in $N_f=2$ lattice QCD with non-perturbatively O(a)-improved Wilson quarks, using O(10,000) measurements to pursue the signal out to source-sink separations of $t_ssim 1.5$ fm. Our results suggest that the axial charge is suffering from a significant amount (5-10%) of excited-state contamination at source-sink separations of up to $t_ssim 1.2$ fm, whereas the excited-state contamination in the scalar and tensor charges seems to be small.
We introduce a stochastic sandwich method with low-mode substitution to evaluate the connected three-point functions. The isovector matrix elements of the nucleon for the axial-vector coupling $g_A^3$, scalar couplings $g_S^3$ and the quark momentum fraction $langle xrangle_{u -d}$ are calculated with overlap fermion on 2+1 flavor domain-wall configurations on a $24^3 times 64$ lattice at $m_{pi} = 330$ MeV with lattice spacing $a = 0.114$ fm.
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
We study the isoscalar and isovector $J=0,1$ mesons with the overlap operator within two flavour lattice QCD. After subtraction of the lowest-lying Dirac eigenmodes from the valence quark propagator all disconnected contributions vanish and all possible point-to-point $J=0$ correlators become identical, signaling a simultaneous restoration of both $SU(2)_L times SU(2)_R$ and $U(1)_A$ symmetries. The ground states of the $pi,sigma,a_0,eta$ mesons do not survive this truncation. All possible $J=1$ states have a very clean exponential decay and become degenerate, demonstrating a $SU(4)$ symmetry of a dynamical QCD-like string.
For embedded boundary electromagnetics using the Dey-Mittra algorithm, a special grad-div matrix constructed in this work allows use of multigrid methods for efficient inversion of Maxwells curl-curl matrix. Efficient curl-curl
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