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Register a new userComparison of the mass preconditioned HMC and the DD-HMC algorithm for two-flavour QCD
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Mass preconditioned HMC and DD-HMC are among the most popular algorithms to simulate Wilson fermions. We present a comparison of the performance of the two algorithms for realistic quark masses and lattice sizes. In particular, we use the locally deflated solver of the DD-HMC environment also for the mass preconditioned simulations.
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The analysis developed by Luscher and Schaefer of the Hybrid Monte Carlo (HMC) algorithm is extended to include Fourier acceleration. We show for the $phi^4$ theory that Fourier acceleration substantially changes the structure of the theory for both the Langevin and HMC algorithms. When expanded in perturbation theory, each five-dimensional auto-correlation function of the fields $phi(x_i, t_i)$, $1le i le N $, corresponding to a specific 4-dimensional Feynman graph separates into two factors: one depending on the Monte-Carlo evolution times $t_i$ and the second depending on the space-time positions $x_i$. This separation implies that only auto-correlation times at the lattice scale appear, eliminating critical slowing down in perturbation theory.
Polynomial approximations to the inverse of the fermion matrix are used to filter the dynamics of the upper energy scales in HMC simulations. The use of a multiple time-scale integration scheme allows the filtered pseudofermions to be evolved using a coarse step size. We introduce a novel generalisation of the nested leapfrog which allows for far greater flexibility in the choice of time scales. We observe a reduction in the computational expense of the molecular dynamics integration of between 3--5 which improves as the quark mass decreases.
We report on a study of 2+1 flavor lattice QCD with the $O(a)$-improved Wilson quarks on a $16^3times 32$ lattice at the lattice spacing $1/aapprox 2$GeV employing Lueschers domain-decomposed HMC(LDDHMC) algorithm. This is dedicated to a preliminary study for the PACS-CS project which plans to complete the Wilson-clover $N_f=2+1$ program lowering the up-down quark masses close to the physical values as much as possible. We focus on three issues: (i) how light quark masses we can reach with LDDHMC, (ii) efficiency of the algorithm compared with the conventional HMC, (iii) parameter choice for the production runs on PACS-CS.
We present results of a hybrid Monte-Carlo algorithm for dynamical, $n_f=2$, four-dimensional QCD with overlap fermions. The fermionic force requires careful treatment, when changing topological sectors. The pion mass dependence of the topological susceptibility is studied on $6^4$ and $12cdot 6^3$ lattices. The results are transformed into physical units.
We show how to improve the molecular dynamics step of Hybrid Monte Carlo, both by tuning the integrator using Poisson brackets measurements and by the use of force gradient integrators. We present results for moderate lattice sizes.
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