There exist two major problems in application of the conventional block BiCGSTAB method to the O(a)-improved Wilson-Dirac equation with multiple right-hand-sides: One is the deviation between the true and the recursive residuals. The other is the con
vergence failure observed at smaller quark masses for enlarged number of the right-hand-sides. The block BiCGGR algorithm which was recently proposed by the authors succeeds in solving the former problem. In this article we show that a preconditioning technique allows us to improve the convergence behavior for increasing number of the right-hand-sides.
The proton mass calculation is still a tough challenge for lattice QCD. We discuss the current status and difficulties based on the recent PACS-CS results for the hadron spectrum in 2+1 flavor QCD.
It is well known that the block Krylov subspace solvers work efficiently for some cases of the solution of differential equations with multiple right-hand sides. In lattice QCD calculation of physical quantities on a given configuration demands us to
solve the Dirac equation with multiple sources. We show that a new block Krylov subspace algorithm recently proposed by the authors reduces the computational cost significantly without loosing numerical accuracy for the solution of the O(a)-improved Wilson-Dirac equation.
We report on the PACS-CS project focusing on a direct simulation of 2+1 flavor QCD on the physical point and chiral analysis of meson and baryon masses off the physical point with both the SU(2) and SU(3) chiral perturbation theories. Configurations
are generated with the O(a)-improved Wilson quark action and the Iwasaki gauge action. The up-down quark is simulated by employing the DDHMC algorithm with several improvements and the UV-filtered PHMC algorithm is implemented for the strange quark. We investigate the convergence behaviors of the SU(2) and SU(3) chiral expansions up to NLO for the pseudoscalar meson sector, where the up-down quark mass ranges from 3 MeV to 24 MeV and the strange quark mass is chosen around the physical value. The fit results for the low energy constants are compared with those recently obtained by other groups. We also discuss the importance of the direct simulation at the physical point by comparing the physical quantities measured on the physical point with those estimated by the extrapolation method.
We present preliminary results of the PACS-CS project which simulates 2+1 flavor lattice QCD toward the physical point with the nonperturbatively O(a)-improved Wilson quark action and the Iwasaki gauge action. Calculations are carried out at beta=1.9
on a 32^3x64 lattice with the use of the domain-decomposed HMC algorithm to reduce the up-down quark mass. The resulting pseudoscalar meson masses range from 730 MeV down to 210 MeV. We discuss the physical results including the chiral analysis in the pseudoscalar meson sector and the hadron spectrum. Some algorithmic issues are also discussed.
