Application of preconditioned block BiCGGR to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD

Understand

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 convergence 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.