Modified block BiCGSTAB for lattice QCD

We present results for application of block BiCGSTAB algorithm modified by the QR decomposition and the SAP preconditioner to the Wilson–Dirac equation with multiple right-hand sides in lattice QCD on 323×64323×64 and 644 lattices at almost physical quark masses. The QR decomposition improves convergence behaviors in the block BiCGSTAB algorithm suppressing deviation between true residual and recursive one. The SAP preconditioner applied to the domain-decomposed lattice helps us minimize communication overhead. We find remarkable cost reduction thanks to cache tuning and reduction of number of iterations.

► We modify block BiCGSTAB by QR decomposition and SAP preconditioner.
► We apply to the Wilson–Dirac equation with multiple right-hand sides in lattice QCD.
► QR improves convergence and suppresses deviation between true and recursive residuals.
► SAP minimizes communication overhead.
► We find remarkable cost reduction at almost physical quark masses on big lattices.