Abstract

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A solver for multiple right hand sides.

Presenter: Kostas Orginos — College of William and Mary / JLab

Andreas Stathopoulos, Kostas Orginos

In present Lattice QCD calculations, where a large number of observables are computed on the same gauge field configurations, the problem of solving the Dirac equation with a large number of right hand sides arises. The number of right hand sides can be as high as a few hundreds. For this reason new possibilities for optimizations in solving the Dirac equation exist. In this talk I present a new algorithm that builds Krylov space information during the conjugate gradient solution of the linear system for the first few right hand sides. This information is used to speed up the solution of the subsequent right hand sides. The algorithm has been tested on the two flavor dynamical anisotropic Wilson fermion lattices generated by the Jlab group. In the limit of large number of right hand sides, asymptotic factors of six to eight speed up are observed. Furthermore, the algorithm in the limit of large number of right hand sides show very small, almost negligible, increase in cost with decreasing quark mass.