Domain Decomposition for the Wilson Dirac Operator
Friday, December 3, 2010 - 9:45am - 10:30am
In lattice QCD, a standard discretization of the Dirac operator is given by the Wilson-Dirac operator, representing a nearest neighbor coupling on a 4d torus with 3x4 variables per grid point. The operator is non-symmetric but (usually) positive definite. Its small eigenmodes are non-smooth due to the stochastic nature of the coupling coefficients. Solving systems with the Wilson-Dirac operator on state-of-the-art lattices, typically in the range of 32-64 grid points in each of the four dimensions, is one of the prominent supercomputer applications today.
In this talk we will describe our experience with the domain decomposition principle as one approach to solve the Wilson-Dirac equation in parallel. We will report results on scaling with respect to the size of the overlap, on deflation techniques that turned out to be very useful for implementations on QPACE, the no 1 top green 500 special purpose computer developed tiogethe with IBM by the SFB-TR 55 in Regensburg and Wuppertal, and on first results on adaptive approaches for obtaining an appropriate coarse system.