A Parallel SSOR Preconditioner for Lattice QCD
Abstract
We present a parallelizable SSOR preconditioning scheme for Krylov subspace iterative solvers which proves to be efficient in lattice QCD applications involving Wilson fermions. Our preconditioner is based on a locally lexicographic ordering of the lattice points. In actual hybrid Monte Carlo applications with the bi-conjugate gradient stabilized method BiCGstab, we achieve a gain factor of about 2 in the number of iterations compared to conventional odd-even preconditioning. Whether this translates into similar reductions in run time will depend on the parallel computer in use. We discuss implementation issues using the `Eisenstat-trick' and machine specific advantages of the method for the APE100/Quadrics parallel computer. In a full QCD simulation with Wilson fermions on a 512-processor Quadrics QH4 we find a gain in cpu-time of a factor of 1.7 over odd-even preconditioning for a 24^3 x 40 lattice.
Keywords
Cite
@article{arxiv.hep-lat/9602019,
title = {A Parallel SSOR Preconditioner for Lattice QCD},
author = {S. Fischer and A. Frommer and U. Glaessner and Th. Lippert and G. Ritzenhoefer and K. Schilling},
journal= {arXiv preprint arXiv:hep-lat/9602019},
year = {2009}
}
Comments
21 pages, Tex-file + Postscript figures