TY  - JOUR
AU  - Cundy, N.
AU  - Eshof v. d., J.
AU  - Frommer, A.
AU  - Krieg, S.
AU  - Lippert, T.
AU  - Schäfer, K.
TI  - Numerical Methods for the QCD Overlap Operator. III. Nested Iterations
JO  - Computer physics communications
VL  - 165
SN  - 0010-4655
CY  - Amsterdam
PB  - North Holland Publ. Co.
M1  - PreJuSER-50021
SP  - 221 - 242
PY  - 2005
N1  - Record converted from VDB: 12.11.2012
AB  - The numerical and computational aspects of chiral fermions in lattice quantum chromodynamics are extremely demanding. In the overlap framework, the computation of the fermion propagator leads to a nested iteration where the matrix vector multiplications in each step of an outer iteration have to be accomplished by an inner iteration; the latter approximates the product of the sign function of the hermitian Wilson fermion matrix with a vector.In this paper we investigate aspects of this nested paradigm. We examine several Krylov subspace methods to be used as an outer iteration for both propagator computations and the Hybrid Monte-Carlo scheme. We establish criteria on the accuracy of the inner iteration which allow to preserve an a priori given precision for the overall computation. It will turn out that the accuracy of the sign function can be relaxed as the outer iteration proceeds. Furthermore, we consider preconditioning strategies, where the preconditioner is built upon an inaccurate approximation to the sign function. Relaxation combined with preconditioning allows for considerable savings in computational efforts up to a factor of 4 as our numerical experiments illustrate. We also discuss the possibility of projecting the squared overlap operator into one chiral sector. (C) 2004 Elsevier B.V. All rights reserved.
KW  - J (WoSType)
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000226893500003
DO  - DOI:10.1016/j.cpc.2004.10.005
UR  - https://juser.fz-juelich.de/record/50021
ER  -