Claudio Rebbi

Solving Lattice QCD systems of equations using mixed precision solvers on GPUs

Abstract Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodynamics (lattice QCD), where the main computational challenge is to efficiently solve the discretized Dirac equation in the presence of an SU ( 3 ) gauge field. Using NVIDIAs CUDA platform we have implemented a Wilson–Dirac sparse matrix–vector product that performs at up to 40, 135 and 212 Gflops for double, single and half precision respectively on NVIDIAs GeForce GTX 280 GPU. We have developed a new mixed precision approach for Krylov solvers using reliable updates which allows for full double precision accuracy while using only single or half precision arithmetic for the bulk of the computation. The resulting BiCGstab and CG solvers run in excess of 100 Gflops and, in terms of iterations until convergence, perform better than the usual defect-correction approach for mixed precision.

K{sup 0}-K{sup 0} mixing beyond the standard model and CP-violating electroweak penguins in quenched QCD with exact chiral symmetry

We present results for the

Dynamical interactions of cosmic strings and flux vortices in superconductors

\ensuremath{\Delta}S=2

Adaptive multigrid algorithm for lattice QCD.

matrix elements which are required to study neutral kaon mixing in the standard model (SM) and beyond . We also provide leading chiral order results for the matrix elements of the electroweak penguin operators which give the dominant

Strongly interacting dynamics and the search for new physics at the LHC

\ensuremath{\Delta}I=3/2

Parity Doubling and the S Parameter below the Conformal Window

contribution to direct

Dynamical quark effects on the hadronic spectrum and qq-potential in lattice QCD

CP

Lattice simulations with eight flavors of domain wall fermions in SU(3) gauge theory

violation in

Chiral-invariant regularization of fermions on the lattice

K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}

Suppression of baryon number violation in electroweak collisions: numerical results

decays. Our calculations were performed with Neuberger fermions on two sets of quenched Wilson gauge configurations at inverse lattice spacings of approximately 2.2 GeV and 1.5 GeV. All renormalizations were implemented nonperturbatively in the regularization-independent/momentum (RI/MOM) scheme, where we accounted for subleading operator product expansion corrections and discretization errors. We find ratios of non-SM to SM matrix elements which are roughly twice as large as in the only other dedicated lattice study of these amplitudes. On the other hand, our results for the electroweak penguin matrix elements are in good agreement with two recent domain-wall fermion calculations. As a by-product of our study, we determine the strange quark mass. Our main results are summarized and discussed in Sec. VII. Within our statistics, we find no evidence for scaling violations.