Mixed action simulations: approaching physical quark masses

Transcription

1 Mixed action simulations: approaching physical quark masses Stefan Krieg NIC Forschungszentrum Jülich, Wuppertal University in collaboration with S. Durr, Z. Fodor, C. Hoelbling, S. Katz, T. Kurth, L. Lellouch, Th. Lippert, K.K. Szabo 18 June 2007

2 Outline Physics aims Algorithm Simulation parameters Performance Matrix Inverters Strong scaling BlueGene Updated Berlin Wall plot Results Talk by Laurent Lellouch Setting the scale Conclusions 2

3 Physics aims 0 0 K K Eliminate uncertainties in the mixing, ΔS=2 matrix elements Calculate F K /F π, which enables a precision extraction of the important ratio of CKM matrix elements V us /V ud Low energy constants (LEC) of chiral perturbation theory (ChPT) Other phenomenological applications 3

4 Algorithm Action Clover improved Wilson fermions Symanzik improved gauge action Stout links Rational HMC for strange quark Mass preconditioning ( Hasenbusch trick ) Multiscale integration scheme (Sexton-Weingarten) Omelyan integrator, increasing the precision of the numerical integration non equidistant leap-frog Inverters Mixed precision CG (config generation) relgmresr(sumr) with single precision SUMR 4

5 Algorithm stability mπ = 200 MeV, β=3.57, a=0.084fm, 64x48³ 5

6 Algorithm stability O(a) improved Wilson + improved gauge action No metastability: cold/hot-start plaquettes agree after ca. 50 trajectories 6

7 Simulation parameters: Ensembles β a[fm] m π [MeV] L3 T inv ³64 24³64 24³64 24³64 24³64 24³64 32³64 48³64 32³96 32³96 40³96 DONE DONE DONE DONE DONE DONE DONE RUNNING DONE RUNNING DONE 7

8 Simulation parameters: strange quark mass We use a nf=3 simulation to set the strange quark mass For each beta, search for the κ where 2 2 mps / mv = 2mK mπ / m Φ We determined the β dependency in the range (β = ) 8

9 Performance: Matrix Inverter/Solver The Simulation performance is dominated by a matrix inverter/solver The solver performance is dominated by the kernel performance Single precision kernel is faster than double precision (double the network and memory bandwidth, depending on the architecture more flop/s peak as well), and has a smaller cache footprint Use adaptive precision techniques to utilize this advantage Our own method allows this: relgmresr(sumr) with single precision SUMR; but CG works as well Minimal losses: Total number of matrix multiplication increases by <10%, single precision kernel can gain more than 100% Of course: Result (solution vector) is double precision precise. 9

10 Performance: strong scaling 10

11 Performance: strong scaling 11

12 Matrix Inverter/Solver: Mixed prec. CG How could a cheap but less precise A -1 = a -1 help solving Ax=b? 1. Compute b Ax 0 = r 2. Compute a -1 r = A -1 r + r s, with r s =ε r 3. Update x: x 1 = x 0 + a -1 r b Ax 1 = b Ax 0 A a -1 r = r AA -1 r r s = ε r This can be implemented in a CG Precision of a -1 can be tuned 12

13 Matrix Inverter/Solver: Mixed prec. GMRESR Use a single precision solver in the preconditioner Add other improvements like relaxation AND eigenmode preconditioning 13

14 Matrix Inverter/Solver 14

15 A new Berlin Wall plot 1 TFlops years TFlops years m PS / m V m PS / m V Plots taken from K. Jansen et al. hep-lat/ ( ), this work ( ), staggered ( ) 15

16 Wilson pseudoscalar meson plateaus mπ = 200 MeV, β=3.57, a=0.084fm, 64x48³ η K π 16

17 Wilson vector meson plateaus πφ K* ρ mπ = 200 MeV, β=3.57, a=0.084fm, 64x48³ 17

18 Overlap pseudoscalar plateaus (preliminary) mπ = 200 MeV, β=3.57, a=0.084fm, 64x48³ η K π 18

19 Overlap rho plateau mπ = 300 MeV, β=3.57, 64x32³, a=0.084fm 19

20 Overlap PCAC mass mπ = 300 MeV, β=3.57, a=0.084fm, 64x32³ 20

21 Overlap B K plateau mπ = 200 MeV, β=3.57, a=0.084fm, 64x48³ 21

22 Setting the scale 22

23 Conclusions Mixed action simulations with overlap on a Wilson clover sea are feasible and can go down to small m π The right action extends the range of m π reachable with clover fermions Mixed precision inverters greatly speed up sea and valence calculations We see no instability at all, thermal cycle of the most pathological ensemble shows no sign of hysteresis Plateaus are smooth and steady where they should be Physics can be reliably extracted using ChPT see Talk by Laurent Lellouch 23