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Wednesday, 18 November 2009 Wilson Matrix of QCD Σμ ((1-γ μ )Ux,y μ δx+μ,y + (1+γ μ )Uy,x μ† δx-μ,y) + (4+m)δx,y
Wednesday, 18 November 2009 Wilson Matrix of QCD Σμ ((1-γ μ )Ux,y μ δx+μ,y + (1+γ μ )Uy,x μ† δx-μ,y) + (4+m)δx,y • U is discretized gauge field (SU(3)) • γ are Dirac matrices (4x4) • 8 off-diagonals in spacetime, mass on diagonal • Off-diagonals are 12x12 matrices (SU(3) x γ) • Each point in spacetime referred to as a spinor • Matrix not Hermitian but γ5-Hermitian • Block “Laplace” in 4 dimensions
Page 1 and 2: Wednesday, 18 November 2009 GPU Mix
Page 3 and 4: Quantum ChromoDynamics • QCD is t
Page 5 and 6: Wednesday, 18 November 2009 topolog
Page 7 and 8: Wednesday, 18 November 2009
Page 9 and 10: Wednesday, 18 November 2009 Lattice
Page 11 and 12: GPU Hardware GTX 280 Flops: single
Page 13 and 14: Iterative Linear Solvers • Many p
Page 15 and 16: Wednesday, 18 November 2009 Dirac o
Page 17: Wednesday, 18 November 2009 Wilson
Page 21 and 22: Wednesday, 18 November 2009 Wilson
Page 23 and 24: !"#$%&' $" $! #" #! " ! Wednesday,
Page 25 and 26: Wednesday, 18 November 2009 SpMV II
Page 27 and 28: ions SpMV IV CD software to use the
Page 29 and 30: Gflops 140 120 100 Wednesday, 18 No
Page 31 and 32: Wednesday, 18 November 2009 Krylov
Page 33 and 34: Mixed-Precision Solvers • Require
Page 35 and 36: Number of iterations 3000 2500 2000
Page 37 and 38: Wednesday, 18 November 2009 Half Pr
Page 39 and 40: Time to solution / s 300 250 200 15
Page 41 and 42: Wednesday, 18 November 2009 Perform
Page 43 and 44: Wednesday, 18 November 2009 Perform
Page 45 and 46: Wednesday, 18 November 2009 • Nee
Page 47 and 48: Matrix-vector products 20000 15000
Page 49 and 50: Wednesday, 18 November 2009 Conclus

Michael Clark Harvard University

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