Implementing Finite Volume algorithms on GPUs - many-core.group ...

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Demonstration problem Solve Euler’s equations in 2D, using finite-volume approach, with slope-limited reconstruction and exact Riemann solver (MUSCL-Hancock) Use single precision only No boundary condition enforcing - just keep outer two cells of grid fixed Time-step calculation - basic reduction to find maximum wave-speed across all cells Using single Tesla C2050 (Fermi) card provided by NVIDIA <strong>Finite</strong> <strong>Volume</strong> Methods Laboratory for Scientific Computing 6 / 22
Data layout in memory We use Struct-of-Arrays approach and store: ρ 1,1 , ρ 2,1 , ρ 3,1 , . . . , ρ N,N , v x 1,1 , vx 2,1 , . . . , vy N,N , . . . so that accessing u i,j = (ρ i,j , v x i,j , vy i,j , p i,j) from each thread (i, j) results in coalesced access from global memory <strong>Finite</strong> <strong>Volume</strong> Methods Laboratory for Scientific Computing 7 / 22
Page 1 and 2: Implementing <stro
Page 3 and 4: Applications of Finite</str
Page 5 and 6: Applications of Finite</str
Page 7 and 8: Shock-bubble simulation shockBubble
Page 9: Euler’s equations Flux-conservati
Page 13 and 14: MUSCL-Hancock scheme Piecewise-cons
Page 15 and 16: MUSCL-Hancock scheme Piecewise-cons
Page 17 and 18: Loading global data into shared mem
Page 19 and 20: Loading global data into shared mem
Page 21 and 22: Within shared memory Thread i − 1
Page 31 and 32: Thread-block layout Each cell depen
Page 33 and 34: Thread-block layout Each cell depen
Page 35 and 36: How fast? We should now check how f
Page 37 and 38: How fast? We should now check how f
Page 39 and 40: Templating over coordinate directio
Page 41 and 42: What block-size should we use? (x-d
Page 43 and 44: Performance on different sized grid
Page 45 and 46: Summary Achieved 147x speed-up for
Page 47: Future investigations Efficient ext

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