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

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Avoid flux-update kernel Initially, performed update as: calcFlux(u, flux, X COORD) flux = f x (u) addFlux(u, flux) u = u + f x (u) calcFlux(u, flux, Y COORD) flux = f y (u) addFlux(u, flux) u = u + f y (u) Instead, we can calculate updated solution directly in extra array: advanceSoln(u, u plus, X COORD) u + = u + f x (u) advanceSoln(u plus, u, Y COORD) u = u + + f y (u + ) Time now: 7.13s (126.6×) <strong>Finite</strong> <strong>Volume</strong> Methods Laboratory for Scientific Computing 15 / 22
What block-size should we use? (x-direction) When performing flux-calculation, want to reduce no. of overlap cells relative to block size Block size Overall time 16 × 8 7.13s 32 × 4 6.93s 64 × 2 6.95s 32 × 8 7.02s 64 × 4 6.98 First 4 lines can have 4 thread blocks per multiprocessor (register limitation) Last two lines are limited to 3 thread blocks per multiprocessor. <strong>Finite</strong> <strong>Volume</strong> Methods Laboratory for Scientific Computing 16 / 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 and 10: Euler’s equations Flux-conservati
Page 11 and 12: Data layout in memory We use Struct
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: Templating over coordinate directio
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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