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

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Within shared memory Thread i − 1 Thread i Thread i + 1 Initial u i−2 , u i−1 , u i u i−1 , u i , u i+1 u i , u i+1 , u i+2 Reconstruct u L i−1 , u i−1, u R i−1 u L i , u i, u R i u L i+1 , u i+1, u R i+1 Slope limit u L∗ i−1 , u i−1, u R∗ i−1 u L∗ i , u i , u R∗ i u L∗ i+1 , u i+1, u R∗ i+1 Advance 1 2 ∆t uL i−1 , u i−1, u R i−1 u L i , u i, u R i u L i+1 , u i+1, u R i+1 syncthreads() Solve R.P. f(u R i−2 , uL i−1 ) f(uR i−1 , uL i ) f(uR i , uL i+1 ) syncthreads() Final Flux ∆t × (f i−2 − f i−1 ) ∆t × (f i−1 − f i ) ∆t × (f i − f i+1 ) <strong>Finite</strong> <strong>Volume</strong> Methods Laboratory for Scientific Computing 10 / 22
Within shared memory Thread i − 1 Thread i Thread i + 1 Initial u i−2 , u i−1 , u i u i−1 , u i , u i+1 u i , u i+1 , u i+2 Reconstruct u L i−1 , u i−1, u R i−1 u L i , u i, u R i u L i+1 , u i+1, u R i+1 Slope limit u L∗ i−1 , u i−1, u R∗ i−1 u L∗ i , u i , u R∗ i u L∗ i+1 , u i+1, u R∗ i+1 Advance 1 2 ∆t uL i−1 , u i−1, u R i−1 u L i , u i, u R i u L i+1 , u i+1, u R i+1 syncthreads() Solve R.P. f(u R i−2 , uL i−1 ) f(uR i−1 , uL i ) f(uR i , uL i+1 ) syncthreads() Final Flux ∆t × (f i−2 − f i−1 ) ∆t × (f i−1 − f i ) ∆t × (f i − f i+1 ) Functions such as fluxInPlace(u) mean that we only need 4 solution vectors per thread. Overall shared-memory: 4 * NUM VARS * blockDim.y * blockDim.x <strong>Finite</strong> <strong>Volume</strong> Methods Laboratory for Scientific Computing 10 / 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 27: 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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