Bench report : OptV1vsOptv2_cs (2012-12-18-15-35)

Bench report : OptV1vsOptv2_cs (2012-12-18-15-35)

Thursday 31 ^st January, 2013

Contents

1 benchs : MassAssembling ( P 1 -Lagrange) 2

1.1 mesh : disque4-1 . . . . 2 1.2 mesh : carre4-1 . . . . 3

2 benchs : MassWAssembling ( P 1 -Lagrange) 5

2.1 mesh : disque4-1 . . . . 5 2.2 mesh : carre4-1 . . . . 6

3 benchs : StiAssembling ( P 1 -Lagrange) 8

3.1 mesh : disque4-1 . . . . 8

3.2 mesh : carre4-1 . . . . 9

1 benchs : MassAssembling ( P ₁ -Lagrange)

1.1 mesh : disque4-1

n q P1OptV1 P1OptV1cs P1OptV2 P1OptV2cs

3576 0.070 (s)

x 1.00 0.064 (s)

x 1.09 0.009 (s)

x 8.08 0.002 (s) x 30.27 14222 0.287 (s)

x 1.00 0.256 (s)

x 1.12 0.041 (s)

x 7.08 0.013 (s) x 22.36 31575 0.645 (s)

x 1.00 0.578 (s)

x 1.12 0.093 (s)

x 6.92 0.030 (s) x 21.68 55919 1.150 (s)

x 1.00 1.035 (s)

x 1.11 0.176 (s)

x 6.55 0.062 (s) x 18.70 86488 1.780 (s)

x 1.00 1.603 (s)

x 1.11 0.283 (s)

x 6.29 0.106 (s) x 16.78 125010 2.588 (s)

x 1.00 2.329 (s)

x 1.11 0.426 (s)

x 6.07 0.159 (s) x 16.29 170355 3.518 (s)

x 1.00 3.164 (s)

x 1.11 0.579 (s)

x 6.08 0.216 (s) x 16.29 225547 4.601 (s)

x 1.00 4.175 (s)

x 1.10 0.765 (s)

x 6.02 0.285 (s) x 16.16 281769 5.648 (s)

x 1.00 5.015 (s)

x 1.13 0.964 (s)

x 5.86 0.377 (s) x 15.00 343082 7.175 (s)

x 1.00 6.390 (s)

x 1.12 1.200 (s)

x 5.98 0.461 (s) x 15.57 424178 8.802 (s)

x 1.00 7.868 (s)

x 1.12 1.562 (s)

x 5.64 0.597 (s) x 14.74 506706 10.531 (s)

x 1.00 9.381 (s)

x 1.12 1.875 (s)

x 5.62 0.730 (s) x 14.43 689716 13.971 (s)

x 1.00 12.419 (s)

x 1.12 2.604 (s)

x 5.37 1.001 (s) x 13.96 885521 18.673 (s)

x 1.00 15.983 (s)

x 1.17 3.321 (s)

x 5.62 1.318 (s) x 14.17 1127090 23.550 (s)

x 1.00 20.895 (s)

x 1.13 4.274 (s)

x 5.51 1.733 (s) x 13.59 1401129 28.766 (s)

x 1.00 26.023 (s)

x 1.11 5.448 (s)

x 5.28 2.142 (s) x 13.43 1671052 34.040 (s)

x 1.00 30.267 (s)

x 1.12 6.416 (s)

x 5.31 2.568 (s) x 13.26 1978602 40.836 (s)

x 1.00 37.134 (s)

x 1.10 7.872 (s)

x 5.19 3.036 (s) x 13.45

Table 1: Computational cost of the MassAssembling functions versus n q , with Matlab (R2012b) : time in seconds (top value) and speedup (bottom value) on unit disk mesh. The speedup reference is P1OptV1 version.

2

10

10

10

10

10

10

10

10

10

10

10

10

10

10

Sparse Matrix size (n

)

time (s)

P1OptV1 P1OptV1cs P1OptV2 P1OptV2cs O(n

) O(n

)

0 0.5 1 1.5 2

x 10

0

5 10 15 20 25 30 35

Sparse Matrix size (n

)

Speed Up X

P1OptV1cs P1OptV2 P1OptV2cs

Figure 1: Computational cost of the MassAssembling functions versus n _q , with Matlab (R2012b) : time in seconds (left) and speedup (right) on unit disk mesh. The speedup reference is P1OptV1 version.

1.2 mesh : carre4-1

10

10

10

10

10

10

10

10

10

10

10

10

10

Sparse Matrix size (n

)

time (s)

P1OptV1 P1OptV1cs P1OptV2 P1OptV2cs O(n

) O(n

)

0 2 4 6 8 10 12 14 16 18

x 10

0

5 10 15 20 25 30 35

Sparse Matrix size (n

)

Speed Up X

P1OptV1cs P1OptV2 P1OptV2cs

Figure 2: Computational cost of the MassAssembling functions versus n _q , with Matlab (R2012b) : time in

seconds (left) and speedup (right) on unit square mesh. The speedup reference is P1OptV1 version.

n q P1OptV1 P1OptV1cs P1OptV2 P1OptV2cs 3043 0.058 (s)

x 1.00 0.053 (s)

x 1.10 0.007 (s)

x 7.95 0.002 (s) x 30.27 12139 0.236 (s)

x 1.00 0.215 (s)

x 1.10 0.034 (s)

x 6.98 0.011 (s) x 22.20 26910 0.536 (s)

x 1.00 0.484 (s)

x 1.11 0.078 (s)

x 6.85 0.025 (s) x 21.88 47834 0.942 (s)

x 1.00 0.835 (s)

x 1.13 0.148 (s)

x 6.38 0.046 (s) x 20.55 74326 1.460 (s)

x 1.00 1.303 (s)

x 1.12 0.231 (s)

x 6.32 0.078 (s) x 18.64 107625 2.142 (s)

x 1.00 1.899 (s)

x 1.13 0.359 (s)

x 5.96 0.133 (s) x 16.11 145828 2.960 (s)

x 1.00 2.576 (s)

x 1.15 0.480 (s)

x 6.17 0.182 (s) x 16.31 189794 3.761 (s)

x 1.00 3.786 (s)

x 0.99 0.636 (s)

x 5.91 0.244 (s) x 15.44 241024 5.657 (s)

x 1.00 5.534 (s)

x 1.02 0.812 (s)

x 6.96 0.319 (s) x 17.74 297290 7.627 (s)

x 1.00 6.568 (s)

x 1.16 1.008 (s)

x 7.56 0.394 (s) x 19.35 360040 9.251 (s)

x 1.00 6.375 (s)

x 1.45 1.219 (s)

x 7.59 0.472 (s) x 19.59 428549 8.779 (s)

x 1.00 7.701 (s)

x 1.14 1.515 (s)

x 5.80 0.617 (s) x 14.24 581973 11.829 (s)

x 1.00 10.416 (s)

x 1.14 2.125 (s)

x 5.57 0.823 (s) x 14.36 762704 15.875 (s)

x 1.00 13.790 (s)

x 1.15 2.905 (s)

x 5.47 1.153 (s) x 13.77 973281 19.644 (s)

x 1.00 17.487 (s)

x 1.12 3.630 (s)

x 5.41 1.484 (s) x 13.24 1197591 28.657 (s)

x 1.00 25.367 (s)

x 1.13 4.466 (s)

x 6.42 1.801 (s) x 15.91 1443408 33.903 (s)

x 1.00 26.128 (s)

x 1.30 5.485 (s)

x 6.18 2.265 (s) x 14.97 1707938 34.942 (s)

x 1.00 31.396 (s)

x 1.11 6.428 (s)

x 5.44 2.654 (s) x 13.17

Table 2: Computational cost of the MassAssembling functions versus n _q , with Matlab (R2012b) : time in seconds (top value) and speedup (bottom value) on unit square mesh. The speedup reference is P1OptV1 version.

4

2 benchs : MassWAssembling ( P ₁ -Lagrange)

2.1 mesh : disque4-1

n q P1OptV1 P1OptV1cs P1OptV2 P1OptV2cs

3576 0.123 (s)

x 1.00 0.115 (s)

x 1.07 0.010 (s)

x 11.74 0.004 (s) x 29.53 14222 0.496 (s)

x 1.00 0.480 (s)

x 1.03 0.044 (s)

x 11.23 0.020 (s) x 24.46 31575 1.114 (s)

x 1.00 1.063 (s)

x 1.05 0.100 (s)

x 11.16 0.044 (s) x 25.34 55919 2.003 (s)

x 1.00 1.886 (s)

x 1.06 0.188 (s)

x 10.65 0.078 (s) x 25.69 86488 3.081 (s)

x 1.00 2.937 (s)

x 1.05 0.289 (s)

x 10.66 0.124 (s) x 24.87 125010 4.565 (s)

x 1.00 4.242 (s)

x 1.08 0.447 (s)

x 10.21 0.184 (s) x 24.85 170355 6.224 (s)

x 1.00 5.763 (s)

x 1.08 0.606 (s)

x 10.26 0.273 (s) x 22.77 225547 8.077 (s)

x 1.00 7.590 (s)

x 1.06 0.816 (s)

x 9.90 0.302 (s) x 26.70 281769 10.139 (s)

x 1.00 9.473 (s)

x 1.07 1.029 (s)

x 9.86 0.422 (s) x 24.01 343082 12.557 (s)

x 1.00 11.602 (s)

x 1.08 1.250 (s)

x 10.04 0.512 (s) x 24.54 424178 15.421 (s)

x 1.00 14.440 (s)

x 1.07 1.635 (s)

x 9.43 0.681 (s) x 22.66 506706 18.165 (s)

x 1.00 16.981 (s)

x 1.07 1.937 (s)

x 9.38 0.810 (s) x 22.44 689716 24.985 (s)

x 1.00 23.296 (s)

x 1.07 2.712 (s)

x 9.21 1.110 (s) x 22.50 885521 32.893 (s)

x 1.00 30.182 (s)

x 1.09 3.398 (s)

x 9.68 1.449 (s) x 22.70 1127090 40.838 (s)

x 1.00 38.438 (s)

x 1.06 4.449 (s)

x 9.18 1.917 (s) x 21.31 1401129 51.274 (s)

x 1.00 47.759 (s)

x 1.07 5.671 (s)

x 9.04 2.358 (s) x 21.74 1671052 60.272 (s)

x 1.00 56.484 (s)

x 1.07 6.622 (s)

x 9.10 2.806 (s) x 21.48 1978602 72.037 (s)

x 1.00 67.137 (s)

x 1.07 8.150 (s)

x 8.84 3.349 (s) x 21.51

Table 3: Computational cost of the MassWAssembling functions versus n q , with Matlab (R2012b) : time in

seconds (top value) and speedup (bottom value) on unit disk mesh. The speedup reference is P1OptV1 version.

10

10

10

10

10

10

10

10

10

10

10

10

10

10

Sparse Matrix size (n

)

time (s)

P1OptV1 P1OptV1cs P1OptV2 P1OptV2cs O(n

) O(n

)

0 0.5 1 1.5 2

x 10

0

5 10 15 20 25 30

Sparse Matrix size (n

)

Speed Up X

P1OptV1cs P1OptV2 P1OptV2cs

Figure 3: Computational cost of the MassWAssembling functions versus n _q , with Matlab (R2012b) : time in seconds (left) and speedup (right) on unit disk mesh. The speedup reference is P1OptV1 version.

2.2 mesh : carre4-1

10

10

10

10

10

10

10

10

10

10

10

10

10

10

Sparse Matrix size (n

)

time (s)

P1OptV1 P1OptV1cs P1OptV2 P1OptV2cs O(n

) O(n

)

0 2 4 6 8 10 12 14 16 18

x 10

0

5 10 15 20 25 30 35

Sparse Matrix size (n

)

Speed Up X

P1OptV1cs P1OptV2 P1OptV2cs

Figure 4: Computational cost of the MassWAssembling functions versus n _q , with Matlab (R2012b) : time in seconds (left) and speedup (right) on unit square mesh. The speedup reference is P1OptV1 version.

6

n q P1OptV1 P1OptV1cs P1OptV2 P1OptV2cs 3043 0.104 (s)

x 1.00 0.098 (s)

x 1.06 0.009 (s)

x 11.68 0.004 (s) x 28.17 12139 0.427 (s)

x 1.00 0.400 (s)

x 1.07 0.043 (s)

x 9.98 0.018 (s) x 24.38 26910 0.948 (s)

x 1.00 0.891 (s)

x 1.06 0.082 (s)

x 11.58 0.032 (s) x 29.68 47834 1.693 (s)

x 1.00 1.604 (s)

x 1.06 0.148 (s)

x 11.46 0.052 (s) x 32.85 74326 2.651 (s)

x 1.00 2.452 (s)

x 1.08 0.228 (s)

x 11.64 0.083 (s) x 31.75 107625 3.820 (s)

x 1.00 3.638 (s)

x 1.05 0.340 (s)

x 11.23 0.131 (s) x 29.17 145828 5.160 (s)

x 1.00 4.885 (s)

x 1.06 0.462 (s)

x 11.17 0.172 (s) x 29.94 189794 6.694 (s)

x 1.00 6.340 (s)

x 1.06 0.636 (s)

x 10.52 0.252 (s) x 26.54 241024 8.587 (s)

x 1.00 8.190 (s)

x 1.05 0.830 (s)

x 10.35 0.329 (s) x 26.07 297290 10.576 (s)

x 1.00 10.077 (s)

x 1.05 1.060 (s)

x 9.98 0.416 (s) x 25.41 360040 12.873 (s)

x 1.00 12.086 (s)

x 1.07 1.280 (s)

x 10.05 0.519 (s) x 24.79 428549 15.287 (s)

x 1.00 14.387 (s)

x 1.06 1.566 (s)

x 9.76 0.651 (s) x 23.47 581973 20.885 (s)

x 1.00 20.017 (s)

x 1.04 2.188 (s)

x 9.55 0.910 (s) x 22.95 762704 32.695 (s)

x 1.00 30.603 (s)

x 1.07 2.878 (s)

x 11.36 1.202 (s) x 27.19 973281 38.842 (s)

x 1.00 37.762 (s)

x 1.03 3.716 (s)

x 10.45 1.566 (s) x 24.81 1197591 43.225 (s)

x 1.00 41.078 (s)

x 1.05 4.563 (s)

x 9.47 1.991 (s) x 21.71 1443408 52.097 (s)

x 1.00 49.040 (s)

x 1.06 5.635 (s)

x 9.25 2.406 (s) x 21.65 1707938 61.711 (s)

x 1.00 58.273 (s)

x 1.06 6.628 (s)

x 9.31 2.847 (s) x 21.68

Table 4: Computational cost of the MassWAssembling functions versus n _q , with Matlab (R2012b) : time in

seconds (top value) and speedup (bottom value) on unit square mesh. The speedup reference is P1OptV1

version.

3 benchs : StiAssembling ( P ₁ -Lagrange)

3.1 mesh : disque4-1

n q P1OptV1 P1OptV1cs P1OptV2 P1OptV2cs

3576 0.293 (s)

x 1.00 0.290 (s)

x 1.01 0.009 (s)

x 31.00 0.003 (s) x 95.82 14222 1.183 (s)

x 1.00 1.162 (s)

x 1.02 0.053 (s)

x 22.33 0.024 (s) x 48.55 31575 2.655 (s)

x 1.00 2.573 (s)

x 1.03 0.107 (s)

x 24.81 0.050 (s) x 52.71 55919 4.774 (s)

x 1.00 4.580 (s)

x 1.04 0.196 (s)

x 24.30 0.086 (s) x 55.36 86488 7.297 (s)

x 1.00 7.085 (s)

x 1.03 0.301 (s)

x 24.22 0.139 (s) x 52.31 125010 10.599 (s)

x 1.00 10.318 (s)

x 1.03 0.467 (s)

x 22.68 0.202 (s) x 52.39 170355 14.182 (s)

x 1.00 13.761 (s)

x 1.03 0.636 (s)

x 22.30 0.304 (s) x 46.59 225547 18.836 (s)

x 1.00 18.114 (s)

x 1.04 0.848 (s)

x 22.21 0.348 (s) x 54.11 281769 23.429 (s)

x 1.00 22.623 (s)

x 1.04 1.053 (s)

x 22.26 0.459 (s) x 51.01 343082 28.536 (s)

x 1.00 27.728 (s)

x 1.03 1.324 (s)

x 21.55 0.555 (s) x 51.44 424178 36.219 (s)

x 1.00 35.079 (s)

x 1.03 1.715 (s)

x 21.12 0.718 (s) x 50.44 506706 43.498 (s)

x 1.00 41.856 (s)

x 1.04 2.020 (s)

x 21.53 0.888 (s) x 49.00 689716 59.819 (s)

x 1.00 56.769 (s)

x 1.05 2.817 (s)

x 21.23 1.201 (s) x 49.79 885521 75.655 (s)

x 1.00 73.277 (s)

x 1.03 3.567 (s)

x 21.21 1.622 (s) x 46.63 1127090 96.174 (s)

x 1.00 93.027 (s)

x 1.03 4.617 (s)

x 20.83 2.078 (s) x 46.29 1401129 119.556 (s)

x 1.00 115.500 (s)

x 1.04 5.980 (s)

x 19.99 2.587 (s) x 46.22 1671052 143.145 (s)

x 1.00 137.595 (s)

x 1.04 6.971 (s)

x 20.54 3.091 (s) x 46.31 1978602 168.589 (s)

x 1.00 163.436 (s)

x 1.03 8.522 (s)

x 19.78 3.572 (s) x 47.20

Table 5: Computational cost of the StiffAssembling functions versus n q , with Matlab (R2012b) : time in seconds (top value) and speedup (bottom value) on unit disk mesh. The speedup reference is P1OptV1 version.

8

10

10

10

10

10

10

10

10

10

10

10

10

10

10

Sparse Matrix size (n

)

time (s)

P1OptV1 P1OptV1cs P1OptV2 P1OptV2cs O(n

) O(n

)

0 0.5 1 1.5 2

x 10

0

10 20 30 40 50 60 70 80 90 100

Sparse Matrix size (n

)

Speed Up X

P1OptV1cs P1OptV2 P1OptV2cs

Figure 5: Computational cost of the StiffAssembling functions versus n _q , with Matlab (R2012b) : time in seconds (left) and speedup (right) on unit disk mesh. The speedup reference is P1OptV1 version.

3.2 mesh : carre4-1

10

10

10

10

10

10

10

10

10

10

10

10

10

10

Sparse Matrix size (n

)

time (s)

P1OptV1 P1OptV1cs P1OptV2 P1OptV2cs O(n

) O(n

)

0 2 4 6 8 10 12 14 16 18

x 10

0

10 20 30 40 50 60 70 80 90 100

Sparse Matrix size (n

)

Speed Up X

P1OptV1cs P1OptV2 P1OptV2cs

Figure 6: Computational cost of the StiffAssembling functions versus n _q , with Matlab (R2012b) : time in

seconds (left) and speedup (right) on unit square mesh. The speedup reference is P1OptV1 version.

n q P1OptV1 P1OptV1cs P1OptV2 P1OptV2cs 3043 0.247 (s)

x 1.00 0.244 (s)

x 1.01 0.009 (s)

x 26.08 0.003 (s) x 96.75 12139 1.007 (s)

x 1.00 0.979 (s)

x 1.03 0.044 (s)

x 23.06 0.022 (s) x 46.30 26910 2.237 (s)

x 1.00 2.194 (s)

x 1.02 0.091 (s)

x 24.70 0.040 (s) x 56.04 47834 4.027 (s)

x 1.00 3.922 (s)

x 1.03 0.165 (s)

x 24.39 0.072 (s) x 55.83 74326 6.304 (s)

x 1.00 6.084 (s)

x 1.04 0.253 (s)

x 24.90 0.110 (s) x 57.44 107625 9.078 (s)

x 1.00 8.854 (s)

x 1.03 0.391 (s)

x 23.24 0.178 (s) x 51.09 145828 12.620 (s)

x 1.00 12.079 (s)

x 1.04 0.529 (s)

x 23.86 0.243 (s) x 52.01 189794 16.071 (s)

x 1.00 15.585 (s)

x 1.03 0.675 (s)

x 23.81 0.285 (s) x 56.45 241024 20.316 (s)

x 1.00 19.754 (s)

x 1.03 0.865 (s)

x 23.48 0.362 (s) x 56.16 297290 25.236 (s)

x 1.00 24.800 (s)

x 1.02 1.095 (s)

x 23.04 0.458 (s) x 55.10 360040 30.398 (s)

x 1.00 29.613 (s)

x 1.03 1.337 (s)

x 22.73 0.570 (s) x 53.32 428549 36.294 (s)

x 1.00 35.275 (s)

x 1.03 1.639 (s)

x 22.14 0.719 (s) x 50.48 581973 49.252 (s)

x 1.00 47.714 (s)

x 1.03 2.289 (s)

x 21.52 0.986 (s) x 49.97 762704 65.972 (s)

x 1.00 62.286 (s)

x 1.06 3.065 (s)

x 21.53 1.380 (s) x 47.79 973281 84.585 (s)

x 1.00 80.347 (s)

x 1.05 3.891 (s)

x 21.74 1.712 (s) x 49.41 1197591 102.292 (s)

x 1.00 98.567 (s)

x 1.04 4.774 (s)

x 21.43 2.134 (s) x 47.93 1443408 121.827 (s)

x 1.00 115.510 (s)

x 1.05 5.838 (s)

x 20.87 2.578 (s) x 47.26 1707938 144.695 (s)

x 1.00 137.993 (s)

x 1.05 6.881 (s)

x 21.03 3.125 (s) x 46.30

Table 6: Computational cost of the StiffAssembling functions versus n _q , with Matlab (R2012b) : time in seconds (top value) and speedup (bottom value) on unit square mesh. The speedup reference is P1OptV1 version.

10