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Bench report : VF_OptV1vsOptV2 (2013-01-30-16-40)

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Bench report : VF_OptV1vsOptV2 (2013-01-30-16-40)

Wednesday 30 th January, 2013

Contents

1 benchs : MassVFAssembling ( P 1 -Lagrange) 2

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

2 benchs : StiElasAssembling ( P 1 -Lagrange) 4

2.1 mesh : carre4-1 . . . . 4

2.2 mesh : disque4-1 . . . . 5

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n q n df P1OptV1 P1OptV2 3043 6086 0.142 (s)

x 1.00 0.034 (s) x 4.20 12139 24278 0.595 (s)

x 1.00 0.143 (s) x 4.16 26910 53820 1.330 (s)

x 1.00 0.335 (s) x 3.97 47834 95668 2.380 (s)

x 1.00 0.590 (s) x 4.04 74326 148652 3.695 (s)

x 1.00 0.945 (s) x 3.91 107625 215250 5.406 (s)

x 1.00 1.396 (s) x 3.87 145828 291656 7.385 (s)

x 1.00 1.882 (s) x 3.92 189794 379588 9.636 (s)

x 1.00 2.497 (s) x 3.86 241024 482048 12.297 (s)

x 1.00 3.236 (s) x 3.80 297290 594580 15.149 (s)

x 1.00 4.033 (s) x 3.76 360040 720080 18.338 (s)

x 1.00 4.865 (s) x 3.77 428549 857098 21.964 (s)

x 1.00 5.831 (s) x 3.77 505379 1010758 25.951 (s)

x 1.00 6.899 (s) x 3.76 581973 1163946 29.780 (s)

x 1.00 8.192 (s) x 3.64

Table 1: MassVFAssembling - Mesh le : carre4-1-< N >.msh

10

3

10

4

10

5

10

6

10

7

10

−2

10

−1

10

0

10

1

10

2

Sparse Matrix size (n

df

)

time (s)

P1OptV1 P1OptV2 O(n

df

) O(n

df

log(n

df

))

0 2 4 6 8 10 12

x 10

5

3.6

3.7 3.8 3.9 4 4.1 4.2 4.3

Sparse Matrix size (n

df

)

Speed Up X

P1OptV2

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1.2 mesh : disque4-1

n q n df P1OptV1 P1OptV2

3576 7152 0.169 (s)

x 1.00 0.040 (s) x 4.28 14222 28444 0.699 (s)

x 1.00 0.171 (s) x 4.10 31575 63150 1.573 (s)

x 1.00 0.396 (s) x 3.97 55919 111838 2.806 (s)

x 1.00 0.699 (s) x 4.01 86488 172976 4.358 (s)

x 1.00 1.124 (s) x 3.88 125010 250020 6.306 (s)

x 1.00 1.664 (s) x 3.79 170355 340710 8.680 (s)

x 1.00 2.277 (s) x 3.81 225547 451094 11.607 (s)

x 1.00 3.021 (s) x 3.84 281769 563538 14.259 (s)

x 1.00 3.828 (s) x 3.73 343082 686164 17.461 (s)

x 1.00 4.736 (s) x 3.69 424178 848356 22.114 (s)

x 1.00 6.107 (s) x 3.62 506706 1013412 26.072 (s)

x 1.00 7.213 (s) x 3.61 582024 1164048 30.208 (s)

x 1.00 8.335 (s) x 3.62 689716 1379432 35.795 (s)

x 1.00 9.863 (s) x 3.63

Table 2: MassVFAssembling - Mesh le : disque4-1-< N >.msh

10

3

10

4

10

5

10

6

10

7

10

−2

10

−1

10

0

10

1

10

2

Sparse Matrix size (n

df

)

time (s)

P1OptV1 P1OptV2 O(n

df

) O(n

df

log(n

df

))

0 2 4 6 8 10 12 14

x 10

5

3.6

3.7 3.8 3.9 4 4.1 4.2 4.3

Sparse Matrix size (n

df

)

Speed Up X

P1OptV2

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

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

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n q n df P1OptV1 P1OptV2 3043 6086 0.325 (s)

x 1.00 0.035 (s) x 9.38 12139 24278 1.321 (s)

x 1.00 0.147 (s) x 9.00 26910 53820 2.982 (s)

x 1.00 0.356 (s) x 8.37 47834 95668 5.307 (s)

x 1.00 0.640 (s) x 8.29 74326 148652 8.284 (s)

x 1.00 0.990 (s) x 8.36 107625 215250 12.055 (s)

x 1.00 1.494 (s) x 8.07 145828 291656 16.271 (s)

x 1.00 2.007 (s) x 8.11 189794 379588 21.335 (s)

x 1.00 2.692 (s) x 7.92 241024 482048 27.168 (s)

x 1.00 3.439 (s) x 7.90 297290 594580 33.509 (s)

x 1.00 4.298 (s) x 7.80 360040 720080 40.699 (s)

x 1.00 5.221 (s) x 7.80 428549 857098 48.700 (s)

x 1.00 6.235 (s) x 7.81 505379 1010758 57.204 (s)

x 1.00 7.366 (s) x 7.77 581973 1163946 66.121 (s)

x 1.00 8.821 (s) x 7.50

Table 3: StiElasAssembling - Mesh le : carre4-1-< N >.msh

10

3

10

4

10

5

10

6

10

7

10

−2

10

−1

10

0

10

1

10

2

10

3

Sparse Matrix size (n

df

)

time (s)

P1OptV1 P1OptV2 O(n

df

) O(n

df

log(n

df

))

0 2 4 6 8 10 12

x 10

5

7.4

7.6 7.8 8 8.2 8.4 8.6 8.8 9 9.2 9.4

Sparse Matrix size (n

df

)

Speed Up X

P1OptV2

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2.2 mesh : disque4-1

n q n df P1OptV1 P1OptV2

3576 7152 0.373 (s)

x 1.00 0.041 (s) x 9.07 14222 28444 1.526 (s)

x 1.00 0.178 (s) x 8.57 31575 63150 3.419 (s)

x 1.00 0.419 (s) x 8.15 55919 111838 6.065 (s)

x 1.00 0.749 (s) x 8.09 86488 172976 9.487 (s)

x 1.00 1.183 (s) x 8.02 125010 250020 13.628 (s)

x 1.00 1.743 (s) x 7.82 170355 340710 18.783 (s)

x 1.00 2.408 (s) x 7.80 225547 451094 24.810 (s)

x 1.00 3.182 (s) x 7.80 281769 563538 31.300 (s)

x 1.00 4.053 (s) x 7.72 343082 686164 38.262 (s)

x 1.00 5.078 (s) x 7.54 424178 848356 47.792 (s)

x 1.00 6.582 (s) x 7.26 506706 1013412 57.178 (s)

x 1.00 7.710 (s) x 7.42 582024 1164048 66.317 (s)

x 1.00 8.866 (s) x 7.48 689716 1379432 77.775 (s)

x 1.00 10.638 (s) x 7.31

Table 4: StiElasAssembling - Mesh le : disque4-1-< N >.msh

10

3

10

4

10

5

10

6

10

7

10

−2

10

−1

10

0

10

1

10

2

10

3

Sparse Matrix size (n

df

)

time (s)

P1OptV1 P1OptV2 O(n

df

) O(n

df

log(n

df

))

0 2 4 6 8 10 12 14

x 10

5

7.2

7.4 7.6 7.8 8 8.2 8.4 8.6 8.8 9 9.2

Sparse Matrix size (n

df

)

Speed Up X

P1OptV2

Figure 4: Computational cost of the StiffElasAssembling functions versus n q , with Matlab (R2012b) : time

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

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