Bench report : P1OptV2vsHanJunvsRahValvsChen (2013-01-23-14-11)

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Bench report : P1OptV2vsHanJunvsRahValvsChen (2013-01-23-14-11)

Tuesday 26^th March, 2013

Contents

1 benchs : MassAssembling (P1-Lagrange) 2

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

2 benchs : StiAssembling (P1-Lagrange) 5

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

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1 benchs : MassAssembling (P₁-Lagrange)

1.1 mesh : carre4-1

nq P1OptV2 P1HanJun P1RahValT P1Chen P1ChenT P1iFEMT

3043 0.008 (s)

x 1.00 0.011 (s)

x 0.75 0.010 (s)

x 0.80 0.008 (s)

x 1.01 0.008 (s)

x 1.02 0.008 (s) x 1.05 26910 0.079 (s)

x 1.00 0.105 (s)

x 0.75 0.090 (s)

x 0.88 0.088 (s)

x 0.90 0.087 (s)

x 0.90 0.077 (s) x 1.02 74326 0.224 (s)

x 1.00 0.295 (s)

x 0.76 0.275 (s)

x 0.82 0.256 (s)

x 0.88 0.255 (s)

x 0.88 0.229 (s) x 0.98 145828 0.484 (s)

x 1.00 0.601 (s)

x 0.81 0.580 (s)

x 0.83 0.554 (s)

x 0.87 0.550 (s)

x 0.88 0.460 (s) x 1.05 241024 0.814 (s)

x 1.00 1.040 (s)

x 0.78 1.000 (s)

x 0.81 0.936 (s)

x 0.87 0.927 (s)

x 0.88 0.794 (s) x 1.03 360040 1.242 (s)

x 1.00 1.599 (s)

x 0.78 1.531 (s)

x 0.81 1.430 (s)

x 0.87 1.406 (s)

x 0.88 1.232 (s) x 1.01 505379 1.830 (s)

x 1.00 2.300 (s)

x 0.80 2.164 (s)

x 0.85 2.079 (s)

x 0.88 2.049 (s)

x 0.89 1.732 (s) x 1.06 668176 2.391 (s)

x 1.00 3.059 (s)

x 0.78 2.945 (s)

x 0.81 2.821 (s)

x 0.85 2.821 (s)

x 0.85 2.464 (s) x 0.97 866481 3.208 (s)

x 1.00 4.049 (s)

x 0.79 3.815 (s)

x 0.84 3.778 (s)

x 0.85 3.628 (s)

x 0.88 3.389 (s) x 0.95 1067083 3.998 (s)

x 1.00 5.098 (s)

x 0.78 4.872 (s)

x 0.82 4.743 (s)

x 0.84 4.662 (s)

x 0.86 4.314 (s) x 0.93 1197591 4.509 (s)

x 1.00 5.799 (s)

x 0.78 5.384 (s)

x 0.84 5.369 (s)

x 0.84 5.196 (s)

x 0.87 4.709 (s) x 0.96 1443408 5.455 (s)

x 1.00 7.085 (s)

x 0.77 6.624 (s)

x 0.82 6.432 (s)

x 0.85 6.555 (s)

x 0.83 6.008 (s) x 0.91 1707938 6.564 (s)

x 1.00 8.409 (s)

x 0.78 7.804 (s)

x 0.84 7.426 (s)

x 0.88 7.697 (s)

x 0.85 7.148 (s) x 0.92 2005296 7.562 (s)

x 1.00 10.018 (s)

x 0.75 9.310 (s)

x 0.81 9.012 (s)

x 0.84 9.180 (s)

x 0.82 8.426 (s) x 0.90 2339961 9.005 (s)

x 1.00 11.936 (s)

x 0.75 11.046 (s)

x 0.82 10.893 (s)

x 0.83 10.795 (s)

x 0.83 10.032 (s) x 0.90 2666201 10.331 (s)

x 1.00 13.377 (s)

x 0.77 12.322 (s)

x 0.84 11.809 (s)

x 0.87 11.600 (s)

x 0.89 11.575 (s) x 0.89

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 square mesh. The speedup reference is P1OptV2 version.

2

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10³ 10⁴ 10⁵ 10⁶ 10⁷ 10⁻³

10⁻² 10⁻¹ 10⁰ 10¹ 10²

Sparse Matrix size (n_q)

time (s)

P1OptV2 P1HanJun P1RahValT P1Chen P1ChenT P1iFEMT O(n_q) O(n_qlog(n_q))

0 0.5 1 1.5 2 2.5 3

x 10⁶ 0.75

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15

Speed Up X

P1HanJun P1RahValT P1Chen P1ChenT P1iFEMT

Figure 1: 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 P1OptV2 version.

1.2 mesh : disque4-1

10³ 10⁴ 10⁵ 10⁶ 10⁷

10⁻³ 10⁻² 10⁻¹ 10⁰ 10¹ 10²

time (s)

0 0.5 1 1.5 2 2.5 3 3.5

x 10⁶ 0.7

0.8 0.9 1 1.1 1.2 1.3 1.4

Speed Up X

Figure 2: Computational cost of the MassAssembling functions versus nq, with Matlab (R2012b) : time in seconds (left) and speedup (right) on unit disk mesh. The speedup reference is P1OptV2 version.

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nq P1OptV2 P1HanJun P1RahValT P1Chen P1ChenT P1iFEMT 3576 0.013 (s)

x 1.00 0.018 (s)

x 0.76 0.016 (s)

x 0.82 0.015 (s)

x 0.91 0.014 (s)

x 0.93 0.010 (s) x 1.35 31575 0.095 (s)

x 1.00 0.129 (s)

x 0.74 0.114 (s)

x 0.84 0.110 (s)

x 0.87 0.109 (s)

x 0.88 0.094 (s) x 1.01 86488 0.291 (s)

x 1.00 0.368 (s)

x 0.79 0.344 (s)

x 0.85 0.324 (s)

x 0.90 0.333 (s)

x 0.87 0.288 (s) x 1.01 170355 0.582 (s)

x 1.00 0.736 (s)

x 0.79 0.673 (s)

x 0.86 0.662 (s)

x 0.88 0.661 (s)

x 0.88 0.575 (s) x 1.01 281769 0.986 (s)

x 1.00 1.303 (s)

x 0.76 1.195 (s)

x 0.83 1.157 (s)

x 0.85 1.162 (s)

x 0.85 1.041 (s) x 0.95 424178 1.589 (s)

x 1.00 2.045 (s)

x 0.78 1.825 (s)

x 0.87 1.764 (s)

x 0.90 1.735 (s)

x 0.92 1.605 (s) x 0.99 582024 2.179 (s)

x 1.00 2.724 (s)

x 0.80 2.588 (s)

x 0.84 2.473 (s)

x 0.88 2.438 (s)

x 0.89 2.267 (s) x 0.96 778415 2.955 (s)

x 1.00 3.660 (s)

x 0.81 3.457 (s)

x 0.85 3.279 (s)

x 0.90 3.240 (s)

x 0.91 3.177 (s) x 0.93 992675 3.774 (s)

x 1.00 4.682 (s)

x 0.81 4.422 (s)

x 0.85 4.216 (s)

x 0.90 4.146 (s)

x 0.91 3.868 (s) x 0.98 1251480 4.788 (s)

x 1.00 6.443 (s)

x 0.74 5.673 (s)

x 0.84 5.852 (s)

x 0.82 5.590 (s)

x 0.86 5.040 (s) x 0.95 1401129 5.526 (s)

x 1.00 6.790 (s)

x 0.81 6.412 (s)

x 0.86 6.055 (s)

x 0.91 5.962 (s)

x 0.93 5.753 (s) x 0.96 1671052 6.507 (s)

x 1.00 8.239 (s)

x 0.79 7.759 (s)

x 0.84 7.464 (s)

x 0.87 7.377 (s)

x 0.88 7.269 (s) x 0.90 1978602 7.921 (s)

x 1.00 9.893 (s)

x 0.80 9.364 (s)

x 0.85 8.884 (s)

x 0.89 8.807 (s)

x 0.90 8.720 (s) x 0.91 2349573 9.386 (s)

x 1.00 12.123 (s)

x 0.77 11.160 (s)

x 0.84 11.000 (s)

x 0.85 10.969 (s)

x 0.86 10.388 (s) x 0.90 2732448 10.554 (s)

x 1.00 14.343 (s)

x 0.74 13.087 (s)

x 0.81 12.788 (s)

x 0.83 12.680 (s)

x 0.83 11.842 (s) x 0.89 3085628 12.034 (s)

x 1.00 16.401 (s)

x 0.73 14.950 (s)

x 0.80 14.637 (s)

x 0.82 14.514 (s)

x 0.83 13.672 (s) x 0.88

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 disk mesh. The speedup reference is P1OptV2 version.

4

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2 benchs : StiAssembling (P₁-Lagrange)

2.1 mesh : carre4-1

nq P1OptV2 P1HanJun P1RahValT P1Chen P1ChenT P1iFEMT

3043 0.009 (s)

x 1.00 0.014 (s)

x 0.65 0.017 (s)

x 0.53 0.013 (s)

x 0.71 0.011 (s)

x 0.82 0.010 (s) x 0.87 26910 0.084 (s)

x 1.00 0.133 (s)

x 0.64 0.134 (s)

x 0.63 0.122 (s)

x 0.69 0.109 (s)

x 0.77 0.102 (s) x 0.83 74326 0.247 (s)

x 1.00 0.376 (s)

x 0.66 0.383 (s)

x 0.64 0.334 (s)

x 0.74 0.302 (s)

x 0.82 0.276 (s) x 0.90 145828 0.523 (s)

x 1.00 0.781 (s)

x 0.67 0.793 (s)

x 0.66 0.701 (s)

x 0.75 0.643 (s)

x 0.81 0.548 (s) x 0.95 241024 0.897 (s)

x 1.00 1.311 (s)

x 0.68 1.377 (s)

x 0.65 1.233 (s)

x 0.73 1.141 (s)

x 0.79 0.960 (s) x 0.93 360040 1.372 (s)

x 1.00 2.041 (s)

x 0.67 2.166 (s)

x 0.63 1.920 (s)

x 0.71 1.755 (s)

x 0.78 1.452 (s) x 0.95 505379 1.968 (s)

x 1.00 3.075 (s)

x 0.64 3.083 (s)

x 0.64 2.705 (s)

x 0.73 2.445 (s)

x 0.80 2.111 (s) x 0.93 668176 2.589 (s)

x 1.00 4.141 (s)

x 0.63 4.108 (s)

x 0.63 3.629 (s)

x 0.71 3.317 (s)

x 0.78 3.035 (s) x 0.85 866481 3.414 (s)

x 1.00 5.026 (s)

x 0.68 5.380 (s)

x 0.63 4.873 (s)

x 0.70 4.349 (s)

x 0.78 4.174 (s) x 0.82 1067083 4.238 (s)

x 1.00 6.174 (s)

x 0.69 6.699 (s)

x 0.63 6.100 (s)

x 0.69 5.445 (s)

x 0.78 4.909 (s) x 0.86 1197591 4.749 (s)

x 1.00 6.898 (s)

x 0.69 7.558 (s)

x 0.63 6.914 (s)

x 0.69 6.113 (s)

x 0.78 5.552 (s) x 0.86 1443408 5.867 (s)

x 1.00 8.636 (s)

x 0.68 9.243 (s)

x 0.63 8.283 (s)

x 0.71 7.516 (s)

x 0.78 7.197 (s) x 0.82 1707938 6.941 (s)

x 1.00 10.238 (s)

x 0.68 10.910 (s)

x 0.64 9.724 (s)

x 0.71 8.759 (s)

x 0.79 8.092 (s) x 0.86 2005296 8.106 (s)

x 1.00 11.984 (s)

x 0.68 12.777 (s)

x 0.63 11.511 (s)

x 0.70 10.464 (s)

x 0.77 10.008 (s) x 0.81 2339961 9.572 (s)

x 1.00 14.476 (s)

x 0.66 15.293 (s)

x 0.63 13.695 (s)

x 0.70 13.004 (s)

x 0.74 12.112 (s) x 0.79 2666201 11.148 (s)

x 1.00 16.394 (s)

x 0.68 17.762 (s)

x 0.63 16.100 (s)

x 0.69 14.751 (s)

x 0.76 14.028 (s) x 0.79

Table 3: 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 P1OptV2 version.

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10³ 10⁴ 10⁵ 10⁶ 10⁷ 10⁻³

10⁻² 10⁻¹ 10⁰ 10¹ 10²

time (s)

0 0.5 1 1.5 2 2.5 3

x 10⁶ 0.5

0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

Speed Up X

Figure 3: 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 P1OptV2 version.

2.2 mesh : disque4-1

10³ 10⁴ 10⁵ 10⁶ 10⁷

10⁻³ 10⁻² 10⁻¹ 10⁰ 10¹ 10²

time (s)

0 0.5 1 1.5 2 2.5 3 3.5

x 10⁶ 0.5

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

Speed Up X

Figure 4: Computational cost of the StiffAssembling functions versus nq, with Matlab (R2012b) : time in seconds (left) and speedup (right) on unit disk mesh. The speedup reference is P1OptV2 version.

6

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nq P1OptV2 P1HanJun P1RahValT P1Chen P1ChenT P1iFEMT 3576 0.014 (s)

x 1.00 0.021 (s)

x 0.66 0.027 (s)

x 0.53 0.021 (s)

x 0.69 0.017 (s)

x 0.83 0.011 (s) x 1.30 31575 0.102 (s)

x 1.00 0.153 (s)

x 0.66 0.157 (s)

x 0.65 0.142 (s)

x 0.71 0.126 (s)

x 0.81 0.119 (s) x 0.86 86488 0.294 (s)

x 1.00 0.444 (s)

x 0.66 0.474 (s)

x 0.62 0.407 (s)

x 0.72 0.360 (s)

x 0.82 0.326 (s) x 0.90 170355 0.638 (s)

x 1.00 0.944 (s)

x 0.68 0.995 (s)

x 0.64 0.851 (s)

x 0.75 0.774 (s)

x 0.82 0.663 (s) x 0.96 281769 1.048 (s)

x 1.00 1.616 (s)

x 0.65 1.621 (s)

x 0.65 1.448 (s)

x 0.72 1.316 (s)

x 0.80 1.119 (s) x 0.94 424178 1.733 (s)

x 1.00 2.452 (s)

x 0.71 2.634 (s)

x 0.66 2.292 (s)

x 0.76 2.092 (s)

x 0.83 1.771 (s) x 0.98 582024 2.369 (s)

x 1.00 3.620 (s)

x 0.65 3.648 (s)

x 0.65 3.194 (s)

x 0.74 2.932 (s)

x 0.81 2.565 (s) x 0.92 778415 3.113 (s)

x 1.00 4.446 (s)

x 0.70 4.984 (s)

x 0.62 4.371 (s)

x 0.71 3.943 (s)

x 0.79 3.694 (s) x 0.84 992675 3.933 (s)

x 1.00 5.948 (s)

x 0.66 6.270 (s)

x 0.63 5.634 (s)

x 0.70 4.862 (s)

x 0.81 4.525 (s) x 0.87 1251480 5.142 (s)

x 1.00 7.320 (s)

x 0.70 8.117 (s)

x 0.63 7.204 (s)

x 0.71 6.595 (s)

x 0.78 6.056 (s) x 0.85 1401129 5.901 (s)

x 1.00 8.510 (s)

x 0.69 9.132 (s)

x 0.65 8.156 (s)

x 0.72 7.590 (s)

x 0.78 7.148 (s) x 0.83 1671052 6.937 (s)

x 1.00 10.174 (s)

x 0.68 10.886 (s)

x 0.64 9.793 (s)

x 0.71 9.233 (s)

x 0.75 8.557 (s) x 0.81 1978602 8.410 (s)

x 1.00 12.315 (s)

x 0.68 13.006 (s)

x 0.65 11.856 (s)

x 0.71 10.845 (s)

x 0.78 10.153 (s) x 0.83 2349573 9.892 (s)

x 1.00 14.384 (s)

x 0.69 15.585 (s)

x 0.63 13.769 (s)

x 0.72 12.778 (s)

x 0.77 12.308 (s) x 0.80 2732448 11.255 (s)

x 1.00 17.035 (s)

x 0.66 17.774 (s)

x 0.63 15.892 (s)

x 0.71 14.259 (s)

x 0.79 13.977 (s) x 0.81 3085628 13.157 (s)

x 1.00 18.938 (s)

x 0.69 20.767 (s)

x 0.63 18.379 (s)

x 0.72 17.419 (s)

x 0.76 16.575 (s) x 0.79

Table 4: 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 P1OptV2 version.