• N: the dimension of the matrix (number of rows and columns)
• K: the half-bandwidth
• d: the diagonal dominance
• NPrtns: the number of partitions used to solve the problem
• Solves: indicates whether we managed to solve the problem or not. OK means solved fine, otherwise a reason is provided for failure
• T-LU: LU time
• T-SwDef: Deflation sweep time (BCR only, Eq. 5a, 5b)
• T-MMDef: Deflation matrix multiplication time (BCR only, Eq. 5c-5e)
• T-PreP: the sum of all preprocessing times, see NOTES
• nItrs: the number of Krylov-solve iterations to solve the problem
• T-SwInf: Inflation sweep time (BCR only, Eq. 5f)
• T-MVInf: Inflation matrix vector multiplication time (BCR only, Eq. 5g, 5h)
• T-Kry: time spent in the Krylov solver (on the GPU)
• T-KryPIt: time per Krylov iteration, see NOTES
• Total: total time to solve the problem, sum of T-PreP + T-Kry
NOTES:
1) All times reported are in miliseconds (1E-3 second)
2) T-KryPIt = T-Kry / max(1, nItrs)
|
N |
K |
d |
NPrtns |
Solves |
T-LU |
T-SwDef |
T-MMDef |
T-PreP |
nItrs |
T-SwInf |
T-MVInf |
T-Kry |
T-KryPIt |
T-Total |
|
200000 |
10 |
1 |
1 |
OK |
24.2722 |
12.2619 |
35.2257 |
81.723 |
0.75 |
10.8961 |
30.2726 |
53.886 |
53.886 |
135.609 |
|
200000 |
10 |
1 |
1 |
OK |
264.775 |
|
|
268.8 |
0.75 |
|
|
1205.52 |
1205.52 |
1474.32 |
|
200000 |
10 |
1 |
4 |
OK |
18.8382 |
11.9788 |
33.528 |
74.094 |
2.75 |
27.2124 |
77.2414 |
131.907 |
47.9662 |
206.001 |
|
200000 |
10 |
1 |
4 |
OK |
66.601 |
|
|
70.712 |
2.75 |
|
|
1153.44 |
419.432 |
1224.15 |
|
200000 |
10 |
1 |
8 |
OK |
18.0295 |
11.8463 |
32.9357 |
72.549 |
2.75 |
26.7645 |
76.7795 |
130.747 |
47.5444 |
203.296 |
|
200000 |
10 |
1 |
8 |
OK |
33.5965 |
|
|
37.748 |
2.75 |
|
|
592.549 |
215.472 |
630.297 |
|
200000 |
10 |
1 |
16 |
OK |
17.2945 |
11.7184 |
32.5456 |
71.26 |
2.75 |
26.2944 |
76.3672 |
129.37 |
47.0436 |
200.63 |
|
200000 |
10 |
1 |
16 |
OK |
17.1801 |
|
|
21.337 |
2.75 |
|
|
311.866 |
113.406 |
333.203 |
|
200000 |
10 |
1 |
20 |
OK |
16.5977 |
11.6324 |
32.0151 |
69.967 |
3.25 |
29.8016 |
87.5231 |
147.046 |
45.2449 |
217.013 |
|
200000 |
10 |
1 |
20 |
OK |
13.9148 |
|
|
18.05 |
3.25 |
|
|
293.888 |
90.4271 |
311.938 |
|
200000 |
10 |
1 |
32 |
OK |
16.7773 |
11.7055 |
32.1499 |
70.402 |
3.25 |
34.2112 |
101.011 |
168.636 |
51.888 |
239.038 |
|
200000 |
10 |
1 |
32 |
OK |
9.04627 |
|
|
13.234 |
3.25 |
|
|
221.763 |
68.2348 |
234.997 |
|
200000 |
10 |
1 |
50 |
OK |
15.939 |
11.4975 |
31.6312 |
68.797 |
3.25 |
33.3065 |
99.0771 |
165.106 |
50.8018 |
233.903 |
|
200000 |
10 |
1 |
50 |
OK |
6.09686 |
|
|
10.262 |
3.25 |
|
|
155.438 |
47.8271 |
165.7 |
|
200000 |
20 |
1 |
1 |
OK |
28.64 |
20.7508 |
42.0272 |
102.011 |
0.75 |
10.7706 |
32.3022 |
57.644 |
57.644 |
159.655 |
|
200000 |
20 |
1 |
1 |
OK |
286.453 |
|
|
292.819 |
0.75 |
|
|
1268.93 |
1268.93 |
1561.75 |
|
200000 |
20 |
1 |
4 |
OK |
27.2449 |
20.3164 |
41.4469 |
99.544 |
2.75 |
27.0089 |
84.0392 |
144.565 |
52.5691 |
244.109 |
|
200000 |
20 |
1 |
4 |
OK |
72.5107 |
|
|
78.974 |
2.75 |
|
|
1208.3 |
439.381 |
1287.27 |
|
200000 |
20 |
1 |
8 |
OK |
31.7517 |
19.8612 |
54.6888 |
116.925 |
2.75 |
26.4718 |
83.2888 |
145.248 |
52.8175 |
262.173 |
|
200000 |
20 |
1 |
8 |
OK |
36.9869 |
|
|
43.465 |
2.75 |
|
|
628.782 |
228.648 |
672.247 |
|
200000 |
20 |
1 |
16 |
OK |
25.5395 |
19.3963 |
40.1342 |
95.461 |
2.75 |
25.453 |
82.2768 |
140.182 |
50.9753 |
235.643 |
|
200000 |
20 |
1 |
16 |
OK |
19.88 |
|
|
26.381 |
2.75 |
|
|
330.277 |
120.101 |
356.658 |
|
200000 |
20 |
1 |
20 |
OK |
24.7589 |
19.2002 |
39.7151 |
94.08 |
2.75 |
24.7431 |
81.4173 |
138.318 |
50.2975 |
232.398 |
|
200000 |
20 |
1 |
20 |
OK |
16.181 |
|
|
22.694 |
2.75 |
|
|
271.816 |
98.8422 |
294.51 |
|
200000 |
20 |
1 |
32 |
OK |
24.8478 |
19.0348 |
39.3229 |
93.643 |
2.75 |
24.8875 |
81.8479 |
138.9 |
50.5091 |
232.543 |
|
200000 |
20 |
1 |
32 |
OK |
11.4103 |
|
|
17.913 |
2.75 |
|
|
184.044 |
66.9251 |
201.957 |
|
200000 |
20 |
1 |
50 |
OK |
24.0469 |
18.8314 |
34.2111 |
87.531 |
2.75 |
24.1588 |
81.5282 |
137.662 |
50.0589 |
225.193 |
|
200000 |
20 |
1 |
50 |
OK |
8.4024 |
|
|
14.921 |
2.75 |
|
|
131.524 |
47.8269 |
146.445 |
|
200000 |
50 |
1 |
1 |
OK |
58.5501 |
41.2044 |
73.1241 |
190.818 |
0.75 |
13.4309 |
33.1776 |
64.084 |
64.084 |
254.902 |
|
200000 |
50 |
1 |
1 |
OK |
1024.78 |
|
|
1037.84 |
0.75 |
|
|
1440.87 |
1440.87 |
2478.7 |
|
200000 |
50 |
1 |
4 |
OK |
56.6425 |
39.1851 |
72.1564 |
185.844 |
2.25 |
27.4019 |
71.8859 |
133.526 |
59.3449 |
319.37 |
|
200000 |
50 |
1 |
4 |
OK |
258.937 |
|
|
272.373 |
2.25 |
|
|
1119.13 |
497.391 |
1391.5 |
|
200000 |
50 |
1 |
8 |
OK |
55.2116 |
38.029 |
70.1837 |
181.203 |
2.25 |
26.0852 |
70.4036 |
130.3 |
57.9111 |
311.503 |
|
200000 |
50 |
1 |
8 |
OK |
132.477 |
|
|
145.998 |
2.25 |
|
|
585.476 |
260.212 |
731.474 |
|
200000 |
50 |
1 |
16 |
OK |
54.2485 |
36.6621 |
63.5333 |
172.157 |
2.25 |
25.0069 |
69.7163 |
128.494 |
57.1084 |
300.651 |
|
200000 |
50 |
1 |
16 |
OK |
77.7881 |
|
|
91.29 |
2.25 |
|
|
308.399 |
137.066 |
399.689 |
|
200000 |
50 |
1 |
20 |
OK |
54.5423 |
36.8539 |
63.7975 |
172.969 |
2.25 |
29.5867 |
82.9023 |
151.567 |
67.3631 |
324.536 |
|
200000 |
50 |
1 |
20 |
OK |
62.6587 |
|
|
76.139 |
2.25 |
|
|
299.377 |
133.056 |
375.516 |
|
200000 |
50 |
1 |
32 |
OK |
53.3693 |
35.2102 |
60.6568 |
167.001 |
2.25 |
28.3475 |
81.314 |
148.275 |
65.9 |
315.276 |
|
200000 |
50 |
1 |
32 |
OK |
46.4562 |
|
|
59.926 |
2.25 |
|
|
204.501 |
90.8893 |
264.427 |
|
200000 |
50 |
1 |
50 |
OK |
54.1348 |
34.8616 |
61.2659 |
168.02 |
2.25 |
23.9793 |
69.3905 |
126.905 |
56.4022 |
294.925 |
|
200000 |
50 |
1 |
50 |
OK |
36.1767 |
|
|
49.661 |
2.25 |
|
|
125.378 |
55.7236 |
175.039 |
|
200000 |
100 |
1 |
1 |
OK |
112.759 |
153.542 |
144.315 |
443.324 |
0.75 |
17.7376 |
38.1031 |
79.407 |
79.407 |
522.731 |
|
200000 |
100 |
1 |
1 |
OK |
928.477 |
|
|
952.584 |
0.75 |
|
|
1468.24 |
1468.24 |
2420.83 |
|
200000 |
100 |
1 |
4 |
OK |
107.101 |
144.532 |
141.485 |
425.821 |
1.75 |
28.5805 |
67.1234 |
135.541 |
77.452 |
561.362 |
|
200000 |
100 |
1 |
4 |
OK |
383.256 |
|
|
407.622 |
1.75 |
|
|
937.645 |
535.797 |
1345.27 |
|
200000 |
100 |
1 |
8 |
OK |
106.033 |
139.546 |
132.421 |
410.689 |
1.75 |
27.0303 |
66.3143 |
133.182 |
76.104 |
543.871 |
|
200000 |
100 |
1 |
8 |
OK |
249.491 |
|
|
273.923 |
1.75 |
|
|
491.617 |
280.924 |
765.54 |
|
200000 |
100 |
1 |
16 |
OK |
104.935 |
134.328 |
128.303 |
400.167 |
1.75 |
25.523 |
65.1988 |
130.266 |
74.4377 |
530.433 |
|
200000 |
100 |
1 |
16 |
OK |
173.02 |
|
|
197.44 |
1.75 |
|
|
268.63 |
153.503 |
466.07 |
|
200000 |
100 |
1 |
20 |
OK |
105.776 |
133.926 |
129.214 |
401.493 |
1.75 |
25.4246 |
65.7276 |
130.398 |
74.5131 |
531.891 |
|
200000 |
100 |
1 |
20 |
OK |
161.856 |
|
|
186.356 |
1.75 |
|
|
224.156 |
128.089 |
410.512 |
|
200000 |
100 |
1 |
32 |
OK |
104.898 |
94.4889 |
122.811 |
354.992 |
1.75 |
24.4107 |
63.6522 |
127.287 |
72.7354 |
482.279 |
|
200000 |
100 |
1 |
32 |
OK |
141.385 |
|
|
165.832 |
1.75 |
|
|
157.089 |
89.7651 |
322.921 |
|
200000 |
100 |
1 |
50 |
OK |
106.549 |
125.307 |
122.265 |
386.605 |
2.25 |
29.4026 |
78.2502 |
154.817 |
68.8076 |
541.422 |
|
200000 |
100 |
1 |
50 |
OK |
132.617 |
|
|
157.248 |
2.25 |
|
|
142.631 |
63.3916 |
299.879 |
|
200000 |
200 |
1 |
1 |
OK |
314.652 |
416.578 |
369.325 |
1193.87 |
0.75 |
28.0272 |
54.5544 |
120.426 |
120.426 |
1314.29 |
|
200000 |
200 |
1 |
1 |
OK |
1189.51 |
|
|
1236.79 |
0.75 |
|
|
1513.09 |
1513.09 |
2749.87 |
|
200000 |
200 |
1 |
4 |
OK |
311.066 |
388.115 |
349.471 |
1141.81 |
1.75 |
44.1715 |
95.5205 |
205.312 |
117.321 |
1347.12 |
|
200000 |
200 |
1 |
4 |
OK |
587.562 |
|
|
635.026 |
1.75 |
|
|
981.52 |
560.869 |
1616.55 |
|
200000 |
200 |
1 |
8 |
OK |
309.716 |
371.777 |
338.377 |
1112.61 |
1.75 |
41.4061 |
93.408 |
200.077 |
114.33 |
1312.69 |
|
200000 |
200 |
1 |
8 |
OK |
438.894 |
|
|
486.534 |
1.75 |
|
|
526.237 |
300.707 |
1012.77 |
|
200000 |
200 |
1 |
16 |
OK |
319.598 |
234.582 |
333.455 |
981.541 |
1.75 |
39.5124 |
91.9493 |
196.647 |
112.37 |
1178.19 |
|
200000 |
200 |
1 |
16 |
OK |
379.314 |
|
|
427.072 |
1.75 |
|
|
303.075 |
173.186 |
730.147 |
|
200000 |
200 |
1 |
20 |
OK |
311.454 |
351.639 |
323.004 |
1078.48 |
1.75 |
38.4374 |
91.1666 |
194.605 |
111.203 |
1273.08 |
|
200000 |
200 |
1 |
20 |
OK |
359.345 |
|
|
407.065 |
1.75 |
|
|
257.224 |
146.985 |
664.289 |
|
200000 |
200 |
1 |
32 |
OK |
313.07 |
209.367 |
296.024 |
911.593 |
1.75 |
36.0572 |
84.9621 |
185.858 |
106.205 |
1097.45 |
|
200000 |
200 |
1 |
32 |
OK |
345.602 |
|
|
393.326 |
1.75 |
|
|
191.223 |
109.27 |
584.549 |
|
200000 |
200 |
1 |
50 |
OK |
321.139 |
318.597 |
293.615 |
1024.85 |
1.75 |
38.7886 |
85.5507 |
189.268 |
108.153 |
1214.11 |
|
200000 |
200 |
1 |
50 |
OK |
323.828 |
|
|
371.735 |
1.75 |
|
|
153.241 |
87.5663 |
524.976 |
|
200000 |
500 |
1 |
1 |
OK |
1686.12 |
1531.96 |
1857.58 |
5390.37 |
0.75 |
66.1551 |
111.682 |
259.685 |
259.685 |
5650.06 |
|
200000 |
500 |
1 |
1 |
OK |
2632.37 |
|
|
2752.13 |
0.75 |
|
|
1736.5 |
1736.5 |
4488.63 |
|
200000 |
500 |
1 |
4 |
OK |
1689.17 |
1429.58 |
1755.6 |
5187.26 |
1.75 |
104.483 |
193.845 |
443.039 |
253.165 |
5630.29 |
|
200000 |
500 |
1 |
4 |
OK |
1840.6 |
|
|
1960.93 |
1.75 |
|
|
1156.11 |
660.635 |
3117.04 |
|
200000 |
500 |
1 |
8 |
OK |
1694.44 |
1339.6 |
1660.19 |
5004.73 |
1.75 |
97.2418 |
186.47 |
428.007 |
244.575 |
5432.73 |
|
200000 |
500 |
1 |
8 |
OK |
1674.52 |
|
|
1795.06 |
1.75 |
|
|
658.463 |
376.265 |
2453.52 |
|
200000 |
500 |
1 |
16 |
OK |
1721.26 |
1230.13 |
1512.86 |
4769.87 |
1.75 |
90.4288 |
175.253 |
409.568 |
234.039 |
5179.44 |
|
200000 |
500 |
1 |
16 |
OK |
1563.2 |
|
|
1683.68 |
1.75 |
|
|
422.92 |
241.669 |
2106.6 |
|
200000 |
500 |
1 |
20 |
OK |
1725.48 |
1183.68 |
1467.61 |
4680.46 |
1.75 |
90.5425 |
170.708 |
405.248 |
231.57 |
5085.71 |
|
200000 |
500 |
1 |
20 |
OK |
1567.65 |
|
|
1688.04 |
1.75 |
|
|
373.04 |
213.166 |
2061.08 |
|
200000 |
500 |
1 |
32 |
NConv |
1779.17 |
975.004 |
1364.82 |
4438.04 |
1000.25 |
41330.8 |
72071.4 |
176319 |
176.275 |
180757 |
|
200000 |
500 |
1 |
32 |
OK |
1519.61 |
|
|
1640.26 |
1.75 |
|
|
306.138 |
174.936 |
1946.4 |
|
200000 |
500 |
1 |
50 |
OK |
1810.88 |
958.235 |
1168.44 |
4227.22 |
1.75 |
82.4225 |
146.198 |
372.312 |
212.75 |
4599.53 |
|
200000 |
500 |
1 |
50 |
OK |
1492.2 |
|
|
1612.55 |
1.75 |
|
|
266.378 |
152.216 |
1878.92 |