Table 1 The smallest eigenvalue solved by Algorithm 1 and Algorithm 1M
From: Adaptive Morley element algorithms for the biharmonic eigenvalue problem
l | \(N_{\mathrm{dof}}\) | \(h_{l}\) | \(\frac{h_{l}}{h_{l_{\min}}^{\alpha}}\) | \(\lambda_{1,h_{l}}\) | CPU(s) | \(N_{\mathrm{dof}}\) | \(h_{l}\) | \(\frac{h_{l}}{h_{l_{\min}}^{\alpha}}\) | \(\lambda_{1,h_{l}}^{M}\) | CPU(s) |
|---|---|---|---|---|---|---|---|---|---|---|
1 | 2945 | 0.044 | 0.210 | 6333.637 | 0.275 | 2945 | 0.044 | 0.210 | 6333.637 | 0.086 |
2 | 2957 | 0.044 | 0.250 | 6368.756 | 0.368 | 2957 | 0.044 | 0.250 | 6368.756 | 0.162 |
3 | 3035 | 0.044 | 0.297 | 6426.312 | 0.452 | 3035 | 0.044 | 0.297 | 6426.312 | 0.239 |
4 | 3135 | 0.044 | 0.354 | 6459.396 | 0.537 | 3135 | 0.044 | 0.354 | 6459.396 | 0.320 |
5 | 3345 | 0.044 | 0.420 | 6506.181 | 0.629 | 3345 | 0.044 | 0.420 | 6506.181 | 0.405 |
6 | 3609 | 0.044 | 0.500 | 6540.464 | 0.726 | 3609 | 0.044 | 0.500 | 6540.464 | 0.499 |
7 | 3979 | 0.044 | 0.595 | 6574.027 | 0.834 | 3979 | 0.044 | 0.595 | 6574.027 | 0.605 |
8 | 4459 | 0.044 | 0.707 | 6588.671 | 0.957 | 4459 | 0.044 | 0.707 | 6588.671 | 0.723 |
9 | 5097 | 0.044 | 0.841 | 6606.244 | 1.10 | 5097 | 0.044 | 0.841 | 6606.244 | 0.860 |
10 | 5787 | 0.044 | 1.00 | 6615.776 | 1.27 | 5787 | 0.044 | 1.00 | 6615.776 | 1.02 |
11 | 6665 | 0.044 | 1.19 | 6631.992 | 1.48 | 6665 | 0.044 | 1.19 | 6631.992 | 1.21 |
12 | 7791 | 0.044 | 1.41 | 6642.939 | 1.71 | 31,697 | 0.022 | 0.841 | 6688.240 | 2.12 |
13 | 9110 | 0.044 | 1.68 | 6656.854 | 1.97 | 34,833 | 0.022 | 1.00 | 6690.595 | 3.15 |
14 | 10,591 | 0.044 | 2.00 | 6662.468 | 2.27 | 39,191 | 0.022 | 1.19 | 6693.066 | 4.43 |
15 | 12,295 | 0.044 | 2.38 | 6665.980 | 2.65 | 173,919 | 0.011 | 0.841 | 6701.061 | 11.4 |
16 | 14,331 | 0.044 | 2.83 | 6671.824 | 3.10 | 189,989 | 0.011 | 1.00 | 6701.477 | 19.4 |
17 | 16,641 | 0.044 | 3.36 | 6676.967 | 3.62 | 211,977 | 0.011 | 1.19 | 6701.750 | 29.0 |
18 | 19,497 | 0.044 | 4.00 | 6680.844 | 4.21 | 948,969 | 0.006 | 0.841 | 6703.147 | 82.8 |
19 | 22,925 | 0.044 | 4.76 | 6684.502 | 4.92 | 1,025,149 | 0.006 | 1.00 | 6703.198 | 141 |
20 | 27,171 | 0.044 | 5.66 | 6686.546 | 5.77 | 1,131,177 | 0.006 | 1.19 | 6703.244 | 210 |
21 | 32,088 | 0.044 | 6.73 | 6689.797 | 6.76 | 5,114,697 | 0.003 | 0.841 | 6703.512 | 587 |
22 | 37,703 | 0.044 | 8.00 | 6692.349 | 7.95 | – | – | – | – | – |
23 | 44,289 | 0.044 | 9.51 | 6694.425 | 9.39 | – | – | – | – | – |
24 | 52,103 | 0.044 | 11.3 | 6695.960 | 11.1 | – | – | – | – | – |
25 | 60,857 | 0.044 | 13.5 | 6696.560 | 13.2 | – | – | – | – | – |
26 | 70,881 | 0.044 | 16.0 | 6697.400 | 15.7 | – | – | – | – | – |
27 | 83,091 | 0.031 | 13.5 | 6698.304 | 18.7 | – | – | – | – | – |
28 | 98,019 | 0.031 | 16.0 | 6699.274 | 22.7 | – | – | – | – | – |
29 | 116,273 | 0.031 | 19.0 | 6699.950 | 27.4 | – | – | – | – | – |
30 | 136,557 | 0.031 | 22.6 | 6700.589 | 33.1 | – | – | – | – | – |
31 | 160,465 | 0.022 | 16.0 | 6701.087 | 40.0 | – | – | – | – | – |
32 | 188,195 | 0.022 | 19.0 | 6701.469 | 48.2 | – | – | – | – | – |
33 | 221,401 | 0.022 | 22.6 | 6701.858 | 58.0 | – | – | – | – | – |
34 | 257,797 | 0.022 | 26.9 | 6702.060 | 69.7 | – | – | – | – | – |
35 | 301,063 | 0.022 | 32.0 | 6702.246 | 84.6 | – | – | – | – | – |
36 | 353,201 | 0.022 | 38.1 | 6702.411 | 102 | – | – | – | – | – |
37 | 416,609 | 0.022 | 45.3 | 6702.557 | 124 | – | – | – | – | – |
38 | 492,039 | 0.022 | 45.3 | 6702.767 | 151 | – | – | – | – | – |
39 | 577,233 | 0.022 | 53.8 | 6702.937 | 182 | – | – | – | – | – |
40 | 677,271 | 0.016 | 45.3 | 6703.035 | 220 | – | – | – | – | – |
41 | 793,765 | 0.016 | 53.8 | 6703.115 | 266 | – | – | – | – | – |
42 | 934,557 | 0.016 | 64.0 | 6703.190 | 321 | – | – | – | – | – |
43 | 1,084,193 | 0.016 | 64.0 | 6703.237 | 388 | – | – | – | – | – |
44 | 1,267,059 | 0.016 | 76.1 | 6703.272 | 465 | – | – | – | – | – |
45 | 1,487,051 | 0.016 | 90.5 | 6703.320 | 558 | – | – | – | – | – |
46 | 1,756,709 | 0.016 | 108 | 6703.362 | 672 | – | – | – | – | – |
47 | 2,065,245 | 0.011 | 90.5 | 6703.407 | 809 | – | – | – | – | – |
48 | 2,420,223 | 0.011 | 108 | 6703.446 | 973 | – | – | – | – | – |
49 | 2,834,373 | 0.011 | 128 | 6703.468 | 1171 | – | – | – | – | – |
50 | 3,319,763 | 0.011 | 128 | 6703.487 | 1415 | – | – | – | – | – |
51 | 3,894,763 | 0.011 | 152 | 6703.505 | 1706 | – | – | – | – | – |
52 | 4,522,239 | 0.011 | 181 | 6703.516 | 2060 | – | – | – | – | – |