Table 2 The smallest eigenvalue solved by Algorithm 2 and Algorithm 2M
From: Adaptive Morley element algorithms for the biharmonic eigenvalue problem
l | \(N_{\mathrm{dof}}\) | \(h_{l}\) | \(\frac{h_{l}}{h_{l_{\min}}^{\alpha}}\) | \(\lambda_{1,h_{l}}^{R}\) | CPU(s) | \(N_{\mathrm{dof}}\) | \(h_{l}\) | \(\frac{h_{l}}{h_{l_{\min}}^{\alpha}}\) | \(\lambda_{1,h_{l}}^{\mathrm{RM}}\) | CPU(s) |
|---|---|---|---|---|---|---|---|---|---|---|
1 | 2945 | 0.044 | 0.210 | 6333.637 | 0.133 | 2945 | 0.044 | 0.210 | 6333.637 | 0.090 |
2 | 2957 | 0.044 | 0.297 | 6373.503 | 0.228 | 2957 | 0.044 | 0.297 | 6373.503 | 0.140 |
3 | 3031 | 0.044 | 0.354 | 6538.971 | 0.280 | 3031 | 0.044 | 0.354 | 6538.971 | 0.192 |
4 | 3067 | 0.044 | 0.420 | 6443.737 | 0.371 | 3067 | 0.044 | 0.420 | 6443.737 | 0.250 |
5 | 3237 | 0.044 | 0.500 | 6489.761 | 0.426 | 3237 | 0.044 | 0.500 | 6489.761 | 0.305 |
6 | 3445 | 0.044 | 0.595 | 6523.466 | 0.487 | 3445 | 0.044 | 0.595 | 6523.466 | 0.365 |
7 | 3811 | 0.044 | 0.707 | 6566.620 | 0.560 | 3811 | 0.044 | 0.707 | 6566.620 | 0.431 |
8 | 4195 | 0.044 | 0.841 | 6595.431 | 0.636 | 4195 | 0.044 | 0.841 | 6595.431 | 0.504 |
9 | 4678 | 0.044 | 1.00 | 6597.955 | 0.720 | 4678 | 0.044 | 1.00 | 6597.955 | 0.588 |
10 | 5293 | 0.044 | 1.19 | 6607.441 | 0.814 | 5293 | 0.044 | 1.19 | 6607.441 | 0.709 |
11 | 6118 | 0.044 | 1.41 | 6623.248 | 0.924 | 25,297 | 0.022 | 0.841 | 6683.573 | 1.15 |
12 | 6997 | 0.044 | 1.68 | 6634.588 | 1.05 | 27,723 | 0.022 | 1.00 | 6686.324 | 1.63 |
13 | 8232 | 0.044 | 2.00 | 6648.804 | 1.20 | 30,933 | 0.022 | 1.19 | 6688.518 | 2.38 |
14 | 9527 | 0.044 | 2.38 | 6658.106 | 1.39 | 139,409 | 0.011 | 0.841 | 6700.069 | 5.87 |
15 | 11,102 | 0.044 | 2.83 | 6663.393 | 1.59 | 153,179 | 0.011 | 1.00 | 6700.762 | 9.71 |
16 | 12,928 | 0.044 | 3.36 | 6667.166 | 1.82 | 168,897 | 0.011 | 1.19 | 6701.161 | 15.4 |
17 | 15,139 | 0.044 | 4.00 | 6673.763 | 2.11 | 740,417 | 0.006 | 0.841 | 6702.983 | 39.1 |
18 | 17,619 | 0.044 | 4.76 | 6678.433 | 2.43 | 807,451 | 0.006 | 1.00 | 6703.097 | 65.4 |
19 | 20,763 | 0.044 | 5.66 | 6682.562 | 2.82 | 882,597 | 0.006 | 1.19 | 6703.149 | 103 |
20 | 24,365 | 0.044 | 6.73 | 6685.164 | 3.27 | 3,907,351 | 0.003 | 0.841 | 6703.486 | 236 |
21 | 28,967 | 0.044 | 8.00 | 6687.944 | 3.81 | 4,218,771 | 0.003 | 1.00 | 6703.504 | 382 |
22 | 34,068 | 0.044 | 9.51 | 6690.675 | 4.50 | – | – | – | – | – |
23 | 40,007 | 0.044 | 11.3 | 6692.914 | 5.39 | – | – | – | – | – |
24 | 47,117 | 0.044 | 13.5 | 6694.937 | 6.46 | – | – | – | – | – |
25 | 55,275 | 0.044 | 16.0 | 6696.294 | 7.64 | – | – | – | – | – |
26 | 64,407 | 0.044 | 19.0 | 6696.867 | 9.09 | – | – | – | – | – |
27 | 75,259 | 0.031 | 13.5 | 6697.823 | 10.8 | – | – | – | – | – |
28 | 88,353 | 0.031 | 16.0 | 6698.752 | 13.2 | – | – | – | – | – |
29 | 104,269 | 0.031 | 19.0 | 6699.457 | 16.1 | – | – | – | – | – |
30 | 123,285 | 0.031 | 22.6 | 6700.133 | 19.4 | – | – | – | – | – |
31 | 145,061 | 0.031 | 26.9 | 6700.774 | 23.3 | – | – | – | – | – |
32 | 170,397 | 0.022 | 22.6 | 6701.291 | 27.9 | – | – | – | – | – |
33 | 199,833 | 0.022 | 26.9 | 6701.638 | 33.5 | – | – | – | – | – |
34 | 235,261 | 0.022 | 26.9 | 6701.906 | 40.0 | – | – | – | – | – |
35 | 272,877 | 0.022 | 32.0 | 6702.117 | 48.6 | – | – | – | – | – |
36 | 319,549 | 0.022 | 38.1 | 6702.292 | 58.8 | – | – | – | – | – |
37 | 375,279 | 0.022 | 45.3 | 6702.462 | 71.1 | – | – | – | – | – |
38 | 444,149 | 0.022 | 53.8 | 6702.631 | 86.1 | – | – | – | – | – |
39 | 522,525 | 0.022 | 64.0 | 6702.819 | 104 | – | – | – | – | – |
40 | 613,375 | 0.022 | 76.1 | 6702.964 | 125 | – | – | – | – | – |
41 | 719,217 | 0.016 | 53.8 | 6703.062 | 149 | – | – | – | – | – |
42 | 844,333 | 0.016 | 64.0 | 6703.144 | 179 | – | – | – | – | – |
43 | 988,863 | 0.016 | 76.1 | 6703.208 | 214 | – | – | – | – | – |
44 | 1,150,057 | 0.016 | 90.5 | 6703.256 | 255 | – | – | – | – | – |
45 | 1,346,861 | 0.016 | 108 | 6703.292 | 304 | – | – | – | – | – |
46 | 1,584,041 | 0.016 | 128 | 6703.337 | 362 | – | – | – | – | – |
47 | 1,873,597 | 0.016 | 152 | 6703.378 | 433 | – | – | – | – | – |
48 | 2,196,067 | 0.011 | 108 | 6703.422 | 509 | – | – | – | – | – |
49 | 2,572,281 | 0.011 | 128 | 6703.454 | 598 | – | – | – | – | – |
50 | 3,010,543 | 0.011 | 152 | 6703.474 | 705 | – | – | – | – | – |
51 | 3,538,161 | 0.011 | 181 | 6703.497 | 831 | – | – | – | – | – |
52 | 4,120,833 | 0.011 | 215 | 6703.510 | 979 | – | – | – | – | – |