Table 2.
Iteration numbers (it.), condition numbers and computational time (in s) for each preconditioning technique using elements; ℓ is the level of uniform refinement. For the L2 error the definition is given in (53), while for the estimated error of convergence eoc the definition is given in (54).
| all-floating | |||||||||||
| ℓ | identity prec. | lumped prec. | Dirichlet prec. | L2 error | eoc | ||||||
| 1 | 61 it. | 53.6 | 20.9 s | 27 it. | 10.3 | 19.7 s | 21 it. | 7.6 | 19.5 s | 1.42E-04 | - |
| 2 | 71 it. | 70.0 | 19.6 s | 38 it. | 19.7 | 18.8 s | 26 it. | 10.4 | 18.4 s | 3.71E-05 | 1.94 |
| 3 | 88 it. | 108.8 | 21.7 s | 45 it. | 26.1 | 22.3 s | 27 it. | 9.7 | 22.3 s | 9.40E-06 | 1.98 |
| 4 | 119 it. | 216.8 | 28.8 s | 62 it. | 53.2 | 26.4 s | 32 it. | 13.1 | 26.6 s | 2.37E-06 | 1.99 |
| 5 | 160 it. | 432.7 | 116.6 s | 91 it. | 126.2 | 99.0 s | 37 it. | 16.8 | 105.9 s | 5.96E-07 | 1.99 |
|
| |||||||||||
| classical | |||||||||||
| ℓ | identity prec. | lumped prec. | Dirichlet prec. | L2 error | eoc | ||||||
| 1 | 80 it. | 98.2 | 7.1 s | 35 it. | 14.1 | 5.9 s | 29 it. | 10.0 | 5.9 s | 1.47E-04 | - |
| 2 | 105 it. | 161.4 | 7.8 s | 58 it. | 41.9 | 6.1 s | 37 it. | 16.4 | 5.8 s | 3.72E-05 | 1.98 |
| 3 | 140 it. | 295.7 | 9.3 s | 85 it. | 105.9 | 7.9 s | 46 it. | 25.4 | 7.7 s | 9.41E-06 | 1.98 |
| 4 | 188 it. | 580.9 | 15.2 s | 125 it. | 252.1 | 13.1 s | 54 it. | 35.8 | 12.2 s | 2.37E-06 | 1.99 |
| 5 | 251 it. | 1150.3 | 103.4 s | 179 it. | 555.7 | 88.2 s | 60 it. | 46.3 | 83.6 s | 5.96E-07 | 1.99 |