Research Article
Numerical Integration of Some Arbitrary Functions over an Ellipsoid by Discretizing into Hexahedral Elements for Biomaterial Studies
Table 5
Integral results for quadratic tetrahedral elements: comparison with GGQ and GQ.
| Sl. No | Functions | Exact value | 10 N | GGQ (N = 5) | N = 10 | N = 15 | N = 20 |
| 1 | | 2.3561 | 2.3632 | 2.3627 | 2.3632 | 2.3632 | 2.3632 | N = 4 | N = 6 | N = 8 | N = 10 | 2.3563 | 2.3563 | 2.3562 | 2.3561 |
| 2 | 1 | 3.1415 | 3.1215 | 3.1215 | | | | N = 4 | N = 6 | N = 8 | N = 10 | 3.1315 | 3.1315 | 3.1415 | 3.1415 |
| 3 | | 0.7500 | 0.7527481408 | 0.7527 | | | | N = 4 | N = 6 | N = 8 | N = 10 | 0.7512 | 0.7512 | 0.7500 | 0.7500 |
| 4 | | 0.6857 | 0.6914 | 0.6914 | | | | N = 4 | N = 6 | N = 8 | N = 10 | 0.6884 | 0.6860 | 0.6859 | 0.6857 |
| 5 | | NInt = 4.6396 | 4.6108 | 4.6108 | | | | N = 4 | N = 6 | N = 8 | N = 10 | 4.6108 | 4.6108 | 4.6108 | 4.6108 |
| 6 | | NInt = 2.2146 | 2.1105 | 2.2008 | | | | N = 4 | N = 6 | N = 8 | N = 10 | 2.2005 | 2.2007 | 2.2008 | 2.2008 |
| 7 | | 3.2313 | 3.2773 | 3.2773 | | | | N = 4 | N = 6 | N = 8 | N = 10 | 3.2631 | 3.2438 | 3.2354 | 3.2313 |
| 8 | | 0.0580 | 0.0419 | 0.04871 | | | | N = 4 | N = 6 | N = 8 | N = 10 | 0.0589 | 0.0585 | 0.0582 | 0.0580 |
| 9 | | Singularity and highly oscillatory function | 1.9206 | | | | N = 4 | N = 6 | N = 8 | N = 10 | 1.9211 | 1.9268 | 9.2614 | 9.2614 |
| 10 | | 2.2884 | 2.2894 | 2.3632 | | | | N = 4 | N = 6 | N = 8 | N = 10 | 2.3426 | 2.3126 | 2.2884 | 2.2884 |
| 11 | | 2.5132 | | 2.4826 | | | | N = 4 | N = 6 | N = 8 | N = 10 | 2.4726 | 2.4966 | 2.5132 | 2.5132 |
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