On the Application of Two Symmetric Gauss Legendre Quadrature Rules for Composite Numerical Integration Over a Tetrahedral Region

摘要

In this paper, we have presented the composite numerical integration formulae, which can be derived by decomposing the tetrahedron into four tetrahedra by joining the centroid to four vertices. We have further shown that the standard tetrahedron can be discretised into 2{sup}3, 3{sup}3,...,8{sup}3 tetrahedra of equal volume. Over each of these the Gauss Legendre quadrature rules developed in section 2 are applicable. We have also applied the composite rule, which is derived in section 3 by discretising the standard tetrahedron into four equal tetrahedra by joining the centroid to its four vertices. This integrates the standard tetrahedron by discretising into 4 × 2{sup}3, 4 × 3{sup}3,...,4 × 8{sup}3 tetrahedra of equal volume.