Addendum to the paper “High‐order symmetric cubature rules for tetrahedra and pyramids”

Abstract

AbstractIn Jaśkowiec and Sukumar (Int J Numer Methods Eng, doi: 10.1002/nme.6528, 2020), we presented high‐order (p = 2–20) symmetric cubatures rules for tetrahedra and pyramids. This algorithm was sensitive to the initial location of the cubature nodes, and it did not converge for p > 11 over prisms and hexahedra (cubes). In this addendum, we resolve this issue and obtain high‐order symmetric rules over prisms and cubes. For the prism, we use the initial guess for the cubature rule as the tensor product of a cubature rule over a triangle and a univariate Gauss quadrature rule, and for the cube the initial guess is the tensor product of univariate Gauss quadrature rules. Verification and convergence tests are presented to affirm the accuracy of the cubature rules. On applying the cubature algorithm described in Jaśkowiec and Sukumar (Int J Numer Methods Eng, 121(11), 2418–2436, 2020), we also construct nonsymmetric high‐order (p = 2–20) cubature rules over prisms, cubes, and pyramids. In the supplementary materials, all cubature rules (128 digits of precision) are provided in a text file and in format.