In 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 $\mathtt{\text{Matlab}}\circledR$ format.

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论文“四面体和金字塔的高阶对称培养规则”的附录

在Jaśkowiec和Sukumar（Int J Numer Methods Eng，doi：10.1002 / nme.6528，2020）中，我们提出了关于四面体和金字塔的高阶（p  = 2 – 20）对称培养皿规则。该算法对孵化器节点的初始位置敏感，并且对于p  > 11不会收敛在棱镜和六面体（立方体）上。在本附录中，我们解决了此问题，并获得了有关棱镜和立方体的高阶对称规则。对于棱镜，我们将对容积规则的初始猜测用作三角形上的容积规则和单变量高斯正交规则的张量积，对于立方体，初始猜测是对单变量高斯正交规则的张量积。进行验证和收敛测试以确认培养规则的准确性。在应用Jaśkowiec和Sukumar（Int J Numer Methods Eng，121（11），2418-2436，2020）中描述的孵化算法时，我们还构造了非对称高阶（p  = 2–20）棱柱，立方体和金字塔上的孵化规则。在补充材料中，所有的孵化规则（精度为128位）都在文本文件和$\mathtt{\text{Matlab的}}\circledR$ 格式。