Prediction of Optimal Numbers of Quadrature Points for Element Matrices with Deep Learning

Abstract

Element stiffness matrices in the FEM are usually calculated with numerical quadrature, such as the Gauss-Legendre quadrature. The accuracy of the quadrature for an element depends on its shape. Deep learning can find the optimal number of quadrature points for an element, which can improve the computational efficiency. In this paper, the DL-based prediction of the optimal number of quadrature points of finite elements is applied to quadratic elements, such as quadratic hexahedral elements and quadratic tetrahedral elements, where non-corner nodes effect the convergence of the numerical quadrature. Basic properties of the proposed method for quadratic elements are investigated in detail through some numerical examples.