Learned Gaussian quadrature for enriched solid finite elements

We propose a novel Gaussian quadrature, referred to as the learned Gaussian quadrature, that is obtained by employing a supervised learning algorithm to find improved weights for the matrix integrations of 2D and 3D enriched solid finite elements. As the algorithm employs the intuitive relationship between a target matrix and improved Gaussian weights, it successfully finds the learned Gaussian quadrature only using a simple network. The learned Gaussian quadrature accurately calculates the matrix with fewer integration points than the standard Gaussian quadrature, thereby increasing the computational efficiency of the enriched finite elements. Using various numerical examples, the theoretical convergence behavior of the enriched solid finite elements with the learned Gaussian quadrature is first investigated, and then, the practical performances are measured. (c) 2023 Elsevier B.V. All rights reserved.