深層学習による要素積分の最適化

抄録

Element stiffness matrices in the FEM are usually calculated using Gauss-Legendre quadrature, and the accuracy of the stiffness matrix of an element depends on the shape of the element. Optimizing quadrature parameters can help to improve the accuracy of the stiffness matrix, and a new method to predict optimal quadrature parameters to be used for each element by deep learning has been proposed. Using the predicted quadrature parameters for the numerical quadrature of an element, one can expect much better accuracy for the stiffness matrix. In this paper, optimal quadrature parameters for many elements are obtained using the steepest decent method, and a feed forward neural network is trained using the obtained parameters. Characteristics of the proposed method are investigated in detail.