SuperMeshing: Boosting the Mesh Density of Stress Field in Plane-Strain Problems Using Deep Learning Method

The increase of the spatial resolution in numerical computation always leads to a decrease in computing efficiency with respect to the constraint of mesh density. In response to this problem of the inability to perform numerical computation, we propose a novel method to boost the mesh-density in the finite element method (FEM) within 2D domains. Running on the von Mises stress fields of the 2D plane-strain problems computed by FEM, the proposed method utilizes a deep neural network named SMNet to learn a nonlinear mapping from low mesh-density to high mesh-density in stress fields and realizes the improvement of numerical computation accuracy and efficiency simultaneously. By introducing residual density blocks into SMNet, we can extract abundant local features and improve prediction capacity. The result indicates that SMNet can effectively increase the spatial resolution of stress fields under multiple scaling factors in mesh-density: 2 ×, 3 ×, and 4 ×. Compared with the targets, the relative error of SMNet is $1.67%$⁠, showing better performance than many other methods. SMNet can be generically used as an enhanced mesh-density boosting model of 2D physical fields for mesh-based numerical methods.