MGNet: a novel differential mesh generation method based on unsupervised neural networks

Mesh generation accounts for a large number of workloads in the numerical analysis. In this paper, we introduce a novel differential method MGNet for structured mesh generation. The proposed method poses the meshing task as an optimization problem. It takes boundary curves as input, employs a well-designed neural network to study the potential meshing (mapping) rules, and finally outputs the mesh with a desired number of cells. The whole process is unsupervised and does not require a priori knowledge or measured datasets. We evaluate the performance of MGNet in terms of mesh quality, network designs, robustness, and overhead on different geometries and governing equations (elliptic and hyperbolic). The experimental results prove that, in all cases, the proposed method is capable of generating acceptable meshes and achieving comparable or superior meshing performance to the traditional algebraic and differential methods. The proposed MGNet also outperforms other neural network-based solvers and enables fast mesh generation using feedforward prediction techniques.