MeshingNet3D: Efficient generation of adapted tetrahedral meshes for computational mechanics

We describe a new algorithm for the generation of high quality tetrahedral meshes using artificial neural networks. The goal is to generate close-to-optimal meshes in the sense that the error in the computed finite element (FE) solution (for a target system of partial differential equations (PDEs)) is as small as it could be for a prescribed number of nodes or elements in the mesh. In this paper we illustrate and investigate our proposed approach by considering the equations of linear elasticity, solved on a variety of three-dimensional geometries. This class of PDE is selected due to its equivalence to an energy minimization problem, which therefore allows a quantitative measure of the relative accuracy of different meshes (by comparing the energy associated with the respective FE solutions on these meshes). Once the algorithm has been introduced it is evaluated on a variety of test problems, each with its own distinctive features and geometric constraints, in order to demonstrate its effectiveness and computational efficiency.