Geometry-aware generative hybrid meshing with anisotropic and isotropic elements

The generation of hybrid anisotropic-isotropic meshes is a crucial step in computational simulations, as it allows for the accurate representation of both isotropic and anisotropic physical properties. However, existing methods used for mesh generation typically rely on user-defined mesh size distributions (MSDs), which can be labor-intensive and may not adapt well to complex geometries. Moreover, due to the highly nonlinear relationship, it is challenging to directly generate the corresponding hybrid anisotropic-isotropic mesh from the geometric shape. In this paper, we propose GAIMesh, a data-driven end-to-end geometry-aware anisotropic-isotropic hybrid mesh generation framework based on artificial intelligence, to conditionally map the geometric shapes to hybrid meshes. The whole framework consists of three parts: geometric feature network (GFN), mesh diffusion network (MDN), and mesh mapping network (MMN). The GFN extracts the geometric features from the rasterized representation of the geometry, which enhances the representational ability of the extracted geometric features and mesh resolution independence. The MDN utilizes diffusion models to progressively refine the MSD conditioned on geometric features, gradually optimizing it from an initial random distribution to the final optimal conditional distribution. The MMN maps the high-dimensional MSD to a distribution of mesh node positions in space, which effectively transforms it into mesh node layouts, completing the spatial mapping from geometry to hybrid meshes. The proposed GAIMesh framework is evaluated on various complex geometries, including general shapes, airfoils, and missiles, demonstrating its ability to directly generate geometrically aligned hybrid meshes from the input geometries. The results exhibit the potential of GAIMesh to be a flexible and reliable tool for automatic hybrid anisotropic−isotropic mesh generation in scientific and industrial fields.