HMSimNet: A hexahedral mesh simplification network model for preserving analysis accuracy

The structure of a hexahedral mesh can be simplified after the mesh has been generated to meet specific requirements, enhancing the analysis precision and efficiency while conserving the storage space. However, the existing methods for mesh simplification do not conduct the physical analysis, so simplified meshes cannot meet the accuracy requirement. To address this shortcoming, this paper presents a network model named HMSimNet for simplifying hexahedral meshes, which can reduce the number of mesh cells while maintaining analysis accuracy. First, the sheets and columns are described using four types of features: geometric, topological, quality, and physical features. Then, a dataset is constructed and used to train the HMSimNet model to learn the relationship between the features and the analysis accuracy. Finally, the probabilities of deleting the sheets and columns are determined by the HMSimNet model, and the sheets and columns with a minor impact on the analysis accuracy are removed iteratively. The experimental results demonstrate that, compared to the input hexahedral meshes, the presented method can significantly reduce the number of hexahedra by approximately 30% while having only a slight impact on the maximum relative error of the analysis.