3D Discrete Skeleton Generation by Wave Propagation on PR-Octree for Finite Element Mesh Sizing

Abstract

This paper proposes a new algorithm to generate a disconnected, three-dimensional (3D) skeleton and an application of such a skeleton to generate a finite element (FE) mesh sizing function of a solid. The mesh sizing function controls the element size and the gradient, and it is crucial in generating a desired FE mesh. Here, a geometry-based mesh sizing function is generated using a skeleton. A discrete skeleton is generated by propagating a wave from the boundary towards the interior on an octree lattice of an input solid model. As the wave propagates, the distance from the boundary and direction of the wave front are calculated at the lattice-nodes (vertices) of the new front. An approximate Euclidean distance metric is used to calculate the distance traveled by the wave. Skeleton points are generated at the region where the opposing fronts meet. The distance at these skeleton points is used to measure both proximity between geometric entities and feature size, and is utilized to generate the mesh size at the lattice-nodes. The proposed octree-based skeleton is more accurate and efficient than traditional voxel-based skeleton and proves to be great tool for mesh sizing function generation.