GPU-Accelerated Optimization Of Tetrahedral Mesh

The finite element method is used extensively in many fields of engineering, including industrial product analysis. Tetrahedral meshes are a commonly choice in three-dimensional domains, and can be generated by advancing front, Delaunay, or octree methods. However, poorly-shaped tetrahedra, which can introduce numerical errors and increase the time, are generated no matter which mesh generation algorithm is used. Hence, it is necessary to improve the quality of the tetrahedra in an existing mesh. Although existing mesh improvement techniques are usually effective, they are quite time consuming. Therefore, this paper proposes using GPU to accelerate the tetrahedral mesh improvement. The contributions of this paper are as follows:1. This paper presents a GPU-accelerated vertex smoothing algorithm. We use vertex coloring method to group vertex, those vertices in one group can be parallelly smoothed. We implement GPU-accelerated laplacian smoothing, and verified the algorithm.2. This paper presents a uniform process of GPU-accelerated algorithm for topology optimization of tetrahedral mesh.3. This paper verifies the process by using it to indicate the GPU-accelerated algorithm design for Flip3-2, Flip2-3and edge contraction.4. This paper simplifies the vertex insertion method for parallel algorithm design. And then, we design a GPU-accelerated vertex insertion under the indication of the uniform process.This paper proposes the GPU-accelerated tetrahedral mesh optimization algorithm, and after a lot of experiments, we consider that the size of the tetrahedral mesh is more larger, then the GPU acceleration is more remarkable, for those big models, our algorithm can increase the time efficiency by more than one order of magnitude.