Designing Parallel Adaptive Laplacian Smoothing for Improving Tetrahedral Mesh Quality on the GPU

Abstract

Mesh quality is a critical issue in numerical computing because it directly impacts both computational efficiency and accuracy. Tetrahedral meshes are widely used in various engineering and science applications. However, in large-scale and complicated application scenarios, there are a large number of tetrahedrons, and in this case, the improvement of mesh quality is computationally expensive. Laplacian mesh smoothing is a simple mesh optimization method that improves mesh quality by changing the locations of nodes. In this paper, by exploiting the parallelism features of the modern graphics processing unit (GPU), we specifically designed a parallel adaptive Laplacian smoothing algorithm for improving the quality of large-scale tetrahedral meshes. In the proposed adaptive algorithm, we defined the aspect ratio as a metric to judge the mesh quality after each iteration to ensure that every smoothing improves the mesh quality. The adaptive algorithm avoids the shortcoming of the ordinary Laplacian algorithm to create potential invalid elements in the concave area. We conducted 5 groups of comparative experimental tests to evaluate the performance of the proposed parallel algorithm. The results demonstrated that the proposed adaptive algorithm is up to 23 times faster than the serial algorithms; and the accuracy of the tetrahedral mesh is satisfactorily improved after adaptive Laplacian mesh smoothing. Compared with the ordinary Laplacian algorithm, the proposed adaptive Laplacian algorithm is more applicable, and can effectively deal with those tetrahedrons with extremely poor quality. This indicates that the proposed parallel algorithm can be applied to improve the mesh quality in large-scale and complicated application scenarios.