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

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.

simple technique for unstructured mesh generation via adaptive finite elements

This work describes a concise algorithm for the generation of triangular meshes with the help of standard adaptive finite element methods. We demonstrate that a generic adaptive finite element solver can be repurposed into a triangular mesh generator if a robust mesh smoothing algorithm is applied between the mesh refinement steps. We present an implementation of the mesh generator and demonstrate the resulting meshes via examples.

Efficient Parallel Algorithms for 3D Laplacian Smoothing on the GPU

In numerical modeling, mesh quality is one of the decisive factors that strongly affects the accuracy of calculations and the convergence of iterations. To improve mesh quality, the Laplacian mesh smoothing method, which repositions nodes to the barycenter of adjacent nodes without changing the mesh topology, has been widely used. However, smoothing a large-scale three dimensional mesh is quite computationally expensive, and few studies have focused on accelerating the Laplacian mesh smoothing method by utilizing the graphics processing unit (GPU). This paper presents a GPU-accelerated parallel algorithm for Laplacian smoothing in three dimensions by considering the influence of different data layouts and iteration forms. To evaluate the efficiency of the GPU implementation, the parallel solution is compared with the original serial solution. Experimental results show that our parallel implementation is up to 46 times faster than the serial version.

Three-Dimensional Numerical Analysis of Horizontal and Vertical Coalescence of Bubbles at Two Submerged Horizontal Orifices on the Wall

In the process of bubbling from two submerged adjacent orifices, bubbles coalescence becomes inevitable. But the study of the evolution and interaction of bubbles from submerged orifices is little, especially numerical simulation. In this paper, combined with mesh smoothing technique, mesh subdivision technique and the technique of axisymmetric coalescence and 3D coalescence, a three-dimensional model of bubbles coalescence at two submerged adjacent orifices on the wall is established by the boundary element method. Then, numerical simulations were carried out for horizontal and vertical coalescence before detachment. Finally, by changing the ventilation rate and the Froude number, the effects of different ventilation rates and buoyancy on the process of bubbles coalescence at two adjacent orifices were investigated. The results show that for horizontal coalescence, the effect of ventilation rate is more pronounced than buoyancy. As the ventilation rate increases or the influence of buoyancy is decreased, the amplitude of internal pressure fluctuation of the bubble decreases and the coalescence time decreases. For vertical coalescence, the effect of buoyancy is more pronounced than ventilation rate. With the influence of buoyancy is decreased, the vertical coalescence time is increased, the internal pressure of the bubble is decreased. The influence of ventilation rate is similar to that of horizontal coalescence.