Research And Implementation Of Tetrahedral Mesh Smoothing Algorithm

Automatic 3D mesh generation research has made much more important progress, and some effective methods have been presented, such as AFT (Advancing Front Technique), Delaunay triangulation algorithm, and Octree algorithm. However, these algorithms may generate poorly shaped or distorted elements inevitably, which cause inaccurate result in finite element computation, even make calculation impossible. In a word, 3D tetrahedral mesh smoothing becomes another key step after tetrahedral mesh generation.A number of algorithms of finite element mesh optimization used extensively are introduced summarily at first. At last, an algorithm of tetrahedral mesh smoothing algorithm based-on non-smooth optimization is investigated primarily. By the end, several mesh generation examples are given to demonstrate the validity of the algorithm.The traditional smoothing algorithm is based on single point movement. Whether separate use or mixed use, the optimization problem of non-insular bad element, especially of zero volume bad elements, can't be settled.A tetrahedral mesh smoothing algorithm based-on non-smooth problem optimization is presented. Firstly the tetrahedral mesh smooth problem is formulated as a min-max constrained optimization problem. And then an efficient solution algorithm based on entropy theory for non-smooth optimization problem is employed. The algorithm provides an equivalent smooth function of the non-smooth objective function and transforms the constrained optimization problem into a minimum unconstraint optimization problem, and then it is solved with the common optimization toolkit. In the process of mesh smoothing, a multi-point concurrent optimization technique is proposed, which can solve the optimization of tetrahedral mesh efficiently, and especially will be suitable for the optimization problem of non-insular bad element.According to the above-mentioned algorithm, a program is implemented in C++ language. The numerical examples show that the algorithm in this paper is efficient, easy to be implemented and can get quality elements.