TETRAHEDRAL MESH SMOOTHING BASED ON NON-SMOOTH OPTIMIZATION PROBLEM

Abstract

A tetrahedral mesh smoothing algorithm based on non-smooth problem optimization is presented. Firstly the tetrahedral mesh smoothing 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. The numerical examples show that the algorithm is efficient, easy to be implemented and can get quality elements.