Global Energy Minimization for Simplex Mesh Optimization: A Radius Ratio Approach to Sliver Elimination

This paper constructs an energy function for simplex mesh based on the radius ratio and develops a corresponding mesh optimization method. The method combines vertex relocation and connectivity improvement, and can effectively remove slivers and improve the overall mesh quality. Based on the structure of the gradient of the energy function, we design a preconditioner, which reduces the number of iterations and improves the efficiency of the optimization algorithm. Numerical experiments show that the proposed method is effective in both sliver removal and mesh quality improvement.