An angle-based optimization approach for 2D finite element mesh smoothing

A new mesh smoothing algorithm that can improve poor-quality meshes, such as meshes with badly shaped elements, is presented. Such meshes are problematic for finite element analysis since the presence of poorly formed mesh elements can reduce the accuracy of the analysis. The new algorithm introduced here improves mesh quality by adjusting the position of the mesh's internal nodes based on optimization of a torsion spring system. The Gauss–Newton method is used to optimize this spring system's objective function to obtain the optimal location of each internal node. Demonstration of the improvement offered by application of the algorithm to real meshes is also made.