A hybrid approach for optimizing planar triangular meshes

Modified Direct Method (MDM) is an iterative scheme based on Jacobi iterations for smoothing planar meshes [4]. The basic idea behind MDM is to make any triangular element be as close to an equilateral triangle as possible. Based on the MDM, a length-weighted MDM is proposed and then combined with edge swapping. In length-weighted MDM, weights of each neighboring node of a smoothed node are determined by the length of its opposite edge. Also, the MDM, Laplacian smoothing and length-weighted MDM are all combined with edge swapping, and then implemented and compared on both structured and unstructured triangular meshes. Examples show that length-weighted MDM is better than the MDM and Laplacian smoothing for structured mesh but worse for unstructured mesh. The hybrid approach of combining length-weighted MDM and edge swapping is much better and can obtain more even optimized meshes than other two hybrid approaches.