The Modified Direct Method: An Iterative Approach for Smoothing Planar Meshes

The Modified Direct Method (MDM) is an iterative method for smoothing planar triangular, quadrilateral and tri-quad meshes, which has been developed from the non-iterative smoothing method for planar meshes that was originated by Balendran [1] . Its simple aim is to make triangular elements as close to equilateral as possible and quadrilateral elements as close to square as possible. The MDM is the computationally simpler of the two methods. The performance of the MDM for both triangular and quadrilateral meshes is effectively identical to that of Laplacian smoothing; however, it outperforms Laplacian smoothing for tri-quad meshes. Test examples show that the MDM is always convergent for triangular, quadrilateral and tri-quad meshes.