The Modified Direct Method: an Approach for Smoothing Planar and Surface Meshes

TL;DR

The Modified Direct Method (MDM) is an iterative mesh smoothing technique that improves mesh quality for planar and surface meshes, outperforming traditional methods like Laplacian smoothing in various mesh configurations.

Contribution

The paper introduces the MDM, a novel iterative smoothing method that enhances mesh quality and convergence for diverse planar and surface mesh types.

Findings

MDM performs comparably to Laplacian smoothing on planar meshes.

MDM outperforms Laplacian smoothing on tri-quad meshes.

MDM increases mean quality and decreases mean square error during smoothing.

Abstract

The Modified Direct Method (MDM) is an iterative mesh smoothing method for smoothing planar and surface meshes, which is developed from the non-iterative smoothing method originated by Balendran [1]. When smooth planar meshes, the performance of the MDM is effectively identical to that of Laplacian smoothing, for triangular and quadrilateral meshes; however, the MDM outperforms Laplacian smoothing for tri-quad meshes. When smooth surface meshes, for trian-gular, quadrilateral and quad-dominant mixed meshes, the mean quality(MQ) of all mesh elements always increases and the mean square error (MSE) decreases during smoothing; For tri-dominant mixed mesh, the quality of triangles always descends while that of quads ascends. Test examples show that the MDM is convergent for both planar and surface triangular, quadrilateral and tri-quad meshes.