Mesh Smoothing Algorithms for Complex Geometric Domains

Whenever a new mesh smoothing algorithm is introduced in the literature, initial experimental analysis is often performed on relatively simple geometric domains where the meshes need little or no element size grading. Here, we present a comparative study of a large number of well-known smoothing algorithms on triangulations of complex geometric domains. Our study reveals the limitations of some well-known smoothing methods. Specifically, the optimal Delaunay triangulation smoothing and weighted centroid of circumcenter smoothing methods are shown to have difficulty achieving smooth grading and adapting to complex domain boundary. We propose modifications and report significant improvements and behavior change in the performance of these algorithms. More importantly, we propose three new smoothing strategies and show their effectiveness in computing premium quality triangulations for complex geometric domains. While the proposed algorithms give the practitioners additional tools to chose from, our comparative study of over a dozen algorithms should guide them selecting the best smoothing method for their particular application.