2D Mesh smoothing based on Markov chain method

The mesh quality is of vital importance to obtain the numerical results precisely. Poorly shaped or distorted elements can be produced by automatic mesh generation tools. In this article, the mesh smoothing algorithm based on the Markov chain Monte Carlo method is proposed to improve the quality of the mesh. The movement of nodes position is converted to a stochastic process to seek the best position for the element quality. Compared with the widely known Laplacian smoothing and optimization-based smoothing techniques, the mesh quality by the proposed method is found better than these methods. Examples are performed to illustrate the applicability of the approach. The numerical results show that the proposed algorithm is effective and valuable.