A local simulated annealing strategy for mesh optimization

We consider a metric-driven mesh optimization procedure for anisotropic simplicial meshes based on the Simulated Annealing method. The use of Simulated Annealing improves the chances of removing pathological clusters of bad elements that have the tendency to lock into frozen configurations in difficult regions of the model such as corners and complex face intersections, prejudicing the overall quality of the final grid. The Simulated Annealing optimization procedure brings substantial improvement in the quality of the worst elements of the grid, compared to the classical greedy Gauss-Seidel optimization, but this improved performance may come at an increased computational cost. In order to remedy this problem, we suggest in this work a local implementation of the scheme which is effective in reducing the computational cost to approximately the same level of a classical greedy algorithm.