A parallel log-barrier method for mesh quality improvement and untangling

The development of parallel algorithms for mesh generation, untangling, and quality improvement is of high importance due to the need for large meshes with millions to billions of elements and the availability of supercomputers with hundreds to thousands of cores. There have been prior efforts in the development of parallel algorithms for mesh generation and local mesh quality improvement in which only one vertex is moved at a time. But for global mesh untangling and for global mesh quality improvement, where all vertices are simultaneously moved, parallel algorithms have not yet been developed. In our earlier work, we developed a serial global mesh optimization algorithm and used it to perform mesh untangling and mesh quality improvement. Our algorithm moved the vertices simultaneously to optimize a log-barrier objective function that was designed to untangle meshes as well as to improve the quality of the worst quality mesh elements. In this paper, we extend our work and develop a parallel log-barrier mesh untangling and mesh quality improvement algorithm for distributed-memory machines. We have used the algorithm with an edge coloring-based algorithm for synchronizing unstructured communication among the processes executing the log-barrier mesh optimization algorithm. The main contribution of this paper is a generic scheme for global mesh optimization, whereby the gradient of the objective function with respect to the position of some of the vertices is communicated among all processes in every iteration. The algorithm was implemented using the OpenMPI 2.0 parallel programming constructs and shows greater strong scaling efficiency compared to an existing parallel mesh quality improvement technique.