Hybrid OpenMP/MPI anisotropic mesh smoothing

Mesh smoothing is an important algorithm for the improvement of element quality in unstructured mesh finite element methods. A new optimisation based mesh smoothing algorithm is presented for anisotropic mesh adaptivity. It is shown that this smoothing kernel is very effective at raising the minimum local quality of the mesh. A number of strategies are employed to reduce the algorithm's cost while maintaining its effectiveness in improving overall mesh quality. The method is parallelised using hybrid OpenMP/MPI programming methods, and graph colouring to identify independent sets. Different approaches are explored to achieve good scaling performance within a shared memory compute node.