A Parallel Algorithm for Mesh Smoothing

Maintaining good mesh quality during the generation and refinement of unstructured meshes in finite-element applications is an important aspect in obtaining accurate discretizations and well-conditioned linear systems. In this article, we present a mesh-smoothing algorithm based on nonsmooth optimization techniques and a scalable implementation of this algorithm. We report mesh improvement results for twodimensional simplicial meshes that demonstrate the effectiveness of this approach for a number of different test cases. We also show the scalability of the parallel algorithm on the IBM SP supercomputer and an ATM-connected network of SPARC Ultras. 1 Introduction Unstructured meshes have proven to be an essential tool in the numerical solution of largescale scientific and engineering applications on complex computational domains. A problem with such meshes is that the shape of the elements in the mesh can vary significantly, and this variation can affect the accuracy of the numerical ..