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An Efficient Parallel Algorithm for Mesh Smoothing

Freitag, Lori, Mark Jones, and Paul Plassmann

Proceedings, 4th International Meshing Roundtable, Sandia National Laboratories, pp.47-58, October 1995


Automatic mesh generation and adaptive refinement methods have proven to be very successful tools for the efficient solution of complex finite element applications. A problem with these methods is that they can produce poorly shaped elements; such elements are undesirable because they introduce numerical difficulties in the solution process. However, the shape of the elements can be improved through the determination of new geometric locations for mesh vertices by using a mesh smoothing algorithm. In this paper we present a new parallel algorithm for mesh smoothing that has a fast parallel runtime both in theory and in practice. We present an efficient implementation of the algorithm that uses non-smooth optimization techniques to find the new location of each vertex. Finally we present experimental results obtained on the IBM SP system demonstrating the efficiency of this approach.

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