Efficient, GPU-based 2D mesh smoothing

Efficient parallel approaches for three popular 2D mesh smoothing algorithms (useful for improving finite element meshes) are presented. The approaches operate on commodity, programmable GPUs and use a single thread per internal vertex of the mesh to reposition those vertices to more optimal locations, according to the smoothing algorithms. The approaches use a custom data structure called a neighbor list for all three algorithms. Following internal vertex detection, the approaches use the neighbor list representation in fast processing on the GPU. A memory-based performance consideration and sample results (suggesting 10 times speedup for two of the algorithms and 50 times speedup for the other) are also presented here.