  In this paper we specifically present a parallel solution to finding the
one-ring neighboring nodes and elements for each vertex in generic meshes. The
finding of nodal neighbors is computationally straightforward but expensive for
large meshes. To improve the efficiency, the parallelism is adopted by
utilizing the modern Graphics Processing Unit (GPU). The presented parallel
solution is heavily dependent on the parallel sorting, scan, and reduction, and
can be applied to determine both the neighboring nodes and elements. To
evaluate the performance, the parallel solution is compared to the
corresponding serial solution. Experimental results show that: our parallel
solution can achieve the speedups of approximately 55 and 90 over the
corresponding serial solution for finding neighboring nodes and elements,
respectively. Our parallel solution is efficient and easy to implement, but
requires the allocation of large device memory.
