Relative Performance of Geometric Search Algorithms for Interpolating Unstructured Mesh Data

Interpolation of field data from unstructured meshes requires the potentially expensive identification of the finite element or volume within which the interpolating point lies. A number of geometric search algorithms have been proposed to reduce this expense at the cost of setting up and storing additional search tables. Using tetrahedral finite element models we show that a structured auxiliary mesh (SAM) algorithm can achieve search speeds well in excess of 100,000 points/sec—at least an order of magnitude better than digital tree or nearest neighbour searches—with only modest setup times and storage requirements. Our novel SAM variant is found to offer the best performance per unit of storage, but at the expense of considerable setup times. We conclude that SAM algorithms can be used to provide a flexible “software-only” approach for real-time interpolation and visualization of unstructured mesh data.