Fast Evaluation of Vector Splines in Three Dimensions

摘要

Vector spline techniques have been developed as general-purpose methods for vector field recon- struction. However, such vector splines involve high computational complexity, which predcludes applications of this technique to many problems using large data sets. In this paper, we develop a fast multipole method for the rapid evaluation of the vector spline in three dimenisons. The algorithm depends on a tree-data structure and two hierarchical approximations: an upward multipole expansion approximation and a downward local Taylor series approximation.