A performance comparison of associated Legendre projections

The associated Legendre projection provides a means for accelerating the dy namical core of a global weather or climate model. Therefore, the goal is t o determine the fastest possible projection algorithm. of which this paper compares six: the standard method, which computes the projection using a fo rward and backward associated Legendre transform; the direct method, which uses a single projection matrix when this approach results in fewer operati ons; the fast multipole method: the weighted orthogonal complement method; the seminaive method; and a projection based on transforms proposed by Mohl enkamp. Timing results indicate that all the projections behave like O(N-3) algorithms up to at least N = 200 spectral truncation. For this range of r esolutions, the weighted orthogonal complement has the lowest operation cou nt, best cache utilization, and best overall timings. (C) 2001 Academic Pre ss.