A Performance Comparison of Associated Legendre Projections
by W. F. Spotz and P. N. Swarztrauber,
168(2001), pp. 339-355.
The associated Legendre projection provides a
means for accelerating the dynamical core of a global
weather or climate model. Therefore, the goal is to
determine the fastest possible projection algorithm, of
which this paper compares four: the standard method
which computes the projection using a forward and
backward associated Legendre transform; the direct
method, which uses a single projection matrix when
this approach results in fewer operations; the fast
multipole method; and the weighted orthogonal
complement method. Timing results indicate that all
the projections behave like O(N3) algorithms up to at
least N=200 spectral truncation. For this range of
resolutions, the weighted orthogonal complement has
the lowest operation count, best cache utilization and
best overall timings.
Mail comments to Paul Swarztrauber.