An important component of a number of computational modeling algorithms is an
interpolation method that preserves the positivity of the function being
interpolated. This report describes the numerical testing of a new
positivity-preserving algorithm that is designed to be used when interpolating
from a solution defined on one grid to different spatial grid. The motivating
application is a numerical weather prediction (NWP) code that uses spectral
elements as the discretization choice for its dynamics core and Cartesian
product meshes for the evaluation of its physics routines. This combination of
spectral elements, which use nonuniformly spaced quadrature/collocation points,
and uniformly-spaced Cartesian meshes combined with the desire to maintain
positivity when moving between these necessitates our work. This new approach
is evaluated against several typical algorithms in use on a range of test
problems in one or more space dimensions. The results obtained show that the
new method is competitive in terms of observed accuracy while at the same time
preserving the underlying positivity of the functions being interpolated.Comment: 58 pages, 17 figure