Series-Expansion Methods

Abstract

Series-expansion methods that are potentially useful in geophysical fluid dynamics include the spectral method, the pseudospectral method, and the finite-element method. The spectral method plays a particularly important role in global atmospheric models, in which the horizontal structure of the numerical solution is often represented as a truncated series of spherical harmonics. Finite-element methods, on the other hand, are not commonly used in multidimensional wave propagation problems because they generally require the solution of implicit algebraic systems and are therefore not as efficient as competing explicit methods. All of these series-expansion methods share a common foundation that will be discussed in the next section.