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Application of Fast Fourier Transforms to the Direct Solution of a Class of Two-Dimensional Separable Elliptic Equations on the Sphere

Shrinivas MoorthiUniversities Space Research Association, Laboratory for Atmospheres, NANA/GSFC, Greenbelt, Maryland

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R. Wayne HigginsUniversities Space Research Association, Laboratory for Atmospheres, NANA/GSFC, Greenbelt, Maryland

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Abstract

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Abstract

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

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