An Efficient Method for a Finite-Difference Solution of the Poisson Equation on the Surface of a Sphere.

摘要

An efficient shooting method is presented for the numerical solution of a discrete Poisson equation on the surface of the sphere. The solution is computed via two-dimensional shooting in the physical domain while the missing initial conditions needed to start the shooting are obtained in a one-dimensional setting in the Fourier domain. For a computational grid with J x J grid points, the operational count of this method is of O((J square/m) log (base 2)J), where m is the number of grid points within each shooting subrange. The actual count is, for most practical purposes, less than 26 arithmetic operations per grid point. Stability of the method is a problem; this problem, however, can be overcome by the use of the multiple shooting technique. Numerical examples are given to demonstrate the applicability of the procedure. (Author)