Multigrid Solution of the Semigeostrophic Invertibility Relation

Abstract

In semigeostrophic theory one can recover the balanced wind and mass fields from the potential vorticity by solving a nonlinear elliptic boundary-value problem. This paper describes the efficient solution of this invertibility relation in two dimensions by a multigrid algorithm. Numerical results show this method is competitive with a generalized Buneman algorithm for the linearized cases to which the latter applies. The fully nonlinear problem is solved to well below the level of truncation error 50?80 times faster than by simple relaxation on a single grid.