An adaptive continuation-multigrid method for the balanced vortex model

Obtaining solutions of the Eliassen balanced vortex model requires solving an invertibility relation, which is a nonlinear elliptic problem of the Monge-Ampere type. Multigrid techniques for this problem are investigated. An adaptive algorithm which combines the full multigrid method with continuation in a parameter related to the strength of the forcing is developed. Numerical results demonstrate the efficiency and robustness of this algorithm.