A modified global Newton solver for viscous-plastic sea ice models

Abstract

We present and analyze a modified Newton solver, the so called operator-related damped Jacobian method, with a line search globalization for the solution of the strongly nonlinear momentum equation in a viscous-plastic (VP) sea ice model.Due to large variations in the viscosities, the resulting nonlinear problem is very difficult to solve. The development of fast, robust and converging solvers is subject to present research. There are mainly three approaches for solving the nonlinear momentum equation of the VP model, a fixed-point method denoted as Picard solver, an inexact Newton method and a subcycling procedure based on an elastic-viscous-plastic model approximation. All methods tend to have problems on fine meshes by sharp structures in the solution. Convergence rates deteriorate such that either too many iterations are required to reach sufficient accuracy or convergence is not obtained at all.To improve robustness globalization and acceleration approaches, which increase the area of fast convergence, are needed. We develop an implicit scheme with improved convergence properties by combining an inexact Newton method with a Picard solver. We derive the full Jacobian of the viscous-plastic sea ice momentum equation and show that the Jacobian is a positive definite matrix, guaranteeing global convergence of a properly damped Newton iteration. We compare our modified Newton solver with line search damping to an inexact Newton method with established globalization and acceleration techniques. We present a test case that shows improved robustness of our new approach, in particular on fine meshes.