Robust and efficient primal-dual Newton-Krylov solvers for viscous-plastic sea-ice models

We present a Newton-Krylov solver for a viscous-plastic sea-ice model. This constitutive relation is commonly used in climate models to describe the large scale sea-ice motion. Due to the strong nonlinearity of the momentum equation, the development of fast, robust and scalable solvers is still a substantial challenge. We propose a novel primal-dual Newton linearization for the momentum equation. In contrast to existing methods, it converges faster and more robustly with respect to mesh refinement, and thus allows fully resolved sea-ice simulations. Combined with an algebraic multigrid-preconditioned Krylov method for the Newton linearized systems, which contain strongly varying coefficients, the resulting solver scales well and can be used in parallel. We present highly resolved benchmark solutions and solve problems with up to 8.4 million spatial unknowns.