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

Yu hsuan Shih, Carolin Mehlmann, Martin Losch, Georg Stadler

Research output: Contribution to journalArticlepeer-review


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 material properties of sea ice. Due to the strong nonlinearity introduced by the material law in the momentum equation, the development of fast, robust and scalable solvers is still a substantial challenge. In this paper, we propose a novel primal-dual Newton linearization for the implicitly-in-time discretized momentum equation. Compared to existing methods, it converges faster and more robustly with respect to mesh refinement, and thus enables numerically converged sea-ice simulations at high resolutions. Combined with an algebraic multigrid-preconditioned Krylov method for the linearized systems, which contain strongly varying coefficients, the resulting solver scales well and can be used in parallel. We present experiments for two challenging test problems and study solver performance for problems with up to 8.4 million spatial unknowns.

Original languageEnglish (US)
Article number111802
JournalJournal of Computational Physics
StatePublished - Feb 1 2023


  • AMG-preconditioned Krylov
  • Localization
  • Primal–dual
  • Sea-ice
  • Stress–velocity Newton
  • Viscous-plastic rheology

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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