SISIPHUS: Scalable Ice-Sheet Solvers and Infrastructure for Petascale, High-Resolution, Unstructured Simulations

SISIPHUS is a model and software infrastructure for climate simulations related to the dynamics of ice sheets -- glaciers that straddle
land and sea as ground ice slides into the ocean. Understanding the dynamics of ice sheets is crucial for accurate predictions of long-term
sea levels changes, as the melt of the ice near its grounding line is expected to be the main contributor to the rise of global sea levels.

The dynamics of ice sheets unfolds on the timescale of decades or even centuries, but at the same time, can undergo sudden changes
when the glaciers protruding from land into the ocean disintegrate in a matter of weeks. These sudden changes are conjectured
to be related to instabilities in the ice sheets associated with the geometry of their grounding lines. Thus, accurate predictions of the future
state of ice sheets and their contribution to the rise of global sea levels necessitates long-term simulations
of the ice sheet dynamics, calculations of its (quasi)stationary states and their bifurcations.

Ice sheet models describe a component of the global climate system and are coupled to other models describing the atmosphere and the ocean.
These other models evolve on much smaller timescales making the global system very stiff because of the presence of rapidly-moving gravity waves
in the ocean and other fast modes. Thus, in order to be able to span decade- and century-long scales of ice sheet evolution, we propose an implicit
formulation of ice sheet dynamics, which allows us to side-step the prohibitively short stiff time scales and still to yield accurate long-term predictions.
Rapid changes in the state of ice sheets can be identified via a stability analysis of their quasi-stationary states and the attendant bifurcations.

Nonlinear Stokesian model of ice sheets

Ice sheets are modeled as an incompressible Stokesian fluid with a nonlinear power law rheology (rendering it non-Newtonian) under a free-surface
evolution, constrained by the nonlinear slip boundary condition at the bedrock boundary, as well as by the atmosphere and ocean models.
[Details of the model to follow.]

Scalable software infrastructure

The simulation infrastructure is based upon scalable linear and nonlinear solvers encapsulated by the PETSc library
(Portable Extensible Toolkit for Scientific Computation) and the ITAPS collection of services ​https://trac.mcs.anl.gov/projects/ITAPS,
delivering scalable meshing, mesh (re)distribution and mesh data coupling services.
The interrelationship between the different components of the SISIPHUS simulation infrastructure are illustrated in Figure 1 below

Figure 1. Conceptual picture of the SISPHUS simulation infrastructure. PETSc components are in green, ITAPS in yellow, climate models
(including the SISIPHUS ice model) in blue. Existing components are dark, components to be added or extended with new capabilities are in lighter colors.

• Model defines the core nonlinear equations to be used in different simulation scenarios.
• The actual equations to be solved are defined in terms of the model according to the simulation needs:
  • Spin up: equilibration of the core equations with the other models (ocean, atmosphere) fixed in their current states.
  • Transient: time stepping through the ice sheet dynamics above the stiff time scales.
  • Bifurcation: parameter continuation and/or bifurcation identification and tracking
• Inverse: data assimilation and inverse problem solution to identify the model parameters.

• Model and the overlaid simulation scenario define the nonlinear system to be solved (generally, one per time or parameter step).
  • Nonlinear residuals and the (action of) the (approximate) Jacobian of the system are formed by the model.
  • SNES (Newton's method) solves the nonlinear system.
  • KSP carries out the inner linear (iterative) solve using the supplied Jacobian action.
  • PC preconditions the system to ensure rapid KSP convergence.

• [Need to expand on the mesh movement etc]

• [Need to expand on the physics-based/splitting preconditioners]

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