Articles | Volume 10, issue 1
Development and technical paper
10 Jan 2017
Development and technical paper |  | 10 Jan 2017

Optimal numerical solvers for transient simulations of ice flow using the Ice Sheet System Model (ISSM versions 4.2.5 and 4.11)

Feras Habbal, Eric Larour, Mathieu Morlighem, Helene Seroussi, Christopher P. Borstad, and Eric Rignot

Abstract. Identifying fast and robust numerical solvers is a critical issue that needs to be addressed in order to improve projections of polar ice sheets evolving in a changing climate. This work evaluates the impact of using advanced numerical solvers for transient ice-flow simulations conducted with the JPL–UCI Ice Sheet System Model (ISSM). We identify optimal numerical solvers by testing a broad suite of readily available solvers, ranging from direct sparse solvers to preconditioned iterative methods, on the commonly used Ice Sheet Model Intercomparison Project for Higher-Order ice sheet Models benchmark tests. Three types of analyses are considered: mass transport, horizontal stress balance, and incompressibility. The results of the fastest solvers for each analysis type are ranked based on their scalability across mesh size and basal boundary conditions. We find that the fastest iterative solvers are  ∼ 1.5–100 times faster than the default direct solver used in ISSM, with speed-ups improving rapidly with increased mesh resolution. We provide a set of recommendations for users in search of efficient solvers to use for transient ice-flow simulations, enabling higher-resolution meshes and faster turnaround time. The end result will be improved transient simulations for short-term, highly resolved forward projections (10–100 year time scale) and also improved long-term paleo-reconstructions using higher-order representations of stresses in the ice. This analysis will also enable a new generation of comprehensive uncertainty quantification assessments of forward sea-level rise projections, which rely heavily on ensemble or sampling approaches that are inherently expensive.

Short summary
This work presents the results from testing a suite of numerical solvers on a standard ice sheet benchmark test. We note the relevance of this test to practical simulations and identify the fastest solvers for the transient simulation. The highlighted solvers show significant speed-ups in relation to the default solver (~1.5–100 times faster) and enable a new capability for solving massive, high-resolution models that are critical for improving projections of ice sheets and sea-level change.