Abstract
We have implemented the Jacobian-free Newton-Krylov (JFNK) method for solving the first-order ice sheet momentum equation in order to improve the numerical performance of the Glimmer-Community Ice Sheet Model (Glimmer-CISM), the land ice component of the Community Earth System Model (CESM). Our JFNK implementation is based on significant re-use of existing code. For example, our physics-based preconditioner uses the original Picard linear solver in Glimmer-CISM. For several test cases spanning a range of geometries and boundary conditions, our JFNK implementation is 1.8-3.6 times more efficient than the standard Picard solver in Glimmer-CISM. Importantly, this computational gain of JFNK over the Picard solver increases when refining the grid. Global convergence of the JFNK solver has been significantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact Newton method. While a diverse set of test cases show that our JFNK implementation is usually robust, for some problems it may fail to converge with increasing resolution (as does the Picard solver). Globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of Picard and JFNK and the use of homotopy methods.
| Original language | English |
|---|---|
| Pages (from-to) | 6531-6545 |
| Number of pages | 15 |
| Journal | Journal of Computational Physics |
| Volume | 230 |
| Issue number | 17 |
| DOIs | |
| State | Published - Jul 20 2011 |
Funding
We would like to thank Carl Gladish for his help in setting up and compiling Glimmer-CISM and William H. Lipscomb for helpful discussions. We also thank two anonymous reviewers for their useful comments. Jean-François Lemieux is grateful to FQRNT and NSERC for Postdoctoral fellowships. This work has been funded by the Department of Energy Office of Advanced Scientific Computing project, “A Scalable, Efficient, and Accurate Community Ice Sheet Model, within the ISICLES initiative. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.
Keywords
- GMRES
- ILU
- Ice rheology
- Ice sheet model
- Newton-Krylov