Implementation of the Jacobian-free Newton-Krylov method for solving the first-order ice sheet momentum balance

Jean François Lemieux, Stephen F. Price, Katherine J. Evans, Dana Knoll, Andrew G. Salinger, David M. Holland, Antony J. Payne

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)6531-6545
Number of pages15
JournalJournal of Computational Physics
Volume230
Issue number17
DOIs
StatePublished - Jul 20 2011

Fingerprint

Newton methods
Newton-Raphson method
newton
Ice
Momentum
ice
momentum
Boundary conditions
land ice
boundary conditions
reuse
refining
Refining
Physics
Earth (planet)
grids
Geometry
physics
geometry

Keywords

  • GMRES
  • Ice rheology
  • Ice sheet model
  • ILU
  • Newton-Krylov

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

Cite this

Implementation of the Jacobian-free Newton-Krylov method for solving the first-order ice sheet momentum balance. / Lemieux, Jean François; Price, Stephen F.; Evans, Katherine J.; Knoll, Dana; Salinger, Andrew G.; Holland, David M.; Payne, Antony J.

In: Journal of Computational Physics, Vol. 230, No. 17, 20.07.2011, p. 6531-6545.

Research output: Contribution to journalArticle

Lemieux, Jean François ; Price, Stephen F. ; Evans, Katherine J. ; Knoll, Dana ; Salinger, Andrew G. ; Holland, David M. ; Payne, Antony J. / Implementation of the Jacobian-free Newton-Krylov method for solving the first-order ice sheet momentum balance. In: Journal of Computational Physics. 2011 ; Vol. 230, No. 17. pp. 6531-6545.
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