Achieving Textbook Multigrid Efficiency for Hydrostatic Ice Sheet Flow

Type
Article

Authors
Brown, Jed
Smith, Barry
Ahmadia, Aron

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
KAUST Supercomputing Laboratory (KSL)

Online Publication Date
2013-03-12

Print Publication Date
2013-01

Date
2013-03-12

Abstract
The hydrostatic equations for ice sheet flow offer improved fidelity compared with the shallow ice approximation and shallow stream approximation popular in today's ice sheet models. Nevertheless, they present a serious bottleneck because they require the solution of a three-dimensional (3D) nonlinear system, as opposed to the two-dimensional system present in the shallow stream approximation. This 3D system is posed on high-aspect domains with strong anisotropy and variation in coefficients, making it expensive to solve with current methods. This paper presents a Newton--Krylov multigrid solver for the hydrostatic equations that demonstrates textbook multigrid efficiency (an order of magnitude reduction in residual per iteration and solution of the fine-level system at a small multiple of the cost of a residual evaluation). Scalability on Blue Gene/P is demonstrated, and the method is compared to various algebraic methods that are in use or have been proposed as viable approaches.

Citation
Achieving Textbook Multigrid Efficiency for Hydrostatic Ice Sheet Flow 2013, 35 (2):B359 SIAM Journal on Scientific Computing

Publisher
Society for Industrial & Applied Mathematics (SIAM)

Journal
SIAM Journal on Scientific Computing

DOI
10.1137/110834512

Additional Links
http://epubs.siam.org/doi/abs/10.1137/110834512

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