Achieving Textbook Multigrid Efficiency for Hydrostatic Ice Sheet Flow

• Published in: SIAM Journal on Scientific Computing
• Main Authors: Brown, Jed, Smith, Barry, Ahmadia, Aron
• Other Authors: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, KAUST Supercomputing Laboratory (KSL), Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: Society for Industrial & Applied Mathematics (SIAM) 2013
• Subjects: hydrostatic; ice sheet; preconditioning; Newton > Krylov; multigrid; Ice Sheet
• Online Access: http://hdl.handle.net/10754/555665; https://doi.org/10.1137/110834512

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.