"Achieving Textbook Multigrid Efficiency for Hydrostatic Ice Sheet Flow"
J. Brown, B. Smith, and A. Ahmadia
Para 2010: State of the Art in Scientific and Parallel Computing, Reykjavik, Iceland, .
Preprint Version: [pdf]
The hydrostatic equations for ice sheet flow offer improved fidelity compared to the shallow ice approximation and shallow stream approximation (SSA) popular in today's ice sheet models. Nevertheless, they present a serious bottleneck because they require the solution of a 3D nonlinear system, as opposed to the 2D system present in SSA. This 3D system is posed on high-aspect domains with strong anisotropy and variation in coefficients, making it expensive to solve by using 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.