Achieving Textbook Multigrid Efficiency for Hydrostatic Ice Sheet Flow
|Title||Achieving Textbook Multigrid Efficiency for Hydrostatic Ice Sheet Flow|
|Publication Type||Journal Article|
|Year of Publication||2013|
|Authors||Brown, J, Smith, BF, Ahmadia, A|
|Journal||SIAM Journal Sci. Comput.|
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.