Articles | Volume 8, issue 4
Model description paper
27 Apr 2015
Model description paper |  | 27 Apr 2015

Albany/FELIX: a parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis

I. K. Tezaur, M. Perego, A. G. Salinger, R. S. Tuminaro, and S. F. Price

Abstract. This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, along with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions of the governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic multilevel preconditioner, constructed based on the idea of semi-coarsening.

Short summary
In this manuscript, we discuss the development and validation of a new momentum balance solver for modeling the flow of glaciers and ice sheets based on the 1st-order Stokes equations. We demonstrate the numerical convergence of our solver (with respect to computational mesh spacing), its flexibility (with respect to both the choice of mesh and finite element type), and its computational performance (robustness and scalability when applied to both idealized and realistic ice sheet simulations).