This paper introduces a new parallel, scalable and robust finite element first-order Stokes solver for ice flow, known as Albany/FELIX, to the land ice and climate modeling communities. This code 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. Several novel contributions to the field of ice sheet modeling are described, most notably: (1) the derivation of several new test cases based on the method of manufactured solutions for simplified 2-D forms of the first-order Stokes equations, which can be used to verify convergence to an exact solution for parts of the governing PDEs in any ice sheet code that discretizes these equations; (2) the description of a homotopy continuation algorithm, which greatly improves the robustness of a Newton nonlinear solver, especially in the absence of a good initial guess; (3) insights into the effects of the parallel decomposition and vertical mesh spacing on solver performance and solution accuracy for ice sheet simulations; (4) the development of a new algebraic multilevel preconditioner that delivers a scalable linear solve when combined with a preconditioned iterative method. The solver’s convergence, accuracy, robustness and scalability is demonstrated on various Greenland ice sheet geometries, discretized using tetrahedral and hexahedral meshes.

Reference:

Tezaur, I.K., M. Perego, A.G. Salinger, R.S. Tuminaro, and S.F. Price. 2015. Albany/FELIX: a parallel, scalable and robust, finite element, first-order Stokes approximation ice sheet solver built for advanced analysis. Geosci. Model Dev., 8, doi: 10.5194/gmd-8-1197-2015.