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Publication Date
20 January 2015

Albany/FELIX: A Parallel, Scalable and Robust, Finite Element, First-Order Stokes Approximation Ice Sheet Solver

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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.




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.

Point of Contact
Irina K Tezaur
Sandia National Laboratories (SNL)
Funding Program Area(s)

Support for all authors was provided through the Scientific Discovery through Advanced Computing (SciDAC) program funded by the U.S. Department of Energy (DOE), Office of Science, Advanced Scientific Computing Research and Biological and Environmental Research.

This research used resources of the National Energy Research Scientific Computing Center (NERSC; supported by  the Office of Science of the U.S. Department of Energy under Contract DE-AC02-05CH11231) and the Oak Ridge Leadership Computing Facility (OLCF; supported by the DOE Office of Science under Contracts DE-AC02-05CH11231 and DE-AC05-00OR22725). The authors thank M. Norman of Oak Ridge National Laboratory for generation of the Greenland geometry datasets, J. Johnson (and students) of the University of Montana for initial development of the ISMIP-HOM plotting scripts, and M. Hoffman and B. Lipscomb at Los Alamos National Laboratory for useful discussions that led to some of the ideas and results presented in this paper.