Albany/FELIX: A parallel, scalable and robust finite element higher-order Stokes ice sheet solver built for advance analysis. 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.
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References in zbMATH (referenced in 8 articles )
Showing results 1 to 8 of 8.
- Heinlein, Alexander; Perego, Mauro; Rajamanickam, Sivasankaran: FROSch preconditioners for land ice simulations of Greenland and Antarctica (2022)
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- Chen, Chao; Cambier, Leopold; Boman, Erik G.; Rajamanickam, Sivasankaran; Tuminaro, Raymond S.; Darve, Eric: A robust hierarchical solver for ill-conditioned systems with applications to ice sheet modeling (2019)
- Cheng, Gong; Shcherbakov, Victor: Anisotropic radial basis function methods for continental size ice sheet simulations (2018)
- Cheng, Gong; Lötstedt, Per; von Sydow, Lina: Accurate and stable time stepping in ice sheet modeling (2017)
- Jiménez, Stephen; Duddu, Ravindra; Bassis, Jeremy: An updated-Lagrangian damage mechanics formulation for modeling the creeping flow and fracture of ice sheets (2017)
- Tuminaro, R.; Perego, M.; Tezaur, I.; Salinger, A.; Price, S.: A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling (2016)
- Isaac, Tobin; Stadler, Georg; Ghattas, Omar: Solution of nonlinear Stokes equations discretized by high-order finite elements on nonconforming and anisotropic meshes, with application to ice sheet dynamics (2015)