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Large Scale Solution of Constrained Systems via Monolithic Multigrid

Luke Olson, University of Illinois at Urbana-Champaign

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Luke Olson, Amanda Bienz, Andrew Reisner, Lukas Spies, Scott MacLachlan

Physical problems with constraints arise in many fields of computational science and engineering, including fluid and solid mechanics, and the modeling of liquid crystals and ferromagnetic materials. When using finite element methods such constraints are naturally imposed using Lagrange multipliers, adding non-physical variables that enforce the physical constraints. Solution of the resulting linear and linearized systems is complicated by the saddle-point structure, although algorithmic development for these problems has advanced substantially in recent years. Even so, the scalable performance of solvers has not been fully realized. The focus of this project is to bridge the gap between scalability and recent algorithmic advancements—in this respect, Blue Waters is critical to the success of the project. In particular, the project will analyze an implementation at scale and seek performance that fully utilizes the potential of the machine.