A Monolithic Algebraic Multigrid Framework for Multiphysics Applications with Examples from Resistive MHD

Peter Ohm, Tobias Wiesner, Eric C. Cyr, Jonathan J. Hu, John N. Shadid, Raymond S. Tuminaro

A multigrid framework is described for multiphysics applications. The framework allows one to construct, adapt, and tailor a monolithic multigrid methodology to different linear systems coming from discretized partial differential equations. The main idea centers on developing multigrid components in a blocked fashion where each block corresponds to separate sets of physical unknowns and equations within the larger discretization matrix. Once defined, these components are ultimately assembled into a monolithic multigrid solver for the entire system. We demonstrate the potential of the framework by applying it to representative linear solution sub-problems arising from resistive MHD.

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