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Fully realizing the potential of multigrid solvers often requires customalgorithms for a given application model, discretizations and even regimes ofinterest, despite considerable effort from the applied math community todevelop fully algebraic multigrid (AMG) methods for almost 40 years. Classicgeometric multigrid (GMG) has been effectively applied to challenging,non-elliptic problems in engineering and scientifically relevant codes, butapplication specific algorithms are generally required that do not lendthemselves to deployment in numerical libraries. However, tools in librariesthat support discretizations, distributed mesh management and high performancecomputing (HPC) can be used to develop such solvers.  This report develops a magnetohydrodynamics (MHD) code in PETSc (PortableExtensible Toolkit for Scientific computing) with a fully integrated GMG solverthat is designed to demonstrate the potential of our approach to providing fastand robust solvers for production applications. These applications must,however, be able to provide, in addition to the Jacobian matrix and residual ofa pure AMG solver, a hierarchy of meshes and knowledge of the application'sequations and discretization. An example of a 2D, two field reduced resistiveMHD model, using existing tools in PETSc that is verified with a ``tilt"instability problem that is well documented in the literature is presented andis an example in the PETSc repository (\path{src/ts/tutorials/ex48.c}).Preliminary CPU-only performance data demonstrates that the solver can berobust and scalable for the model problem that is pushed into a regime withhighly localized current sheets, which generates strong, localizednon-linearity, that is a challenge for iterative solvers.

A bespoke multigrid approach for magnetohydrodynamics models of magnetized plasmas in PETSc