A MONOLITHIC ALGEBRAIC MULTIGRID FRAMEWORK FOR MULTIPHYSICS APPLICATIONS WITH EXAMPLES FROM RESISTIVE MHD

We consider monolithic algebraic multigrid (AMG) algorithms for the solution of block linear systems arising from multiphysics simulations. While the multigrid idea is applied directly to the entire linear system, AMG operators are constructed by leveraging the matrix block structure. In particular, each block corresponds to a set of physical unknowns and physical equations. Multigrid components are constructed by first applying existing AMG procedures to matrix sub-blocks. The resulting AMG sub-components are then composed together to define a monolithic AMG preconditioner. Given the problem-dependent nature of multiphysics systems, different blocking choices may work best in different situations, and so software flexibility is essential. We apply different blocking strategies to systems arising from resistive magnetohydrodynamics in order to demonstrate the associated trade-offs.