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 idea is applied directly to entire system, AMG operators are constructed by leveraging matrix structure. In particular, each corresponds a set physical unknowns and equations. Multigrid components first applying existing procedures sub-blocks. The resulting sub-components then composed together define preconditioner. Given problem-dependent nature systems, different blocking choices may work best in situations, so software flexibility essential. apply strategies resistive magnetohydrodynamics order demonstrate associated trade-offs.