A Scalable Approximate Inverse Block Preconditioner for an Incompressible Magnetohydrodynamics Model Problem

Abstract

We introduce a new approximate inverse preconditioner for a mixed finite element discretization of an incompressible magnetohydrodynamics model problem. The derivation exploits the nullity of the discrete curl-curl operator in the Maxwell subproblem. We show that the inverse of the coefficient matrix contains zero blocks and use discretization considerations to obtain a practical preconditioner based on further sparsification. We demonstrate the viability of our approach with a set of numerical experiments.