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.
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