Block-Structured Indefinite Linear Systems with Rank-Deficient Blocks


Large, sparse, symmetric linear systems with a saddle-point structure come in several flavors. In this talk I will provide an overview of algebraic properties of matrices associated with such systems, which have a special rank structure. We will focus on situations where the leading block is singular with a high nullity, and describe mathematical and algebraic properties that allow us to design preconditioned iterative solvers with indefinite preconditioners that rely on null spaces of the operators involved. We will illustrate some of the observations on a 4-by-4 block linear system arising from an incompressible magnetohydrodynamics model problem.

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