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Approximate Inverse Techniques for Block-Partitioned Matrices

This paper proposes some preconditioning options when the system matrix is in block-partitioned form. This form may arise naturally, for example, from the incompressible Navier--Stokes equations, or may be imposed after a domain decomposition reordering. Approximate inverse techniques are used to generate sparse approximate solutions whenever these are needed in forming the preconditioner. The storage requirements for these preconditioners may be much less than for incomplete LU factorization (ILU) preconditioners for tough, large-scale computational fluid dynamics (CFD) problems. The numerical experiments show that these preconditioners can help solve difficult linear systems whose coefficient matrices are highly indefinite.