A New Class of Dimension Expanded Preconditioners for Efficient Solution of Saddle Point Linear Systems

ABSTRACT We describe a class of preconditioners for solving block saddle point linear problems derived from an augmented block structure of the initial problem. The methods can be seen as a variant of the dimension expanded preconditioning technique proposed by Luo et al. for solving saddle point problems. We compute the eigenvalue distribution and corresponding eigenvectors of the preconditioned matrices and propose a convergence analysis using the Krylov subspace methods. The results of our numerical experiments for solving the Stokes equations, two‐dimensional leaky lid‐driven cavity problems, and randomly generated academic examples showcase the potential of the proposed methods to solve realistic saddle point linear systems fast and efficiently, also compared to other popular existing methods for this class of problems.