A dimension expanded preconditioning technique for block two-by-two linear equations

Abstract

In this article, we introduce a novel block preconditioner for block two-by-two linear equations by expanding the dimension of the coefficient matrix. Theoretical results on the eigenvalues distribution of the preconditioned matrix are obtained, and a feasible implementation is discussed. Some numerical examples, including the solution of the Navier-Stokes equations, are presented to support the theoretical findings and demonstrate the preconditioner’s efficiency.

Keywords

• block two-by-two
• linear equations
• preconditioner
• navier-stokes equations
• 65f08
• 65f10