Dimensionally Consistent Preconditioning for Saddle-Point Problems

Abstract The preconditioned iterative solution of large-scale saddle-point systems is great importance in numerous application areas, many them involving partial differential equations. Robustness with respect to certain problem parameters often a concern, and it can be addressed by identifying proper scalings preconditioner building blocks. In this paper, we consider new perspective finding effective robust preconditioners. Our approach based on the consideration natural physical units underlying respective problem. This point view, which refer as dimensional consistency, suggests combination intrinsic It turns out that scaling obtained way leads robustness relevant cases. As consequence, advertise consistency preconditioning systematic designing parameter preconditoners for arising from models phenomena.