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