Prediction of the steady state flying height and attitude of air-bearing sliders in hard disk drives via simulations is the basis of their design process. Over the past few years air-bearing surfaces have become increasingly complex incorporating deep etches and steep wall profiles. In this paper we present a novel method of solving the inverse problem for air-bearing sliders in hard disk drives that works well for such new designs. We also present a new method for calculating the static air-bearing stiffness by solving three linear systems of equations. The formulation is implemented, and convergence studies are carried out for the method. Mesh refinements based on flux jumps and pressure gradients are found to work better than those based on other criteria.