Fig. 8.

Comparison of the number of Jacobian and residual computations for (a) the penalty, (b) the weakly penalized and (c) the PL formulation. The methods are compared over the passive inflation simulation (Section 3.1.2) on mesh ₂ ($k={10}^7$ for the penalty, weakly penalized and Perturbed Lagrangian (PL) methods). The solid black line presents the number of Jacobian and residual computations for the classic Newton–Raphson scheme and the dotted lines present the number of Jacobian (black line) and residual (red line) computations when the SNR scheme is applied. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this article.)