For the Fully Coupled attribute, you can define one of the settings for the double dogleg method. Also see Termination Criterion for the Fully Coupled and Segregated Attribute Nodes.

The double dogleg method (Ref. 27) is available for stationary problems. It is a Newton trust region method and can as such adjust the direction as well as the step length when solving the nonlinear equation , : .

subject to . Here, is the Jacobian of F at the current point uk, Fk = F(uk), and the size of the double dogleg step s is required to be bounded by the current trust region radius . Both the Cauchy point — that is, the minimizer of m in the steepest descent direction — and the Newton point are utilized by the double dogleg method. In each iteration, the algorithm dynamically adjusts the size of the trust region depending on the predicted decrease of m compared to the actual one. If the Newton step size, initially optionally reduced with the Initial damping factor, is smaller than the trust region radius, the Newton step is taken. Otherwise, the step size will be equal to the trust region radius. The direction of the step will in this case be in the steepest descent direction if the size of the Cauchy step is larger than the trust region radius; otherwise, the direction will be a convex combination of the Cauchy step and the Newton step. For further details, see Ref. 27. For difficult problems, you can choose to start the computation by a damped Newton step. Enter the damping factor between 0 and 1 in the Initial damping factor field. The algorithm terminates if the norm of the scaled residual is less than the given tolerance, . You can choose the type of scaling in the Residual scaling list. See the Fully Coupled Method and Termination settings.