An Accelerated Newton Method for Nonlinear Materials in Structure Mechanics and Fluid Mechanics

We analyze a modified Newton method that was first introduced by Turek and coworkers. The basic idea of the acceleration technique is to split the Jacobian A′(x) into a “good part” \(A^{\prime }_1(x)\) and into a troublesome part \(A^{\prime }_2(x)\). This second part is adaptively damped if the convergence rate is bad and fully taken into account close to the solution, such that the solver is a blend between a Picard iteration and the full Newton scheme. We will provide first steps in the analysis of this technique and discuss the effects that accelerate the convergence.