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Published in:
2019 | OriginalPaper | Chapter
An Accelerated Newton Method for Nonlinear Materials in Structure Mechanics and Fluid Mechanics
Authors : Thomas Richter, Carolin Mehlmann
Published in: Numerical Mathematics and Advanced Applications ENUMATH 2017
Publisher: Springer International Publishing
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Abstract
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.