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

  • Thomas RichterEmail author
  • Carolin Mehlmann
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


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.



The authors acknowledge the financial support by the Deutsche Forschungsgemeinschaft (314838170), GRK 2297 MathCoRe, the Federal Ministry of Education and Research of Germany (05M16NMA) and the German Federal Environmental Foundation.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of Magdeburg, Institute for Analysis and NumericsMagdeburgGermany

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