an:07136720
Zbl 1432.76166
Richter, Thomas; Mehlmann, Carolin
An accelerated Newton method for nonlinear materials in structure mechanics and fluid mechanics
EN
Radu, Florin Adrian (ed.) et al., Numerical mathematics and advanced applications. ENUMATH 2017. Selected papers based on the presentations at the European conference, Bergen, Norway, September 25--29, 2017. Cham: Springer. Lect. Notes Comput. Sci. Eng. 126, 345-353 (2018).
2018
a
76M10 74S05 65H10 74R10 65N30 76A05 65N22 76A10
Summary: We analyze a modified Newton method that was first introduced in [\textit{S. Mandal} et al., Lect. Notes Comput. Sci. Eng. 112, 481--490 (2016; Zbl 1387.76058)]. The basic idea of the acceleration technique is to split the Jacobian \(A'(x)\) into a ``good part'' \(A'_1(x)\) and into a troublesome part \(A'_2(x)\). 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.
For the entire collection see [Zbl 1411.65009].
Zbl 1387.76058