B. Heise and M. Jung
Robust parallel Newton-multilevel methods
Technical Report No. 96-4, Institut für Mathematik, Arbeitsgruppe Numerische Mathematik und Optimierung, Johannes Kepler Universität Linz
The present paper is devoted to the numerical solution of nonlinear boundary value problems arising in the magnetic field computation and in solid mechanics. These problems are discretized by using finite elements. The nonlinearity is handled by a nested Newton solver, and the linear systems of algebraic equations within each Newton step are solved by means of various iterative solvers, namely multigrid methods and conjugate gradient methods with DD preconditioners as well as BPX preconditioners. All solvers are based on a non-overlapping domain decomposition data structure such that they are well-suited for implementations on parallel machines with MIMD architecture. We compare by numerical examples the performance of the different iterative solvers which are applied within each Newton step.