A Newton-Multigrid algrithm for elasto-plastic/viscoplastic problems

Abstract

This work is concerned with large scaled nonlinear systems of equations resulting from discretization of problems in plasticity and viscoplasticity in the context of the finite element method. The main purpose is to show, how standard linear multigrid methods can be applied for solving the associated linear systems of equations in the frame of the Newton-algorithm. To this end, a so-called Galerkin-approach is used for construction of coarse grid matrices by transformation of fine grid matrices. It will be shown, how this transformation can be performed very efficiently element-by-element wise. Stopping criteria for the inner iteration are based on theories for so-called inexact Newton methods, where the linear systems are only solved approximately, however which preserve the rapid local convergence of Newtons method. In the numerical examples it is demonstrated, how the proposed strategy reduces the CPU-time for large scaled problems compared to solution techniques, where the associated systems of linear equations are solved directly.