A Newton-multigrid algorithm for elasto-plastic/viscoplastic problems (Q1804511)

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. Stopping criteria for the inner iteration are based on theories for so-called inexact Newton methods, where the linear systems are only solved approximately, which preserve however the rapid local convergence of Newton method.