On a Robust Multigrid-Preconditioned Solver for Incremental Plasticity Problems

Plasticity models have a long history in the engineering and mathematical community. The rigorous mathematical and numerical analysis of different elasto-plastic models has been a topic of mathematical research during the last two decades, see e.g. [2], [6], [7], [8] and the literature cited there. The method presented in this paper is based on the approach proposed by C. Carstensen [1]. In contrast to [1], we introduce some regularization of the local minimization problems making the nonsmooth cost functional differentiable. We develop an adjusted multigrid preconditioned conjugate gradient (PCG) method for the Schur-complement problems arising at each incremental step. Moreover, we prove that the elastic multigrid preconditioner is sufficient for an effective and robust solving of large scale elasto-plastic problems.