Domain decomposition preconditioning for non-linear elasticity problems

Abstract

We consider domain decomposition techniques for a non-linear elasticity problem. Our main focus is on non-linear preconditioning, realized in the framework of additive Schwarz preconditioned inexact Newton (ASPIN) methods. The standard 1-level ASPIN method is extended to a 2-level method by adding a non-linear coarse solver. Numerical experiments show that the coarse component is necessary for scalability in terms of linear iterations inside the Newton loop. Moreover, for problems that are dominated by nonlinearities that are not localized in space the non-linear coarse iterations are crucial for achieving computational efficiency.