An adaptive dynamic relaxation method for solving nonlinear finite element problems. Application to brain shift estimation

Abstract

Dynamic relaxation is an explicit method that can be used for computing the steady‐state solution for a discretized continuum mechanics problem. The convergence speed of the method depends on the accurate estimation of the parameters involved, which is especially difficult for nonlinear problems. In this paper, we propose a completely adaptive dynamic relaxation method in which the parameters are updated during the iteration process, converging to their optimal values. We use the proposed method for computing intra‐operative organ deformations using non‐linear finite element models involving large deformations, non‐linear materials and contacts. The simulation results prove the accuracy and the computational efficiency of the method. The proposed method is also very well suited for GPU implementation. Copyright © 2010 John Wiley & Sons, Ltd.