Abstract: Physically based simulation of the rod dynamics often takes long time to reach an equilibrium state because of inertia and time integration scheme.Therefore,in the application of interactive virtual assembly,such simulation methods often lead hurdles of assessing assembly configuration.In this paper,we propose an efficient and stable optimization method to simulate the quasi-static deformation of a rod with large steps,and focus on collision handling under the framework of optimization.A gradient based collision prediction is used to improve the stability of response and prevent sticking under large step size iteration.An local anisotropic Levenberg-Marquardt(LM) trust region method is applied to avoid jittering.In the results,we demonstrate that our method often converges to the equilibrium state with only a few iterations,and much faster than physically based simulation method under various environments.