Automatic time stepping algorithms for implicit numerical simulations of non-linear dynamics
Résumé
When an implicit integration scheme is used, variable step strategies are especially well suited to deal with problems characterized by high non-linearities. Constant step size strategies generally lead to divergence or extremely costly computations. An automatic time stepping algorithm is proposed that is based on estimators of the integration error of the differential dynamic balance equations. Additionally, the proposed algorithm automatically takes decisions regarding the necessity of updating the tangent matrix or stopping the iterations, further reducing the computational cost. As an illustration of the capabilities of this algorithm, several numerical simulations of both academic and industrial problems are presented.