We propose a preconditioning strategy for the governing equations of multibody systems in index-3 differential-algebraic form. The method eliminates the amplification of errors and the ill-conditioning which affect numerical solutions of high index differential algebraic equations for small time steps. We develop a new theoretical analysis of the perturbation problem and we apply it to the derivation of preconditioners for the Newmark family of integration schemes. The theoretical results are confirmed by numerical experiments.

On the Optimal Scaling of Index Three DAEs in Multibody Dynamics

BOTTASSO, CARLO LUIGI;TRAINELLI, LORENZO
2008-01-01

Abstract

We propose a preconditioning strategy for the governing equations of multibody systems in index-3 differential-algebraic form. The method eliminates the amplification of errors and the ill-conditioning which affect numerical solutions of high index differential algebraic equations for small time steps. We develop a new theoretical analysis of the perturbation problem and we apply it to the derivation of preconditioners for the Newmark family of integration schemes. The theoretical results are confirmed by numerical experiments.
2008
Differential algebraic equations; Constraints; Lagrange multipliers; Multibody dynamics; High index
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/544621
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