Abstract
Time Discontinuous Galerkin methods require the factorization of a matrix larger than that exploited in standard implicit schemes. Therefore, they lend themselves to implementations based on predictor-multicorrector solution algorithms. In this paper, various convergent and computationally efficient iterative methods implemented in the unknown displacements for determining the solution of non linear systems are proposed. The iterative solutions presented here differ from those implemented in the unknown velocities in that they are computationally superior. The results of numerical simulations relevant to Duffing oscillators and to a stiff spring pendulum discretized with finite elements which are designed to evaluate the efficacy of these iterative methods with non-linear systems, show a low-computational expense when compared to earlier iterative schemes.
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Received: 27 May 2002 / Accepted: 28 January 2003
The financial support from the Italian Ministry for Education, Universities and Research (MIUR) is acknowledged. However, opinions expressed in this paper are those of the writers, and do not necessarily reflect the views of the sponsoring agency.
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Bonelli, A., Bursi, O. Iterative solutions for implicit Time Discontinuous Galerkin methods applied to non-linear elastodynamics. Computational Mechanics 30, 487–498 (2003). https://doi.org/10.1007/s00466-003-0426-3
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DOI: https://doi.org/10.1007/s00466-003-0426-3