Extending Broyden's method to interaction problems

Authors

  • Robby Haelterman Royal Military Academy, Belgium
  • Joris Degroote Ghent University, Belgium
  • Jan Vierendeels Ghent University, Belgium
  • Dirk Van heule Royal Military Academy, Belgium

DOI:

https://doi.org/10.33993/jnaat372-889

Keywords:

quasi-Newton method, iterative method
Abstract views: 212

Abstract

The solution of problems involving the interaction of different systems is a domain of ongoing research, although often a good solver already exists for each system separately. In this paper we draw our ideas from one of the best known all-round quasi-Newton methods: Broyden's rank-one update, which we extend to algorithms using 2 approximate Jacobians. A comparison is made with the iterative substructuring method and Aitken's acceleration method. It is shown that a Broyden method using only a single approximate Jacobian performs best.

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References

Broyden, C.G., A class of methods for solving nonlinear simultaneous equations, Math. Comp., 19, pp. 577-593, 1965. DOI: https://doi.org/10.1090/S0025-5718-1965-0198670-6

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Vierendeels, J., Lanoye, L., Degroote, J. and Verdonck, P., Implicit coupling of partitioned fluid-structure interaction problems with reduced order models, Comput. & Structures, 85, pp. 970-976, 2007, https://doi.org/10.1016/j.compstruc.2006.11.006 , April 2008. DOI: https://doi.org/10.1016/j.compstruc.2006.11.006

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Published

2008-08-01

How to Cite

Haelterman, R., Degroote, J., Vierendeels, J., & Van heule, D. (2008). Extending Broyden’s method to interaction problems. Rev. Anal. Numér. Théor. Approx., 37(2), 169–180. https://doi.org/10.33993/jnaat372-889

Issue

Vol. 37 No. 2 (2008)

Section

Articles

License

Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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