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: 184

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

Deparis, S., Discacciati, M., Fourestey, G. and Quarteroni, A., Fluid-structure algorithms based on Steklov-Poincaré operators, Computer Methods in Applied Mechanics and Engineering, 195/41-43, pp. 5797-5812, 2006, https://doi.org/10.1016/j.cma.2005.09.029 DOI: https://doi.org/10.1016/j.cma.2005.09.029

Küttler, U. and Wall, W., Fixed-point fluid-structure interaction solvers with dynamic relaxation, Computational Mechanics 2008,https://doi.org/10.1007/s00466-008-0255-5 DOI: https://doi.org/10.1007/s00466-008-0255-5

Michler, C., Van Brummelen, E.H., de Borst, R., Error-amplification analysis of subiteration-preconditioned GMRES for fluid-structure interaction, Comput. Methods Appl. Mech. Engrg., 195, pp. 2124-2148, 2006, https://doi.org/10.1016/j.cma.2005.01.018 DOI: https://doi.org/10.1016/j.cma.2005.01.018

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

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