A domain decomposition method for quasi-incompressible formulations with discontinuous pressure field
Application to the mechanical study of a flexible bearing
Keywords:
Domain decomposition method, Newton-Krylov, quasi incompressibility, mixed formulationAbstract
We study the implementation of a domain decomposition method for structures with quasi-incompressible components. We chose a mixed formulation where the pressure field is discontinuous on the interfaces between substructures. We propose an extension of classical preconditioners to this class of problems. The numerical simulation of the mechanical behaviour of the flexible bearing of the nozzle of a solid propellant booster is then conducted using various Newton-Krylov parallel approaches. We present the main mechanical results and compare the numerical performance of the parallel approaches to a sequential approach.
Downloads
References
[BRE 91] BREZZI F., FORTIN M., Mixed and hybrid finite element methods, Springer series
in Computational Mathematics, 1991.
[DDM02] “Proceedings of the 14th international conference on domain decomposition methods,
Mexico”, 2002.
[FAR 94] FARHAT C., ROUX F.-X., “Implicit parallel processing in structural mechanics”,
Computational Mechanics Advances, vol. 2, 1994, p. 1-24.
[GOS 02] GOSSELET P., REY C., “On a selective reuse of Krylov subspaces for Newton
Krylov approaches in non-linear elasticity”, 14th international conference on domain
decomposition methods, Mexico, 2002.
[LAM 99] LAMBERT-DIANI J., REY C., “New phenomenological behavior laws for rubbers
and thermoplastic elastomers”, Eur. J. Mech. A/Solids, vol. 18, 1999, p. 1027-1043.
[LET 94a] LETALLEC P., “Domain Decomposition Methods in Computational Mechanics”,
Computational Mechanics Adv., vol. 1, 1994.
[LET 94b] LETALLEC P., “Numerical methods for non-linear three-dimensional elasticity”,
PG C., JL. L., Eds., Handbook of numerical analysis, vol. 3, Elsevier, 1994.
[MAN 93] MANDEL J., “Balancing domain decomposition”, Comm. Appl. Numer. Meth.,
vol. 9, 1993, p. 233-241.
[REY 96] REY C., “Une technique d’accélération de la résolution de problèmes d’élasticité
non-linéaire par décomposition de domaines”, Comptes rendus de l’académie des sciences,
vol. 322 of II b, p. 601-606, 1996.
[REY 98] REY C., RISLER F., “A Rayleigh-Ritz preconditioner for the iterative solution to
large scale nonlinear problems”, Numerical Algorithms, vol. 17, 1998, p. 279-311.
[RIS 00] RISLER F., REY C., “Iterative accelerating algorithms with Krylov subspaces for the
solution to large-scale non-linear problems”, Numer. Algorithms, vol. 23, 2000, p. 1-30.
[RIV 51] RIVLIN R., SAUNDERS D., “Large elastic deformation of isotropic materials. Experiments
on the deformation of rubber.”, Phil. Trans. Roy. Soc., vol. A243, 1951, p. 251-288.
[RIX 99] RIXEN D., FARHAT C., “A simple and efficient extension of a class of substructure
based preconditioners to heterogeneous structural mechanics problems”, Int. J. Num. Meth.
Engrg., vol. 44, 1999.
[SAA 87] SAAD Y., “On the Lanczos method for solving symmetric linear systems with several
right-hand sides”, Math. Comp., vol. 48, 1987, p. 651-662.