Newton's method in shape optimisation: A three-dimensional case

BIT Numerical Mathematics

Volumn 40, Issue 1, 2000, Pages 102-120

  Novruzi, A ^a   Roche, J R ^a  

^a UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

Author keywords

Newton methods; Shape optimisation

Indexed keywords

EID: 0042686332     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022370419231     Document Type: Article

References (22)

1. R. Dautray and J.-L. Lions, Analyse Mathématique et Calcul Numérique, Masson, Paris, 1988.
2. C. Farhat and F.-X. Roux, Implicit parallel processing in structural mechanics, Comput. Mech. Adv., 2:1 (1994), pp.1-124.
3. R. Fletcher, Practical Methods of Optimization, John Wiley, Chichester, 1987.
4. E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, Boston, MA, 1984.
5. G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed., Johns Hopkins University Press, Baltimore, MD., 1989.
6. Y. Goto and N. Fujii, Second order numerical method for domain optimization problems, J. Optim. Theory Appl., 67 (1990), pp. 533-550.
7. W. Gropp, E. Lusk and A. Skjellum, Using MPI, Portable Parallel Programming with the Message-Passing Interface, MIT Press, Cambridge, MA, 1994.
8. 2AN, 23 (1989), pp. 155-177.
9. R. Kress Linear Integral Equations, Springer-Verlag, Berlin, 1989.
10. S. Murat and J. Simon, Sur le contrôle par un domaine géométrique, Rapport du Laboratoire d'Analyse Numérique, Université de Paris , 1976.
11. S. G. Nash and A. Sofer, Block truncated-Newton methods for parallel optimization, Math. Programming, Ser. B, 45:1 (1989), pp. 529-546.
12. J.-C. Nedelec, Approximation des équations intégrales en mécanique et en physique, Rapport Interne, Ecole Polytechnique, 1977.
13. A. Novruzi, Contribution en Optimisation de Formes et Applications, Thèse de l'Université Henri Poincaré, Nancy 1, 1997.
14. A. Novruzi and J. R. Roche, Second order derivatives, Newton method, application to shape optimization, Rapport INRIA, 1995.
15. A. Novruzi and J. R. Roche, Newton method in 3-dimensional shape optimization problems. Application to electromagnetic casting, Rapport INRIA, 1998.
16. M. Pierre and J. R. Roche, Numerical simulation of tridimensional electromagnetic shaping of liquid metals, Numer. Math., 65 (1993), pp. 203-217.
17. J. Simon, Differentiation with respect to the domain in boundary value problems, Numer. Funct. Anal. Optim., 2 (1980), pp. 649-687.
18. J. Sokolowski and J. P. Zolesio, Introduction to Shape Optimization, Shape Sensitivity Analysis, Springer Verlag, Berlin, 1992.
19. E. F. Van de Velde, Concurrent Scientific Computing, Springer-Verlag, New York, 1994.
20. T. J. Ypma, The effect of rounding errors on Newton-like methods, IMA J. Numer. Anal., 3 (1983) pp. 109-118.
21. A. S. Zenios and J. M. Mulvey, Vectorization and multitasking of nonlinear network programming algorithms, Math. Programming, Ser. B, 42:2 (1988), pp. 449-470.
22. A. S. Zenios and M. C. Pinar, Parallel block-partitioning of truncated Newton for nonlinear network optimization, SIAM J. Sci. Stat. Comput., 12:5 (1992), pp. 1173-1193.