Free Access
Issue
ESAIM: M2AN
Volume 34, Number 1, January/February 2000
Page(s) 31 - 45
DOI https://doi.org/10.1051/m2an:2000129
Published online 15 April 2002
  1. G.P. Astrakhantsev, Method of fictitious domains for a second-order elliptic equation with natural boundary conditions. USSR Comput. Math. Math. Phys. 18 (1978) 114-121. [CrossRef] [Google Scholar]
  2. C. Atamian, G.V. Dinh, R. Glowinski, J. He and J. Périaux, On some imbedding methods applied to fluid dynamics and electro-magnetics. Comput. Methods Appl. Mech. Engrg. 91 (1991) 1271-1299. [CrossRef] [MathSciNet] [Google Scholar]
  3. I. Babuska, The finite element method with Lagrangian multipliers. Numer. Math. 20 (1973) 179-192. [CrossRef] [Google Scholar]
  4. A. Bespalov, Yu.A. Kuznetsov, O. Pironneau and M.-G. Vallet, Fictitious domain with separable preconditioners versus unstructured adapted meshes. Impact Comput. Sci. Eng. 4 (1992) 217-249. [CrossRef] [Google Scholar]
  5. C. Börgers, A triangulation algorithm for fast elliptic solvers based on domain imbedding. SIAM J. Numer. Anal. 27 (1990) 1187-1196. [CrossRef] [MathSciNet] [Google Scholar]
  6. C. Börgers and O.B. Widlund, On finite element domain imbedding methods. SIAM J. Numer. Anal. 27 (1990) 963-978. [CrossRef] [MathSciNet] [Google Scholar]
  7. V. Braibant and C. Fleury, Shape optimal design using B-splines. Comput. Methods Appl. Mech. Engrg. 44 (1984) 247-267. [CrossRef] [Google Scholar]
  8. J.H. Bramble, The Lagrangian multiplier method for Dirichlet's problem. Math. Comp. 37 (1981) 1-11. [MathSciNet] [Google Scholar]
  9. J.H. Bramble, J.E. Pasciak and A.H. Schatz, The construction of preconditioners for elliptic problems by substructuring, I. Math. Comp. 47 (1986) 103-134. [Google Scholar]
  10. R.A. Brockman, Geometric sensitivity analysis with isoparametric finite elements. Comm. Appl. Numer. Math. 3 (1987) 495-499. [CrossRef] [Google Scholar]
  11. T.F. Chan, Analysis of preconditioners for domain decomposition. SIAM J. Numer. Anal. 24 (1987) 382-390. [CrossRef] [MathSciNet] [Google Scholar]
  12. J. Danková and J. Haslinger, Fictitious domain approach used in shape optimization: Neumann boudary condition, in Control of Partial Differential Equations and Applications (Laredo, 1994), Lecture Notes in Pure and Appl. Math., Dekker, New York 174 (1996) 43-49. [Google Scholar]
  13. J. Danková and J. Haslinger, Numerical realization of a fictitious domain approach used in shape optimization. I. Distributed controls. Appl. Math. 41 (1996) 123-147. [MathSciNet] [Google Scholar]
  14. P. Duysinx, W.H. Zhang and C. Fleury, Sensitivity analysis with unstructured free mesh generators in 2-D and 3-D shape optimization, in Structural Optimization 93, Vol. 2, Rio de Janeiro (1993) 205-212. [Google Scholar]
  15. P.E. Gill, W. Murray and M.H. Wright, Practical Optimization. Academic Press, New York (1981). [Google Scholar]
  16. R. Glowinski, T. Hesla, D.D. Joseph, T.-W. Pan and J. Périaux, Distributed Lagrange multiplier methods for particulate flows, in Computational Science for the 21st Century, M.-O. Bristeau, G. Etgen, W. Fitzgibbon, J.L. Lions, J. Périaux and M.F. Wheeler Eds., Wiley, Chichester (1997) 270-279. [Google Scholar]
  17. R. Glowinski and Yu.A. Kuznetsov, On the solution of the Dirichlet problem for linear elliptic operators by a distributed Lagrande multiplier method. C.R. Acad. Sci. Paris Sér. I Math. 327 (1998) 693-698. [Google Scholar]
  18. R. Glowinski, T.-W. Pan, A.J. Kearsley and J. Périaux, Numerical simulation and optimal shape for viscous flow by a fictitious domain method. Internat. J. Numer. Methods Fluids 20 (1995) 695-711. [CrossRef] [MathSciNet] [Google Scholar]
  19. R. Glowinski, T.-W. Pan and J. Périaux, A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Engrg. 111 (1994) 283-303. [Google Scholar]
  20. A. Greenbaum, Iterative Methods for Solving Linear Systems. Frontiers in Applied Mathematics, SIAM, Philadelphia, PA, USA 17 (1997). [Google Scholar]
  21. J. Haslinger, Imbedding/control approach for solving optimal shape design problems. East-West J. Numer. Math. 1 (1993) 111-119. [MathSciNet] [Google Scholar]
  22. J. Haslinger, Comparison of different fictitious domain approaches used in shape optimization. Tech. Rep. 15, Laboratory of Scientific Computing, University of Jyväskylä (1996). [Google Scholar]
  23. J. Haslinger, K.H. Hoffmann and M. Kocvara, Control/fictitious domain method for solving optimal shape design problems. RAIRO Modél. Math. Anal. Numér. 27 (1993) 157-182. [MathSciNet] [Google Scholar]
  24. J. Haslinger and D. Jedelský, Genetic algorithms and fictitious domain based approaches in shape optimization. Structural Optimization 12 (1996) 257-264. [CrossRef] [Google Scholar]
  25. J. Haslinger and A. Klarbring, Fictitious domain/mixed finite element approach for a class of optimal shape design problems. RAIRO Modél. Math. Anal. Numér. 29 (1995) 435-450. [MathSciNet] [Google Scholar]
  26. J. Haslinger and P. Neittaanmäki, Finite Element Approximation for Optimal Shape, Material and Topology Design, 2nd ed., Wiley, Chichester (1996). [Google Scholar]
  27. J. He, Méthodes de domaines fictifs en méchanique des fluides applications aux écoulements potentiels instationnaires autour d'obstacles mobiles. Ph.D. thesis, Université Paris VI (1994). [Google Scholar]
  28. E. Heikkola, Y. Kuznetsov, T. Rossi and P. Tarvainen, Efficient preconditioners based on fictitious domains for elliptic FE-problems with Lagrange multipliers, in ENUMATH 97 - Proceedings of the 2nd European Conference on Numerical Mathematics and Advanced Applications, H.G. Bock, G. Kanschat, R. Rannacher, F. Brezzi, R. Glowinski, Yu.A. Kuznetsov and J. Périaux Eds., World Scientific Publishing Co., Inc., River Edge, NJ (1998) 646-661. [Google Scholar]
  29. K. Kunisch and G. Peichl, Shape optimization for mixed boundary value problems based on an embedding method. Dynam. Contin. Discrete Impuls. Systems 4 (1998) 439-478. [MathSciNet] [Google Scholar]
  30. Yu.A. Kuznetsov, Efficient iterative solvers for elliptic finite element problems on nonmatching grids. Russian J. Numer. Anal. Math. Modelling 10 (1995) 187-211. [CrossRef] [MathSciNet] [Google Scholar]
  31. Yu.A. Kuznetsov, Iterative analysis of finite element problems with Lagrange multipliers, in Computational Science for the 21st Century, M.-O. Bristeau, G. Etgen, W. Fitzgibbon, J.L. Lions, J. Périaux and M.F. Wheeler Eds., Wiley, Chichester (1997) 170-178. [Google Scholar]
  32. Yu.A. Kuznetsov and M.F. Wheeler, Optimal order substructuring preconditioners for mixed finite element methods on nonmaching grids. East-West J. Numer. Math. 3 (1995) 127-143. [MathSciNet] [Google Scholar]
  33. R. Mäkinen, Finite-element design sensitivity analysis for non-linear potential problems. Comm. Appl. Numer. Math. 6 (1990) 343-350. [CrossRef] [Google Scholar]
  34. G.I. Marchuk, Yu.A. Kuznetsov and A.M. Matsokin, Fictitious domain and domain decomposition methods. Soviet J. Numer. Anal. Math. Modelling 1 (1986) 3-35. [CrossRef] [MathSciNet] [Google Scholar]
  35. NAG, The NAG Fortran Library Manual: Mark 18. NAG Ltd, Oxford (1997). [Google Scholar]
  36. C.C. Paige and M.A. Saunders, Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 12 (1975) 617-629. [CrossRef] [MathSciNet] [Google Scholar]
  37. O. Pironneau, Optimal Shape Design for Elliptic Systems. Springer-Verlag, New York (1984). [Google Scholar]
  38. W. Proskurowski and P.S. Vassilevski, Preconditioning capacitance matrix problems in domain imbedding. SIAM J. Sci. Comput. 15 (1994) 77-88. [CrossRef] [MathSciNet] [Google Scholar]
  39. T. Rossi, Fictitious Domain Methods with Separable Preconditioners. Ph.D. thesis, Department of Mathematics, University of Jyväskylä (1995). [Google Scholar]
  40. T. Rossi and J. Toivanen, A parallel fast direct solver for block tridiagonal systems with separable matrices of arbitrary dimension. SIAM J. Sci. Comput. 20 (1999) 1778-1793. [CrossRef] [MathSciNet] [Google Scholar]
  41. J. Sokolowski and J.-P. Zolesio, Introduction to Shape Optimization. Shape Sensitivity Analysis. Springer-Verlag, Berlin (1992). [Google Scholar]
  42. P.N. Swarztrauber, The methods of cyclic reduction and Fourier analysis and the FACR algorithm for the discrete solution of Poisson's equation on a rectangle. SIAM Rev. 19 (1977) 490-501. [CrossRef] [MathSciNet] [Google Scholar]
  43. J. Toivanen, Fictitious Domain Method Applied to Shape Optimization. Ph.D. thesis, Department of Mathematics, University of Jyväskylä (1997). [Google Scholar]
  44. L. Tomas, Optimisation de Forme et Domaines Fictifs: Analyse de Nouvelles Formulations et Aspects Algorithmiques. Ph.D. thesis, École Centrale de Lyon (1997). [Google Scholar]

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