@article{M2AN_2000__34_1_31_0,
author = {M\"akinen, Raino A. E. and Rossi, Tuomo and Toivanen, Jari},
title = {A moving mesh fictitious domain approach for shape optimization problems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {34},
year = {2000},
pages = {31-45},
mrnumber = {1735978},
zbl = {0948.65064},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2000__34_1_31_0}
}
Mäkinen, Raino A. E.; Rossi, Tuomo; Toivanen, Jari. A moving mesh fictitious domain approach for shape optimization problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) pp. 31-45. http://gdmltest.u-ga.fr/item/M2AN_2000__34_1_31_0/
[1] , Method of fictitious domains for a second-order elliptic equation with natural boundary conditions. USSR Comput. Math. Math. Phys. 18 (1978) 114-121. | MR 468228 | Zbl 0394.35028
[2] , , , and , On some imbedding methods applied to fluid dynamics and electro-magnetics. Comput. Methods Appl. Mech. Engrg. 91 (1991) 1271-1299. | MR 1145790
[3] , The finite element method with Lagrangian multipliers. Numer. Math. 20 (1973) 179-192. | MR 359352 | Zbl 0258.65108
[4] , , and , Fictitious domain with separable preconditioners versus unstructured adapted meshes. Impact Comput. Sci. Eng. 4 (1992) 217-249. | MR 1188325 | Zbl 0760.76068
[5] , A triangulation algorithm for fast elliptic solvers based on domain imbedding. SIAM J. Numer. Anal. 27 (1990). 1187-1196. | MR 1061125 | Zbl 0715.65088
[6] and , On finite element domain imbedding methods. SIAM J. Numer. Anal. 27 1990) 963-978. | MR 1051116 | Zbl 0705.65078
[7] and , Shape optimal design using B-splines. Comput. Methods Appl. Mech. Engrg. 44 (1984) 247-267. | Zbl 0525.73104
[8] , The Lagrangian multiplier method for Dirichlet's problem. Math. Comp. 37 (1981) 1-11. | MR 616356 | Zbl 0477.65077
[9] , and , The construction of preconditioners for elliptic problems by substructuring, I. Math. Comp. 47 (1986) 103-134. | MR 842125 | Zbl 0615.65112
[10] , Geometric sensitivity analysis with isoparametric finite elements. Comm. Appl. Numer. Math. 3 (1987) 495-499. | Zbl 0623.73081
[11] , Analysis of preconditioners for domain decomposition. SIAM J. Numer. Anal. 24 (1987) 382-390. | MR 881372 | Zbl 0625.65100
[12] and , 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. | MR 1364636 | Zbl 0864.49022
[13] and , Numerical realization of a fictitious domain approach used in shape optimization. I. Distributed controls. Appl. Math. 41 (1996) 123-147. | MR 1373477 | Zbl 0854.49004
[14] , and , 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.
[15] , and , Practical Optimization. Academic Press, New York (1981). | MR 634376 | Zbl 0503.90062
[16] , , , and , 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. | Zbl 0919.76077
[17] and , On the solution of the Dirichlet problem for linear elliptic operators by a distributed Lagrande multiplier method. CR. Acad. Sci. Paris Sér. I Math. 327 (1998) 693-698. | MR 1652674 | Zbl 1005.65127
[18] , , and , Numerical simulation and optimal shape for viscous flow by a fictitious domain method. Internat J. Numer. Methods Fluids 20 (1995) 695-711. | MR 1333904 | Zbl 0837.76068
[19] , and , A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Engrg. 111 (1994) 283-303. | MR 1259864 | Zbl 0845.73078
[20] , Iterative Methods for Solving Linear Systems, Frontiers in Applied Mathematics, SIAM, Philadelphia, PA, USA 17 (1997). | MR 1474725 | Zbl 0883.65022
[21] , Imbedding/control approach for solving optimal shape design problems. East-West J. Numer. Math. 1 (1993) 111-119. | MR 1253630 | Zbl 0835.65089
[22] , Comparison of different fictitious domain approaches used in shape optimization. Tech. Rep. 15, Laboratory of Scientific Computing, University of Jyväskylä (1996).
[23] , and , Control/fictitious domain method for solving optimal shape design problems. RAIRO Modél. Math. Anal. Numér. 27 (1993) 157-182. | Numdam | MR 1211614 | Zbl 0772.65043
[24] and , Genetic algorithms and fictitious domain based approaches in shape optimization. Structural Optimization 12 (1996) 257-264.
[25] and , Fictitious domain/mixed finite element approach for a class of optimal shape design problems. RAIRO Modél. Math. Anal. Numér. 29 (1995) 435-450. | Numdam | MR 1346278 | Zbl 0831.65072
[26] and , Finite Element Approximation for Optimal Shape, Material and Topology Design, 2nd ed., Wiley, Chichester (1996). | MR 1419500 | Zbl 0845.73001
[27] , Méthodes de domaines fictifs en méchanique des fluides applications aux écoulements potentiels instationnaires autour d'obstacles mobiles. Ph.D. thesis, Université Paris VI (1994).
[28] , , and , 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. | MR 1704135 | Zbl 0970.65047
[29] and , Shape optimization for mixed boundary value problems based on an embedding method. Dynam. Contin. Discrete Impuls. Systems 4 (1998) 439-478. | MR 1639129 | Zbl 0914.49027
[30] , Efficient iterative solvers for elliptic finite element problems on nonmatching grids. Russian J. Numer. Anal. Math. Modelling 10 (1995) 187-211. | MR 1343473 | Zbl 0839.65031
[31] , 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. | Zbl 0911.65110
[32] and , Optimal order substructuring preconditioners for mixed finite element methods on nonmaching grids, East-West J. Numer. Math. 3 (1995) 127-143. | MR 1342888 | Zbl 0832.65134
[33] , Finite-element design sensitivity analysis for non-linear potential problems. Comm. Appl. Numer. Math. 6 (1990) 343-350. | MR 1062294 | Zbl 0716.65097
[34] , and , Fictitious domain and domain decomposition methods. Soviet J. Numer. Anal. Math. Modelling 1 (1986) 3-35. | MR 897996 | Zbl 0825.65027
[35] NAG, The NAG Fortran Library Manual: Mark 18. NAG Ltd, Oxford (1997).
[36] and , Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 12 (1975) 617-629. | MR 383715 | Zbl 0319.65025
[37] , Optimal Shape Design for Elliptic Systems, Springer-Verlag, New York (1984). | MR 725856 | Zbl 0534.49001
[38] and , Preconditioning capacitance matrix problems in domain imbedding. SIAM J. Sci. Comput. 15 (1994) 77-88. | MR 1257155 | Zbl 0806.65118
[39] , Fictitious Domain Methods with Separable Preconditioners. Ph.D. thesis, Department of Mathematics, University of Jyväskylä (1995). | Zbl 0835.65056
[40] and , A parallel fast direct solver for block tridiagonal Systems with separable matrices of arbitrary dimension. SIAM J. Sci. Comput. 20 (1999) 1778-1793. | MR 1694683 | Zbl 0931.65020
[41] and , Introduction to Shape Optimization. Shape Sensitivity Analysis. Springer-Verlag, Berlin (1992). | MR 1215733 | Zbl 0761.73003
[42] , 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. | MR 438732 | Zbl 0358.65088
[43] , Fictitious Domain Method Applied to Shape Optimization. Ph.D. thesis, Department of Mathematics, University of Jyväskylä (1997). | MR 1483322 | Zbl 0885.65070
[44] , Optimisation de Forme et Domaines Fictifs: Analyse de Nouvelles Formulations et Aspects Algorithmiques. Ph.D. thesis, École Centrale de Lyon (1997).