@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: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {31--45}, publisher = {Dunod}, address = {Paris}, volume = {34}, number = {1}, year = {2000}, mrnumber = {1735978}, zbl = {0948.65064}, language = {en}, url = {http://www.numdam.org/item/M2AN_2000__34_1_31_0/} }
TY - JOUR AU - Mäkinen, Raino A. E. AU - Rossi, Tuomo AU - Toivanen, Jari TI - A moving mesh fictitious domain approach for shape optimization problems JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2000 SP - 31 EP - 45 VL - 34 IS - 1 PB - Dunod PP - Paris UR - http://www.numdam.org/item/M2AN_2000__34_1_31_0/ LA - en ID - M2AN_2000__34_1_31_0 ER -
%0 Journal Article %A Mäkinen, Raino A. E. %A Rossi, Tuomo %A Toivanen, Jari %T A moving mesh fictitious domain approach for shape optimization problems %J ESAIM: Modélisation mathématique et analyse numérique %D 2000 %P 31-45 %V 34 %N 1 %I Dunod %C Paris %U http://www.numdam.org/item/M2AN_2000__34_1_31_0/ %G en %F 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: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 1, pp. 31-45. http://www.numdam.org/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 | Zbl
,[2] On some imbedding methods applied to fluid dynamics and electro-magnetics. Comput. Methods Appl. Mech. Engrg. 91 (1991) 1271-1299. | MR
, , , and ,[3] The finite element method with Lagrangian multipliers. Numer. Math. 20 (1973) 179-192. | MR | Zbl
,[4] Fictitious domain with separable preconditioners versus unstructured adapted meshes. Impact Comput. Sci. Eng. 4 (1992) 217-249. | MR | Zbl
, , and ,[5] A triangulation algorithm for fast elliptic solvers based on domain imbedding. SIAM J. Numer. Anal. 27 (1990). 1187-1196. | MR | Zbl
,[6] On finite element domain imbedding methods. SIAM J. Numer. Anal. 27 1990) 963-978. | MR | Zbl
and ,[7] Shape optimal design using B-splines. Comput. Methods Appl. Mech. Engrg. 44 (1984) 247-267. | Zbl
and ,[8] The Lagrangian multiplier method for Dirichlet's problem. Math. Comp. 37 (1981) 1-11. | MR | Zbl
,[9] The construction of preconditioners for elliptic problems by substructuring, I. Math. Comp. 47 (1986) 103-134. | MR | Zbl
, and ,[10] Geometric sensitivity analysis with isoparametric finite elements. Comm. Appl. Numer. Math. 3 (1987) 495-499. | Zbl
,[11] Analysis of preconditioners for domain decomposition. SIAM J. Numer. Anal. 24 (1987) 382-390. | MR | Zbl
,[12] 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 | Zbl
and ,[13] Numerical realization of a fictitious domain approach used in shape optimization. I. Distributed controls. Appl. Math. 41 (1996) 123-147. | MR | Zbl
and ,[14] 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.
, and ,[15] Practical Optimization. Academic Press, New York (1981). | MR | Zbl
, and ,[16] 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
, , , and ,[17] 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 | Zbl
and ,[18] Numerical simulation and optimal shape for viscous flow by a fictitious domain method. Internat J. Numer. Methods Fluids 20 (1995) 695-711. | MR | Zbl
, , and ,[19] A fictitious domain method for Dirichlet problem and applications. Comput. Methods Appl. Mech. Engrg. 111 (1994) 283-303. | MR | Zbl
, and ,[20] Iterative Methods for Solving Linear Systems, Frontiers in Applied Mathematics, SIAM, Philadelphia, PA, USA 17 (1997). | MR | Zbl
,[21] Imbedding/control approach for solving optimal shape design problems. East-West J. Numer. Math. 1 (1993) 111-119. | MR | Zbl
,[22] Comparison of different fictitious domain approaches used in shape optimization. Tech. Rep. 15, Laboratory of Scientific Computing, University of Jyväskylä (1996).
,[23] Control/fictitious domain method for solving optimal shape design problems. RAIRO Modél. Math. Anal. Numér. 27 (1993) 157-182. | Numdam | MR | Zbl
, and ,[24] Genetic algorithms and fictitious domain based approaches in shape optimization. Structural Optimization 12 (1996) 257-264.
and ,[25] 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 | Zbl
and ,[26] Finite Element Approximation for Optimal Shape, Material and Topology Design, 2nd ed., Wiley, Chichester (1996). | MR | Zbl
and ,[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] 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 | Zbl
, , and ,[29] Shape optimization for mixed boundary value problems based on an embedding method. Dynam. Contin. Discrete Impuls. Systems 4 (1998) 439-478. | MR | Zbl
and ,[30] Efficient iterative solvers for elliptic finite element problems on nonmatching grids. Russian J. Numer. Anal. Math. Modelling 10 (1995) 187-211. | MR | Zbl
,[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
,[32] Optimal order substructuring preconditioners for mixed finite element methods on nonmaching grids, East-West J. Numer. Math. 3 (1995) 127-143. | MR | Zbl
and ,[33] Finite-element design sensitivity analysis for non-linear potential problems. Comm. Appl. Numer. Math. 6 (1990) 343-350. | MR | Zbl
,[34] Fictitious domain and domain decomposition methods. Soviet J. Numer. Anal. Math. Modelling 1 (1986) 3-35. | MR | Zbl
, and ,[35] NAG, The NAG Fortran Library Manual: Mark 18. NAG Ltd, Oxford (1997).
[36] Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 12 (1975) 617-629. | MR | Zbl
and ,[37] Optimal Shape Design for Elliptic Systems, Springer-Verlag, New York (1984). | MR | Zbl
,[38] Preconditioning capacitance matrix problems in domain imbedding. SIAM J. Sci. Comput. 15 (1994) 77-88. | MR | Zbl
and ,[39] Fictitious Domain Methods with Separable Preconditioners. Ph.D. thesis, Department of Mathematics, University of Jyväskylä (1995). | Zbl
,[40] A parallel fast direct solver for block tridiagonal Systems with separable matrices of arbitrary dimension. SIAM J. Sci. Comput. 20 (1999) 1778-1793. | MR | Zbl
and ,[41] Introduction to Shape Optimization. Shape Sensitivity Analysis. Springer-Verlag, Berlin (1992). | MR | Zbl
and ,[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 | Zbl
,[43] Fictitious Domain Method Applied to Shape Optimization. Ph.D. thesis, Department of Mathematics, University of Jyväskylä (1997). | MR | Zbl
,[44] Optimisation de Forme et Domaines Fictifs: Analyse de Nouvelles Formulations et Aspects Algorithmiques. Ph.D. thesis, École Centrale de Lyon (1997).
,