References
- [1] G. Alessandrini and A. Diaz Valenzuela, Unique determination of multiple cracks by two measurements, SIAM. J. Control Optim. 34 (3), 1996, 913-921.10.1137/S0363012994262853
- [2] G. Alessandrini, E. Beretta and S. Vessela Determining linear cracks by boundary measurements: Lipschitz stability, SIAM J. Math. Anal. 27, 1996, 361-375.10.1137/S0036141094265791
- [3] S. Andrieux and A. Ben Abda Identification of planar cracks by complete overdetermined data: inversion formulae, Inverse Problems, 12, 1996, 553-563.10.1088/0266-5611/12/5/002
- [4] A. Ben Abda, H. Ben Ameur and M. Jaoua Identification of 2D cracks by elastic boundary measurements, Inverse Problems 15, 1999, 67-77.10.1088/0266-5611/15/1/011
- [5] N. Nishimura and S. Kobayashi A boundary integral equation method for an inverse problem related to crack detection, Int. J. Num. Methods Eng., 32(1991), pp. 1371-1387.10.1002/nme.1620320702
- [6] H. Ammari, S. Moskow, and M. Vogelius, Boundary integral formulas for reconstruction of electromagnetic imperfections of small diameter, ESAIM, Cont. Opt. Cal. Variat. vol. 9, 2004, 49-66.10.1051/cocv:2002071
- [7] M. Vogelius, and D. Volkov, Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities, Math. Model. Numer. Anal. 34 (2000), 723-748.10.1051/m2an:2000101
- [8] E. Beretta, E. Francini, and M. Vogelius, Asymptotic formulas for for steady state voltage potentials in the presence of thin inhomogeneities. A rigorous error analysis, J. Math. Pures Appl. 82, 2003, 1277-1301.10.1016/S0021-7824(03)00081-3
- [9] D.J. Cedio-Fengya, S. Moskow, and M. Vogelius, Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction, Inverse Problems. vol. 14, 1998, 553-595.10.1088/0266-5611/14/3/011
- [10] A. Friedman, and M. Vogelius, Identification of small inhomogeneties of extreme conductivity by boundary measurements: a theorem on continuous dependence, Arch. Rat. Mech. Anal., 105, 1989, 299-326.10.1007/BF00281494
- [11] C. Alves, and H. Ammari, Boundary integral formulae for the reconstruction of imperfections of small diameter in an elastic medium, SIAM, J. Appl. Math. 62, 2001, 94-106.10.1137/S0036139900369266
- [12] H. Ammari, H. Kang, G. Nakamura and K. Tanuma, Complete asymptotic expansions of solutions of the system of elastostatics in the presence of an inclusion of small diameter and detection of an inclusion, J. Elasticity 67, 2002, 97-129.10.1142/9789812776228_0112
- [13] H. Ammari, M. Vogelius and D. Volkov, Asymptotic formulas for perturbations in the electromagnetic fields due to presence of inhomogeneities of small diameter II. The full Maxwell’s equations, J. Math. Pures Appl. 80, 2001, 769-814.10.1016/S0021-7824(01)01217-X
- [14] F. Caubet, M. Dambrine, D. Kateb, and C. Z. Timimoun, A Kohn-Vogelius formulation to detect an obstacle immersed in a fluid. Inverse Probl. Imaging, 7(1):123-157, (2013).10.3934/ipi.2013.7.123
- [15] S. Andrieux, T.N. Baranger, A. Ben Abda, Solving Cauchy problems by minimizing an energy-like functional Inverse Problems, 22 (2006) 115-134.10.1088/0266-5611/22/1/007
- [16] S. Garreau, Ph. Guillaume, M. Masmoudi, The topological asymptotic for PDE systems: The elastics case, SIAM J. contr. Optim. 39(6), 1756-1778, (2001).10.1137/S0363012900369538
- [17] Ph. Guillaume and K. Sid Idris, The topological asymptotic expansion for the Dirichlet Problem. SIAM J. Control. Optim. 41, 1052-1072, (2002).10.1137/S0363012901384193
- [18] Ph. Guillaume, K. Sid Idris, Topological sensitivity and shape optimization for the Stokes equations, SIAM J. Control Optim. 43 (1) 1-31, (2004).10.1137/S0363012902411210
- [19] M. Hassine, Shape optimization for the Stokes equations using topological sensitivity analysis. ARIMA, 5:216-229, (2006).10.46298/arima.1865
- [20] S. Amstutz, The topological asymptotic for the Navier-Stokes equations. ESAIM Control Optim. Calc. Var., 11(3):401-425 (electronic), (2005).10.1051/cocv:2005012
- [21] M. Abdelwahed, M. Hassine, Topological optimization method for a geometric control problem in Stokes flow. Appl. Numer. Math. 59(8), 1823-1838, (2009).10.1016/j.apnum.2009.01.008
- [22] M. Hassine, M. Masmoudi, The topological asymptotic expansion for the quasi-Stokes problem. ESAIM. Control, Optimisation and Calculus of Variations, vol. 10, no. 4, pp. 478-504, 2004.10.1051/cocv:2004016
- [23] M. Masmoudi, J. Pommier, and B. Samet, The topological asymptotic expansion for the Maxwell equations and some applications. Inverse Problems, 21(2):547-564, (2005).10.1088/0266-5611/21/2/008
- [24] S.T. Chung and T.H. Kwon, Numerical simulation of fiber orientation in injection moulding of short-fiber-reinforced thermoplastics, Polym. Eng. Sci. 7 (35), 1995, 604-618.10.1002/pen.760350707
- [25] X. Fan, N. Phan-Thien and R. Zheng, A direct simulation of fiber suspensions, J. Non-Newtonian Fluid Mech. 74, 1998), 113-135.10.1016/S0377-0257(97)00050-5
- [26] T. Gotz, Simulating particles in Stokes flow, J. Comput. Appl. Math. 175 (2005), 415-427.10.1016/j.cam.2004.06.019
- [27] C. Pozrikidis, Dynamic simulation of the flow of suspensions of two-dimensional particles with arbitrary shapes, Eng. Anal. Boundary Elements 25 (1) (2001), pp.19-30.10.1016/S0955-7997(00)00045-X
- [28] H. Zhou and C. Pozrikidis, Adaptive singularity method for Stokes flow past particles, J. Comput. Phys. 117 (1995), pp. 79-89.10.1006/jcph.1995.1046
- [29] R. Codina, U. Scha er and E. Oñate, Mould filling simulation using finite elements, Int. J. Numer. Meth. Fluid Flow 4, 1994, 291-310.10.1108/EUM0000000004108
- [30] G. Dhatt, D.M. Gao, A. Ben Cheikh, A finite element simulation of metal flow in moulds, Int. J. Numer. Meth. Eng. 30, 1990, 821-831.10.1002/nme.1620300416
- [31] K.M. Shyue, A fluid-mixture type algorithm for compressible multicomponent flow with van der Waals equation of state, J. Comput. Phys. 156 (1999), pp. 43-88.10.1006/jcph.1999.6349
- [32] A. Ben Abda, M. Hassine, M. Jaoua, M. Masmoudi, Topological sensitivity analysis for the location of small cavities in Stokes flow,SIAM J. Contr. Optim, 2871-2900, (2009).10.1137/070704332
- [33] F. Caubet, M. Dambrine, Localization of small obstacles in Stokes flow. Inverse Problems, 28(10):105007, 31, (2012).10.1088/0266-5611/28/10/105007
- [34] L. Afraites, M. Dambrine, K. Eppler AND K.Kateb, Detecting perfectly insulated obstacles by shape optimization techniques of order two., Discrete Contin.Dyn. Syst., no 8(2), 389-416, (2007).10.3934/dcdsb.2007.8.389