Publications

Articles

[1] The topological asymptotic for the Helmholtz equation. SIAM J. Control Optim. Vol. 42(5), pp. 1523-1544, 2003 (with B. Samet and M. Masmoudi). [pdf]

[2] Crack detection by the topological gradient method. Control and Cybernetics 34(1), pp. 81-101, 2005, special issue (with I. Horchani and M. Masmoudi). [pdf]

[3] The topological asymptotic for the Navier-Stokes equations. ESAIM: COCV 11(3), pp. 401-425, 2005. [pdf]

[4] Topological sensitivity analysis for some nonlinear PDE systems. J. Math. Pures et Appliquées 85(4), pp. 540-557, 2006. [pdf]

[5] A new algorithm for topology optimization using a level-set method. J. Comp. Phys. 216(2), pp. 573-588, 2006 (with H. Andrä). [pdf]

[6] Sensitivity analysis with respect to a local perturbation of the material property. Asymptotic Analysis 49(1,2), pp. 87-108, 2006. [pdf]

[7] Topological sensitivity in the context of ultrasonic nondestructive testing. Engineering Analysis with Boundary Elements 32, pp. 936-947, 2008, special issue (with N. Dominguez). [pdf]

[8] Topological sensitivity analysis for time-dependent problems. ESAIM: COCV 14(3), pp. 427-455, 2008 (with T. Takahashi and B. Vexler). [pdf]

[9] A penalty method for topology optimization subject to a pointwise state constraint. ESAIM: COCV 16(3), pp. 523-544, 2010. [pdf]

[10] Topological optimization of structures subject to Von Mises stress constraints. Structural and Multidisciplinary Optimization 41(3), pp. 407-420, 2010 (with A.A. Novotny). [pdf]

[11] Augmented Lagrangian for cone constrained topology optimization. Comput. Optim. Appl. 49(1), pp. 101-122, 2011. [pdf]

[12] Optimality conditions for shape and topology optimization subject to a cone constraint. SIAM J. Control Optim. 48(6), pp. 4056-4077, 2010 (with M. Ciligot-Travain). [pdf]

[13] Topological asymptotic analysis of the Kirchhoff plate bending problem. ESAIM: COCV 17(3), pp. 705-721, 2011 (with A.A. Novotny). [pdf]

[14] Topological derivative in multi-scale linear elasticity models applied to the synthesis of microstructures. Int. J. Num. Meth. Eng. 84(6), pp. 733-756, 2010 (with S.M. Giusti, A.A. Novotny and E.A. De Souza Neto). [pdf]

[15] A semismooth Newton method for topology optimization. Nonlinear Analysis 73(6), pp. 1585-1595, 2010. [pdf]

[16] Analysis of a level-set method for topology optimization. Optim. Methods Soft. 26(4-5), 2011, pp. 555-573. [pdf]

[17] Topological derivative-based optimization of microstructures considering different multiscale models. Computer Modeling in Engineering and Sciences 62(1), pp. 23-56, 2010 (with S.M. Giusti, A.A. Novotny and E.A. De Souza Neto).

[18] Connections between topological sensitivity analysis and material interpolation schemes in topology optimization. Struc. Multidisc. Optim. 43(6), pp. 755-765, 2011. [pdf]

[19] Topological derivative-based topology optimization of structures subject to Drucker-Prager stress constraints. Comp. Meth. Appl. Mech. Eng. 233-236, pp. 123-136, 2012 (with A.A. Novotny and E.A. De Souza Neto). [pdf]

[20] Topology optimization methods with gradient-free perimeter approximation. Interfaces and Free Boundaries 14, pp. 401-430, 2012 (with N. Van Goethem). [pdf]

[21] Regularized perimeter for topology optimization. SIAM J. Control Optim. 51(3), pp. 2176-2199, 2013. [pdf]

[22] A semismooth Newton method for a class of semilinear optimal control problems with box and volume constraints. Comput. Optim. Appl. 56(2), pp. 369-403, 2013 (with A. Laurain). [preprint]

[23] Topological sensitivity analysis for elliptic differential operators of order 2m. J. Differential Equations 256(4), pp. 1735-1770, 2014 (with A.A. Novotny and N. Van Goethem). [pdf]

[24] Minimal partitions and image classification using a gradient-free perimeter approximation. Inverse Problems and Imaging 8(2), pp. 361-387, 2014 (with A.A. Novotny and N. Van Goethem). [pdf]

[25] Edge detection using topological gradients: a scale-space approach. J. Math. Imaging Vision 52(2), pp. 249-266, 2015 (with J. Fehrenbach). [preprint]

[26] A notion of compliance robustness in topology optimization. ESAIM:COCV 22(1), pp. 64-87, 2016 (with M. Ciligot-Travain). [pdf]

[27] Analysis of the incompatibility operator and application in intrinsic elasticity with dislocations. SIAM J. Math Analysis 48(1), pp. 320-348, 2016 (with N. Van Goethem). [preprint]

[28] Topology optimization of eletric motors using topological derivative for nonlinear magnetostatics. IEEE transactions on Magnetics 52(3), 2016 (with P. Gangl and U. Langer)

[29] Topological derivatives for a class of quasilinear elliptic equations.  J. Math. Pures Appl. 107(4), pp. 367-408, 2017 (with A. Bonnafé). [preprint]

[30] Incompatibility-governed elasto-plasticity for continua with dislocations. Proc. A 473(2199), 2017  (with N. Van Goethem). [preprint] [supplementary note]

[31] A consistent relaxation of optimal design problems for coupling shape and topological derivatives. Numerische Mathematik 140(1), pp. 35-94, 2018 (with C. Dapogny and A. Ferrer). [preprint]

[32] Topological derivative for nonlinear magnetostatic problem. Electron. Trans. Numer. Anal. 51, pp. 169-218, 2019 (with P. Gangl). [journal]

[33] The incompatibility operator: from Riemann’s intrinsic view of geometry to a new model of elasto-plasticity. Topics in Applied analysis and Optimization (CIM series in Mathematical Sciences), pp. 33-70, 2019 (with N. Van Goethem). [preprint]

[34] Existence and asymptotic results for an intrinsic model of small strain incompatible elasticity. DCDS-B 25(10), pp. 3769-3805, 2020 (with N. Van Goethem). [preprint]

[35] Variational approximation of interfaces energies and applications. Interfaces and Free Boundaries 23, pp. 59-102, 2021 (with D. Gourion and M. Zabiba). [preprint]

[36] An introduction to the topological derivative. Eng. Comp. 39(1), pp. 3-33, 2022 (special issue “On the topological derivative method and its applications in computational engineering”). [preprint]

[37] A consistent approximation of the total perimeter functional for topology optimization algorithms. ESAIM:COCV 28(18), 2022 (with C. Dapogny and A. Ferrer). [preprint] [journal]

[38] Damping optimization of viscoelastic cantilever beams and plates under free vibration. Computers and Structures 268, 2022 (with A. Joubert, G. Allaire and J. Diani). [preprint]

[39] Damping optimization of viscoelastic thin structures, application and analysis (with A. Joubert, G. Allaire and J. Diani). Structural and Multidisciplinary Optimization 66(149), 2023. [preprint]

[40] A second order model of small-strain incompatible elasticity (with N. Van Goethem). Mathematics and Mechanics of Solids 29(3), pp503-530, 2024. [preprint]

Submitted

Nonlocal approximation of the anisotropic perimeter and application to topology optimization (with B. Bogosel). [preprint]

Theses

Theoretical and numerical aspects in topological shape optimization. Doctoral thesis, 2003. [pdf]

Topological sensitivity analysis and applications in shape optimization. Habilitation thesis, 2011. [pdf]