List of publications

Marc DAMBRINE


Frontpage     Curriculum Vitae     Publications in chronological order     Showcase in shape optimization

Publications by themes



Shape Optimization

  1. M. Dambrine, C. Geiersbach, H. Harbrecht
    Two-norm discrepancy and convergence of the stochastic gradient method with application to shape optimization . arxiv HAL
  2. F. Caubet, C. Conca, M. Dambrine, R. Zelada
    How to insulate a pipe ? HAL
  3. M. Dambrine, F. Caubet, G. Gargantini, J. Maynadier
    Shape optimization of polynomial functionals under uncertainties on the right-hand side of the state equation HAL


  4. M. Dambrine, G. Gargantini, H. Harbrecht, J. Maynadier
    Shape optimization under constraints on the probability of a quadratic functional to exceed a given treshold.
    Accepted to SIAM/ASA Journal on Uncertainty Quantification univ. Basel HAL

  5. M. Dambrine, G. Gargantini, H. Harbrecht, V. Karnaev
    Shape optimization of a thermoelastic body under thermal uncertainties.
    Journal of Computational Physics Volume 527, 15 April 2025, 113794. univ. Basel HAL

  6. M. Dambrine, F. Caubet, G. Gargantini, J. Maynadier
    Shape optimization under a constraint on the worst case scenario
    SIAM Journal on Scientific Computing, Vol. 46, Iss. 6, 2024. HAL

  7. M. Dambrine, H. Harbrecht, and B. Puig.
    Bernoulli free boundary problems under uncertainty : The convex case.
    Computational Methods in Applied Mathematics, 23(2) :333-352, 2023.L HAL

  8. F. Caubet, M. Dambrine and R. Mahadevan.
    Shape derivatives of eigenvalues for mixture problems: Computing the semi-derivative of a minimum.
    Applied Mathematics and Optimization, 86(1), 2022.

  9. F. Caubet, M. Dambrine and R. Mahadevan.
    Shape Derivative for Some Eigenvalue Functionals in Elasticity Theory.
    SIAM J. Control Optim., 59(2), 1218-1245, 2021.

  10. M. Dambrine and H. Harbrecht
    Shape optimization for composite materials and scaffold structures.
    SIAM Multiscale Model. Simul., 18(2), 1136-1152, 2020.
  11. M. Dambrine and B. Puig
    Oriented distance point of view on random sets with application to shape optimization.
    ESAIM: Control, Optimization and Calculus of Variations, 26 (2020).

  12. M. Dambrine and J. Lamboley.
    Stability in shape optimization with second variation.
    Journal of Differential Equations, 267(5) :3009-3045, 2019.

  13. M. Dambrine, H. Harbrecht, M.D. Peters, and B. Puig.
    On Bernoulli's free boundary problem with a random boundary.
    International Journal for Uncertainty Quantification, 7(4) :335-353, 2017.

  14. C. Conca, M. Dambrine, R. Mahadevan, and D. Quintero.
    Minimization of the groundstate of the mixture of two conducting materials in a small contrast regime.
    Mathematical Methods in the Applied Sciences, 39(13) :3549-3564, 2016.

  15. M. Dambrine, D. Kateb, and J. Lamboley.
    An extremal eigenvalue problem for the Wentzell-Laplace operator.
    Annales de l'Institut Henri Poincare (C) Analyse Non Linéaire, 33(2) :409-450, 2016.

  16. M. Dambrine and A. Laurain.
    A first order approach for worst-case shape optimization of the compliance for a mixture in the low contrast regime.
    Structural and Multidisciplinary Optimization, 54(2) :215-231, 2016.

  17. M. Dambrine, C. Dapogny, and H. Harbrecht.
    Shape optimization for quadratic functionals and states with random right-hand sides.
    SIAM Journal on Control and Optimization, 53(5) :3081-3103, 2015.

  18. F. Caubet, M. Dambrine, and D. Kateb.
    Shape optimization methods for the inverse obstacle problem with generalized impedance boundary conditions.
    Inverse Problems, 29(11), 2013.

  19. F. Caubet and M. Dambrine.
    Stability of critical shapes for the drag minimization problem in Stokes flow.
    Journal des Mathématiques Pures et Appliquées, 100(3) :327-346, 2013.

  20. M. Dambrine and D. Kateb.
    On the shape sensitivity of the first Dirichlet eigenvalue for two-phase problems.
    Applied Mathematics and Optimization, 63(1) :45-74, 2011.

  21. M. Dambrine and D. Kateb.
    On the ersatz material approximation in level-set methods.
    ESAIM - Control, Optimisation and Calculus of Variations, 16(3) :618-634,2010.

  22. L. Afraites, M. Dambrine, and D. Kateb.
    On second order shape optimization methods for electrical impedance tomography.
    SIAM Journal on Control and Optimization,47(3) :1556-1590, 2008.

  23. L. Afraites, M. Dambrine, K. Eppler, and D. Kateb.
    Detecting perfectly insulated obstacles by shape optimization techniques of order two.
    Discrete and Continuous Dynamical Systems - Series B, 8(2) :389-416, 2007.

  24. L. Afraites, M. Dambrine, and D. Kateb.
    Shape methods for the transmission problem with a single measurement.
    Numerical Functional Analysis and Optimization, 28(5-6) :519-551, 2007.

  25. M. Dambrine, J. Sokolowski, and A. Zochowski.
    On stability analysis in shape optimisation : Critical shapes for Neumann problem.
    Control and Cybernetics, 32(3 SPEC.ISS.) :503-528, 2003..
  26. Marc Dambrine.
    On variations of the shape Hessian and sufficient conditions for thestability of critical shapes.
    RACSAM. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. AMat., 96(1) :95-121, 2002.
  27. M. Dambrine and M. Pierre.
    About stability of equilibrium shapes.
    ESAIM: Mathematical Modelling and Numerical Analysis, 34(4) :811-834, 2000.

Optimization in finite dimension

  1. Ch-E Bréhier, M. Dambrine, N. En-Nebbazi
    Asymptotic error analysis for stochastic gradient optimization schemes with first and second order modified equations . arxiv HAL


  2. M. Dambrine, Ch. Dossal, A. Rondepierre, and B. Puig.
    Stochastic differential equations for modeling first-order optimization methods.
    SIAM Journal on Optimization, Vol. 34, Iss. 2, 2024. HAL

  3. L. Barbet, M. Dambrine, A. Daniilidis, and L. Rifford.
    Sard theorems for Lipschitz functions and applications in optimization.
    Israel Journal of Mathematics,212(2) :757-790, 2016.

  4. L. Barbet, M. Dambrine, and A. Daniilidis.
    The Morse-Sard theorem for Clarke critical values.
    Advances in Mathematics, 242 :217-227, 2013.

Numerical Analysis

  1. D. Capatina, F. Caubet, M. Dambrine, R. Zelada
    Nitsche extended finite element method of a Ventcel transmission problem with discontinuities at the interface.
    Accepted to ESAIM M2AN HAL
  2. M. Dambrine, I. Greff, H. Harbrecht, and B. Puig.
    Numerical solution of the homogeneous Neumann boundary value problem on domains with a thin layer of random thickness.
    Journal of Computational Physics, 330 :943-959, 2017.

  3. M. Dambrine, I. Greff, H. Harbrecht, and B. Puig.
    Numerical solution of the Poisson equation on domains with a thin layer of random thickness.
    SIAM Journal on Numerical Analysis, 54(2) :921-941, 2016.

  4. M. Dambrine, H. Harbrecht, and B. Puig.
    Computing quantities of interest for random domains with second order shape sensitivity analysis.
    ESAIM : Mathematical Modelling and Numerical Analysis, 49(5) :1285-1302, 2015.

  5. V. Bonnaillie-Noël, M. Dambrine, F. Hérau, and G. Vial.
    Artificial conditions for the linear elasticity equations.
    Mathematics of Computation, 84(294) :1599-1632, 2015.

  6. J.P. Boufflet, M. Dambrine, G. Dupire, and P. Villon.
    On the necessity of Nitsche term. Part ii : An alternative approach.
    Applied Numerical Mathematics, 62(5) :521-535,2012.

  7. V. Bonnaillie-Noël, D. Brancherie, M. Dambrine, and G. Vial.
    Artificial boundary conditions to compute correctors in linear elasticity.
    Numerical Analysis and Applications, 5(2) :129-135, 2012.

  8. G. Dupire, J.P. Boufflet, M. Dambrine, and P. Villon.
    On the necessity of Nitsche term.
    Applied Numerical Mathematics, 60(9) :888-902, 2010.

  9. V. Bonnaillie-Noël, D. Brancherie, M. Dambrine, S. Tordeux, and G. Vial.
    Effect of micro-defects on structure failure : Coupling asymptotic analysis and strong discontinuity.
    European Journal of Computational Mechanics, 19(1-3) :165-175, 2010.

  10. D. Brancherie, M. Dambrine, G. Vial, and P. Villon.
    Effect of surface defects on structure failure : A two-scale approach.
    European Journal of Computational Mechanics,17(5-7) :613-624, 2008.

Inverse problems

  1. F. Caubet, M. Dambrine, J. Dardé
    On the penalization by the perimeter in shape optimization applied to Dirichlet inverse obstacle problem HAL


  2. M. Dambrine and V. Karnaev.
    Robust obstacle reconstruction in an elastic medium.
    Discrete and Continuous Dynamical Systems - B, 29(1) :124-150, 2024. HAL

  3. M. Dambrine and S. Zerrouq.
    Robust inverse homogenization of elastic micro-structures.
    Journal of Optimization Theory and Applications, 199 :209-232, 2023.

  4. M. Dambrine, A. Khan, M. Sama, and H.-J. Starkloff.
    Stochastic elliptic inverse problems. solvability, convergence rates, discretization, and applications.
    Journal of Convex Analysis, 30 :851-885, 2023.

  5. M. Dambrine, A. Khan, and M. Sama.
    A stochastic regularized second-order iterative scheme for optimal control and inverse problems in stochastic partial differential equations.
    Philosophical Transactions of the Royal Society A : Mathematical, Physical and Engineering Sciences, 380(2236), 2022.

  6. M. Dambrine, H. Harbrecht and B. Puig
    Incorporating knowledge on the measurement noise in electrical impedance tomography.
    ESAIM: Control, Optimization and Calculus of Variations, 25 (2019).

  7. F. Caubet, M. Dambrine, and H. Harbrecht.
    A new method for the data completion problem and application to obstacle detection.
    SIAM Journal on Applied Mathematics,79(1) :415-435, 2019.

  8. F. Caubet, M. Dambrine, and D. Kateb.
    Shape optimization methods for the inverse obstacle problem with generalized impedance boundary conditions.
    Inverse Problems, 29(11), 2013.

  9. F. Caubet, M. Dambrine, D. Kateb, and C.Z. Timimoun.
    A Kohn-Vogelius formulation to detect an obstacle immersed in a fluid.
    Inverse Problems and Imaging,7(1) :123-157, 2013.

  10. F. Caubet and M. Dambrine.
    Localization of small obstacles in Stokes flow.
    Inverse Problems, 28(10), 2012.

  11. M. Badra, F. Caubet, and M. Dambrine.
    Detecting an obstacle immersed in a fluid by shape optimization methods.
    Mathematical Models and Methods in Applied Sciences,21(10) :2069-2101, 2011.

  12. M. Dambrine and D. Kateb.
    A remark on precomposition on H1/2(S1) and epsilon-identifiability of disks in tomography.
    Journal of Mathematical Analysis and Applications, 337(1) :594-616, 2008.

  13. L. Afraites, M. Dambrine, and D. Kateb.
    On second order shape optimization methods for electrical impedance tomography.
    SIAM Journal on Control and Optimization,47(3) :1556-1590, 2008.

  14. L. Afraites, M. Dambrine, K. Eppler, and D. Kateb.
    Detecting perfectly insulated obstacles by shape optimization techniques of order two.
    Discrete and Continuous Dynamical Systems - Series B, 8(2) :389-416, 2007.

  15. L. Afraites, M. Dambrine, and D. Kateb.
    Shape methods for the transmission problem with a single measurement.
    Numerical Functional Analysis and Optimization, 28(5-6) :519-551, 2007.

  16. M. Dambrine and D. Kateb.
    Conformal mapping and inverse conductivity problem with one measurement.
    ESAIM - Control, Optimisation and Calculus of Variations,13(1) :163-177, 2007.

PDE and asymptotic analysis of solutions of PDE

  1. M.Dambrine, V. Bonnaillie-Noël, M. Dalla Riva and P. Musolino.
    Global representation and multi-scale expansion for the Dirichlet problem in a domain with a small hole close to the boundary.
    Communications in Partial Differential Equations Volume 46,Pages 282-309, 2021.

  2. M. Dambrine, B. Puig, and G. Vallet.
    A mathematical model for marine dinoflagellates blooms.
    DCDS-S Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020424

  3. V. Bonnaillie-Noël, M. Dalla Riva, M. Dambrine, and P. Musolino.
    A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary.
    Journal des Mathématiques Pures et Appliquées, 116 :211-267, 2018.

  4. V. Bonnaillie-Noël, M. Dambrine, and C. Lacave.
    Interactions between moderately close inclusions for the two-dimensional Dirichlet-Laplacian.
    Applied Mathematics Research eXpress, 2016(1) :1-23, 2016.17

  5. V. Bonnaillie-Noël and M. Dambrine.
    Interactions between moderately close circular inclusions : The Dirichlet-Laplace equation in the plane.
    Asymptotic Analysis, 84(3-4) :197-227, 2013.

  6. M. Dambrine and D. Kateb.
    Persistency of wellposedness of Ventcel's boundary value problem under shape deformations.
    Journal of Mathematical Analysis and Applications, 394(1) :129-138, 2012.

  7. C. Amrouche, M. Dambrine, and Y. Raudin.
    An Lp theory of linear elasticity in the half-space.
    Journal of Differential Equations, 253(3) :906-932, 2012.

  8. V. Bonnaillie-Noël, M. Dambrine, F. Hérau, and G. Vial.
    On generalized Ventcel'stype boundary conditions for Laplace operator in a bounded domain.
    SIAM Journal on Mathematical Analysis, 42(2) :931-945, 2010.

  9. V. Bonnaillie-Noël, M. Dambrine, S. Tordeux, and G. Vial.
    Interactions between moderately close inclusions for the Laplace equation.
    Mathematical Models and Methods in Applied Sciences, 19(10) :1853-1882, 2009.

  10. M. Dambrine and G. Vial.
    A multiscale correction method for local singular perturbations of the boundary.
    Mathematical Modelling and Numerical Analysis, 41(1) :111-127, 2007.

  11. V. Bonnaillie-Noël, M. Dambrine, S. Tordeux, and G. Vial.
    On moderately close inclusions for the Laplace equation.
    C. R. Math. Acad. Sci. Paris, 345(11) :609-614,2007.

  12. M. Dambrine and G. Vial.
    Influence of a boundary perforation on the Dirichlet energy.
    Control and Cybernetics, 34(1) :117-136, 2005.