Marc DAMBRINE

Publications by themes

Shape Optimization     Optimization in finite dimension     Numerical analysis of PDEs     Inverse problems     PDEs and asymptotic analysis of solutions of PDEs

Shape Optimization

1. F. Caubet, C. Conca, M. Dambrine, R. Zelada
   Shape optimization with Ventcel transmission conditions: application to the design of a heat exchanger HAL
   
   
2. M. Dambrine, C. Geiersbach, H. Harbrecht
   Two-norm discrepancy and convergence of the stochastic gradient method with application to shape optimization . arxiv HAL
   
   
3. F. Caubet, C. Conca, M. Dambrine, R. Zelada
   How to insulate a pipe ? HAL
   
   
   
4. M. Dambrine, F. Caubet, G. Gargantini, J. Maynadier
   Shape optimization of polynomial functionals under uncertainties on the right-hand side of the state equation
   Accepted to SIAM Journal on Control and Optimization HAL
   
   
5. 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
   
   
6. 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
   
   
7. 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
   
   
8. 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
   
   
9. 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.
   
   
10. 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.
    
    
11. M. Dambrine and H. Harbrecht
    Shape optimization for composite materials and scaffold structures.
    SIAM Multiscale Model. Simul., 18(2), 1136-1152, 2020.
    
12. 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).
    
    
13. M. Dambrine and J. Lamboley.
    Stability in shape optimization with second variation.
    Journal of Differential Equations, 267(5) :3009-3045, 2019.
    
    
14. 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.
    
    
15. 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.
    
    
16. 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.
    
    
17. 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.
    
    
18. 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.
    
    
19. 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.
    
    
20. 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.
    
    
21. 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.
    
    
22. 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.
    
    
23. 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.
    
    
24. 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.
    
    
25. 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.
    
    
26. 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..
    
    
27. 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.
    
    
28. M. Dambrine and M. Pierre.
    About stability of equilibrium shapes.
    ESAIM: Mathematical Modelling and Numerical Analysis, 34(4) :811-834, 2000.