Marc Dambrine

Responsabilités

Responsable de l'équipe MNFC

Responsable de la seconde année du parcours PPPE de la licence MISHS

Membre du panel d'experts Mathématiques du HCERES

Membre élu de la commission de la recherche de l'UPPA

Président du comité d'experts 25-26 de l'UPPA

Thèmes de recherche

Je suis un analyste appliqué. Je m’intéresse essentiellement à la dépendance de la solution d’un problème aux limites par rapport au domaine avec des applications centrées autour de la mécanique des solides. Mes travaux portent principalement sur l’optimisation de forme et l’analyse asymptotique de perturbations singulières du domaine :

• En optimisation de forme, je me suis beaucoup intéressé à la question de la stabilité des formes critiques et aux problèmes inverses géométriques. Ma spécificité dans la communauté est l’étude et l’usage des dérivées secondes.

• En analyse asymptotique, mes travaux visent à comprendre l’influence d’un ou plusieurs défauts de petites tailles pouvant être proches les uns des autres ou du bord sur la solution d’un problème aux limites de nature elliptique. L’objectif du travail est d’obtenir des asymptotiques constructives et calculables valides au voisinage des défauts.

Depuis une dizaine d'année je m'intéresse à la problématique de la prise en compte d’incertitudes (géométriques,sur les paramètres matériaux ou les chargements) en optimisation de forme et plus spécialement en optimisation de structures. .

Encadrement

Direction de thèses en cours

• depuis 2023 N. En Nezzabi, Univ. de Pau et des Pays de l’Adour, codirection 50% avec Ch.-E. Brehier, Thèse cofinancée par la Région Nouvelle Aquitaine et l’UPPA
• depuis 2022 R. Zelada, Univ. de Pau et des Pays de l’Adour cotutelle avec U. de Chile, codirection 50% avec C. Conca, avec la participation de F. Caubet comme co encadrant (25%), Optimisation d’un échangeur thermique, Thèse financé par le gouvernement chilien
• depuis 2021 G. Gargantini, Univ. de Pau et des Pays de l’Adour, codirection 50% avec F. Caubet (25%, Univ. de Pau et des Pays de l’Adour) et J. Maynadier (25%, Safran Helicopter Engines), Optimisation de forme et incertitudes dans la conception de structures mécaniques, thèse CIFRE avec Safran Helicopter Engines

Publications

[57] Stochastic differential equations for modeling first-order optimization methods..   
with Ch. Dossal, A. Rondepierre, and B. Puig
SIAM Journal on Optimization, 2024.

[56]  Robust obstacle reconstruction in an elastic medium..   
with V. Karnaev
Discrete and Continuous Dynamical Systems - B, 29(1) :124-150, 2024.

[55]   Robust inverse homogenization of elastic micro-structures.   
with S. Zerrouq
Journal of Optimization Theory and Applications, 199 :209-232, 2023.

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

[53]   Bernoulli free boundary problems under uncertainty : The convex case.  
with H. Harbrecht and B. Puig
Computational Methods in Applied Mathematics, 23(2) :333-352, 2023.

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

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

[50] Shape derivatives of eigenvalues for mixture problems. Part two : elasticity problems.
with F. Caubet and R. Mahadevan.
SIAM Control and Optimization,, 59(2), 1218-1245.

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

[48] A mathematical model for marine dinoflagellates blooms.
with  B. Puig, and G. Vallet
DCDS serie S, doi: 10.3934/dcdss.2020424

[47] Shape optimization for composite materials and scaffold structures,
with H. Harbrecht
SIAM Multiscale Modeling & Simulation 2020, Vol. 18, No. 2, pp. 1136-1152

[46] Oriented distance point of view on random sets with application to shape optimization ,
with B. Puig
ESAIM: Control, Optimization and Calculus of Variations, https://doi.org/10.1051/cocv/2020007

[45] Stability in shape optimization with second variation.
with J. Lamboley.
Journal of Differential Equations, 267(5) :3009-3045, 2019.

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

[43] Incorporating knowledge on the measurement noise in electrical impedance tomography
with H. Harbrecht and B. Puig
ESAIM: Control, Optimisation and Calculus of Variations,25 (2019) 84

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

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

[40] Numerical solution of the homogeneous Neumann boundary value problem on domains with a thin layer of random thickness.
with H. Harbrecht, I. Greff and B. Puig
Journal of Computational Physics, 54-2 (2016), pp. 921-941

[39] Numerical solution of the Poisson equation on domains with a thin layer on random thickness.
with H. Harbrecht, I. Greff and B. Puig
SIAM Numerical Analysis, 54-2 (2016), pp. 921-941

[38] A first order approach for the worst-case shape optimization of the compliance for a mixture in the low contrast regime.
with A. Laurain.
Structural and Multidisciplinary Optimization, 54 (2016), no. 2, 215-231.

[37] Minimization of the ground state of the mixture of two conducting materials in a small contrast regime.
with C. Conca, R. Mahadevan and D. Quintero.
Mathematical Methods in the Applied Sciences, 39 (2016), no. 13,3549-3564.

[36] Shape optimization for quadratic functionals and states with random right-hand sides.
with C. Dapogny and H. Harbrecht.
SIAM Control and Optimization. 53 (2015), no. 5, 3081-3103.

[35] Interactions between moderately close inclusions for the 2D Dirichlet-Laplacian.
with V. Bonnaillie-Noël and C. Lacave.
Applied Mathematics Research eXpress, 2016, no. 1, 1-23. doi:10.1093/amrx/abv008.

[34] Sard theorems for Lipschitz functions and applications in optimization.
with L. Barbet, A. Daniilidis, and L. Rifford.
Israel Journal of Mathematics, 212 (2016), no. 2, 757-790.

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

[32] An extremal eigenvalue problem for the Wentzell-Laplace operator.
with J. Lamboley and D. Kateb.
Annales de l’IHP, Analyse non linéaire, 33(2), 409-450.

[31] Artificial conditions for the linear elasticity equations.
with V. Bonnaillie-Noël, F. Hérau and G. Vial.
Math. Comp. 84 (2015), 1599-1632 .

[30] Interactions between moderately close circular inclusions: the Dirichlet-Laplace equation in the plane.
with V. Bonnaillie-Noël.
Asymptotic Analysis. 84 (2013) 197-227.

[29] Morse-Sard theorem for Clarke critical values.
with L. Barbet and A. Daniilidis.
Advances in Mathematics. (2013), 242, 217-227.

[28] Shape optimization methods for the Inverse Obstacle Problem with generalized impedance boundary conditions.
with F. Caubet and D. Kateb.
Inverse Problems. (2013) 29:115011.

[27] Stability of critical shapes for the drag minimization problem in Stokes flow.
with F. Caubet.
Journal des Mathématiques Pures et Appliquées. (2013), 100, 327-346.

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

[25] Localisation of small obstacles in Stokes flow.
with F. Caubet.
Inverse Problems. (2012), 28 :105007.

[24] A Lp theory of linear elasticity in the half-space.
with C. Amrouche and Y. Raudin.
Journal of Differential Equations. (2012), 253, 906?932.

[23] Persistency of wellposedness of Ventcel’s boundary value problem under shape deformations.
with D. Kateb.
Journal of Mathematical Analysis and Applications. (2012), 394, 129-138.

[22] On the necessity of Nitsche term. Part II: an alternative approach.
with G. Dupire, J.-P. Boufflet and P. Villon.
Applied Numerical Mathematics. (2012), 62, Vol. 5, 521-535.

[21] Artificial boundary conditions to compute correctors in linear elasticity.
with V Bonnaillie-Noël, D Brancherie, and G. Vial.
Numerical Analysis and Applications. (2012), 5, Vol. 2, 129-135.

[20] Multiscale expansion and numerical approximation for surface defects.
with V. Bonnaillie-Noël, D. Brancherie, F. Hérau, S. Tordeux and G. Vial,
ESAIM Proc. 33 (2011), p. 22-35

[19] Detecting an obstacle immersed in a fluid by shape optimization methods.
with M. Badra and F. Caubet.
M3AS: Mathematical Models and Methods in Applied Sciences. (2011), 21, Vol. 10, 20692101.

[18] On the sensitivity with respect to the shape of the first Dirichlet eigenvalue for two-phase problems.
with D. Kateb.
Applied Mathematics and Optimization. (2011), vol. 63, no. 1, 45-74.

[17] On the necessity of Nitsche term.
with G. Dupire, J.-P. Boufflet and P. Villon.
Applied Numerical Mathematics. (2010), vol. 60, no. 9, 888-902.

[16] On generalized Ventcel’s type boundary conditions for Laplace operator in a bounded domain.
with V. Bonnaillie-Noël, F. Hérau and G. Vial.
SIAM Journal of Mathematical Analysis. (2010), vol. 42, 931-945.

[15] Effect of micro-defects on structure failure : coupling asymptotic analysis and strong discontinuity approach.
with V. Bonnaillie-Noël, D. Brancherie, S. Tordeux and G. Vial.
European Journal of Computational Mechanics. (2010), vol. 19, 165-175.

[14] On the ersatz material approximation in level-set methods.
with D. Kateb.
ESAIM: Control, Optimisation and Calculus of Variations. (2010), vol. 16 , 618-634.

[13] Interactions between moderately close inclusions for the Laplace equation.
with V. Bonnaillie-Noël, S. Tordeux and G. Vial.
M3AS: Mathematical Models and Methods in Applied Sciences. (2009), vol. 19, 1853 – 1882.

[12] Effect of surface defects on structure failure: a two-scale approach.
with D. Brancherie, G. Vial and P. Villon.
European Journal of Computational Mechanics. (2008), vol. 17, no 5-7, pp. 613-624.

[11] On second order shape optimization methods for electrical impedance tomography.
with L. Afraites and D. Kateb.
SIAM Control and Optimization. (2008), vol 47-3, pp. 1556-1590.

[10] A remark on precomposition on H1/2(S1) and epsilon-identifiability of disks in tomography.
with D. Kateb.
Journal of Mathematical Analysis and Applications. (2008), vol 337, pp. 594-616.

[9] Detecting perfectly insulated obstacles by shape optimization techniques of order two.
with L. Afraites, K. Eppler and D. Kateb.
Discrete and Continuous Dynamical Systems - serie B. (2007), vol 8-2, pp. 389 - 416 ;

[8] Conformal mappings and shape derivatives for the transmission problem with a single measurement.
with L. Afraites and D. Kateb.
Numerical Functional Analysis and Optimization. (2007), vol 28- 5 & 6 , pp. 519 - 551 ;

[7] On moderately close inclusions for the Laplace equation.
with V. Bonnaillie-Noël, S. Tordeux and G. Vial.
C. R. Acad. Sci. Paris. (2007), vol. 345, num. 11, pp. 609-614.

[6] A multiscale correction method for local singular perturbations of the boundary.
with G. Vial.
ESAIM: Mathematical Modelling and Numerical Analysis. (2007) vol 41, pp. 111-128.

[5] Conformal mapping and inverse conductivity problem with one measurement.
with D. Kateb.
ESAIM: Control, Optimization and Calculus of Variations. (2007), vol 13-1, pp. 163–177.

[4] On the influence of a boundary perforation on the Dirichlet energy.
with G. Vial.
Control and cybernetics. (2005), vol. 34-1, pp. 117-136.

[3] On stability analysis in shape optimisation : critical shapes for Neumann problem.
with J. Sokolowski and A. Zochowski.
Control and cybernetics. (2003), vol 32-3, pp. 503-528.

[2] About the variations of the shape Hessian and sufficient conditions of stability for critical shapes.
Revista Real Academia Ciencias-RACSAM. (2002), vol 96-1, pp. 95-121.

[1] About stability of equilibrium shapes.
with M. Pierre.
ESAIM: Mathematical Modelling and Numerical Analysis. (2000), vol 34-4, pp. 811-834.