, The american bureau of shipping (abs), ship energy efficiency measures: Status and guidance, vol.2, p.3

G. Allaire, Conception optimale de structures, Mathématiques et Applications, vol.58, p.120, 2007.

K. J. Bai, A variational method in potential flow with a free surface, 1972.

G. K. Batchelor, An Introduction to fluid dynamics, vol.14, p.112, 1967.

M. G. Bauer, Le problème de Neumann-Kelvin I, Ann. Mat. Pura Appl, vol.124, issue.4, pp.234-255, 1980.

M. G. Bauer, Le problème de Neumann-Kelvin II, Ann. Mat. Pura Appl, vol.124, issue.4, pp.257-280, 1980.

K. A. Belibassakis, T. P. Gerotathis, K. V. Kostas, C. G. Politis, P. D. Kaklis et al., A BEM-isogeometric method for the ship wave-resistance problem, Ocean Engineering, vol.60, issue.3, pp.53-67, 2013.

J. Boucher, R. Labbé, C. Clanet, and M. Benzaquen, Thin or bulky: optimal aspect ratios for ship hulls, Phys. Rev. Fluids, vol.3, issue.074802, 2018.

M. Bouhadef, Contribution à l'étude des ondes de surface d'un canal. Application à l'écoulement au dessus d'un obstacle immergé, R Centre d'études Aerodynamiques et Thermiques), 1988.

R. Brard and . Le-problème-de-neumann-kelvin, Comptes Rendus Hebdomadaries des Séances de l'Academie des Sciences, vol.7, pp.163-167, 1974.

C. A. Brebbia and J. Dominguez, Boundary element methods for potential problems, Applied Mathematical Modelling, vol.1, issue.8, pp.372-378, 1977.

E. Bängtsson, D. Noreland, and M. Berggren, Shape optimization of an acoustic horn, Computer methods in applied mechanics and engineering, vol.192, issue.1, pp.1533-1571, 2002.

C. Chen, C. Kublik, and R. Tsai, An implicit boundary integral method for interfaces evolving by Mullins-Sekerka dynamics, Mathematics for Nonlinear Phenomena: Analysis and Computation: International Conference in Honor of Professor Yoshikazu Giga on his 60th Birthday, vol.215, 2015.

W. Contributors, Kelvin wake pattern generated by a small boat, vol.12, 2018.

W. Contributors, Wikipedia, the free encyclopedia, vol.12, 2018.

M. Costabel, Principles of boundary element methods, Computer Physics Reports, vol.6, issue.1, pp.243-274, 1987.

M. Costabel and F. L. Louër, Shape derivatives of boundary integral operators in electromagnetic scattering. part I: Shape differentiability of pseudo-homogeneous boundary integral operators, Integral Equations and Operator Theory, vol.72, issue.4, pp.509-535, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00453948

M. G. Crandall and P. Lions, Condition d'unicité pour les solutions generalisées des équations de Hamilton-Jacobi de premier order, C. R. Acad. Sci, vol.292, p.73, 1981.

J. Dambrine and M. Pierre, Regularity of optimal ship forms based on michell's wave resistance, Appl. Math. Optim, pp.1-40

J. Dambrine, M. Pierre, and G. Rousseaux, A theoretical and numerical determination of optimal ship forms based on michell's wave resistance, ESAIM Control Optim. and Calc. Var, vol.22, p.115, 2016.

I. M. , Imo's contribution to sustainable maritime development: Capacitybuilding for safe, secure and efficient shipping on clean oceans through the integrated technical co-operation programme. www.Imo.org, 2010.

N. James, J. Dambrine, and G. Rousseaux, Cut-cell method: application to water waves generated by a submerged obstacle, 11th World Congress on Computational Mechanics, p.121, 2014.

A. Jameson and L. Martinelli, Aerodynamic shape optimization techniques based on control theory, pp.151-221, 2000.

L. Kelvin, On stationary waves in flowing water, Phil. Mag, vol.22, issue.353

M. Kirsch, Ein beitrag zur berechnung des wellenwiderstandes im kanal. Schriftenreihe Schiffbau. Technische Universität Hamburg-Harburg, vol.99, pp.123-126, 1962.

K. V. Kostas, A. I. Ginnis, C. Politis, and P. Kaklis, Shape-optimization of 2d hydrofoils using an isogeometric BEM solver, Computer-Aided Design, vol.82, issue.1, pp.79-87, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01382200

R. Kress, Linear Integral equations, Applied Mathematical Series, vol.82, p.87, 1989.

S. N. Kruzkov, Generalized solutions of the Hamilton-Jacobi equations of eikonal type. I. formulation of the problems; existence, uniqueness and stability theorems; some properties of the solutions, Math. USSR Sbornik, vol.27, p.73, 1975.

C. Kublik, N. M. Tanushev, and R. Tsai, An implicit interface boundary integral method for Poisson's equation on arbitrary domains, Journal of Computational Physics, vol.247, p.88, 2013.

C. Kublik and R. Tsai, Integration over curves and surfaces defined by the closest point mapping, Research in the Mathematical Sciences, vol.3, issue.1, p.81, 2016.

N. Kuznetsov, V. Maz'ya, and B. Vainberg, Linear Water Waves, vol.32, p.120, 2002.

C. Liu, L. Chen, W. Zhao, and H. Chen, Shape optimization of sound barrier using an isogeometric fast multipole boundary element method in two dimensions, Engineering Analysis with Boundary Elements, vol.85, issue.1, pp.142-157, 2017.

S. T. Magazine, , 2004.

J. H. Michell, The wave resistance of a ship, Philosophical Magazine, vol.45, pp.106-123

F. Murat and J. Simon, Sur le contrôle par un domaine géométrique, Laboratoire Analyse Numerique Universite P. et M. Curie (ParisVI), 1976.

F. Noblesse, Velocity representation of free-surface flow and Fourier-Kochin representation of waves, Applied Ocean Research, vol.23, issue.8, pp.41-52, 2001.

F. Noblesse, F. Huang, and C. Yang, The Neumann-Michell theory of ship waves, J. Eng. Math, vol.79, issue.6, pp.51-71, 2013.

F. W. Olver, Asymptotics and special function, vol.24, p.26, 1974.

S. Osher and R. Fedkiw, Level set methods and dynamic implicit surfaces, Number 153 in Applied Mathematical Sciences, vol.9, p.75, 2003.

S. Osher and J. Sethian, Fronts propagating with curvature dependent speed: Algorithms based on hamilton-jacobi formulations, Journal of Computational Physics, vol.79, issue.9, pp.12-49, 1988.

J. E. Peter and R. P. Dwight, Review: Numerical sensitivity analysis for aerodynamic optimization: A survey of approaches, Computers & Fluids, vol.39, issue.1, pp.373-391, 2010.

O. Pironneau, Optimal shape design for elliptic systems, Springer Series in Computational Physics, 1984.

T. Pontianak, Transportasi motor air melintasi sungai kapuas, 2015.

M. Rahman, Three dimensional Green's function for ship motion at forward speed, International Journal of Mathematics and Mathematical Sciences, vol.13, p.21, 1990.
DOI : 10.1155/s0161171290000813

URL : http://downloads.hindawi.com/journals/ijmms/1990/347046.pdf

L. Rayleigh, The form of standing waves on the surface of running water, Proc. Lond. Math. Soc, vol.15, issue.69

J. S. Russel, Report on waves, British Association Report

D. Schieborn, Viscosity solutions of Hamilton-Jacobi equations of Eikonal type on ramified spaces, p.72, 2006.

C. Schilling, S. Schmidt, and V. Schulz, Efficient shape optimization for certain and uncertain aerodynamic design, Computers & Fluids, vol.46, issue.1, pp.78-87, 2011.

J. A. Sethian, Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, p.74, 1999.

C. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shockcapturing schemes, Journal of Computational Physics, vol.77, issue.2, p.75, 1988.

J. Simon, Differentiation with respect to the domain in boundary value problems. Numerical Functional Analysis and Optimization, vol.2, pp.649-687, 1980.

M. Sussman, P. Smereka, and S. Osher, A level set approach for computing solutions to incompressible two-phase flow, Journal of Computational Physics, vol.114, issue.1, p.74, 1994.

F. , Mathematical note on the fundamental solution (Kelvin source) in ship hydrodynamics, IMA Journal of Applied Mathematics, vol.32, issue.8, pp.335-351, 1984.

H. A. Van-der and . Vorst, Iterative Krylov methods for large linear systems, Cambridge Monographs on Applied and Computational Mathematics, p.89, 2003.

J. V. Wehausen and E. V. Laitone, Surface waves. Encyclopedia of Physics, vol.8, p.21, 1960.

G. Weinblum, Applications of wave resistance theory to the problem of ship design. Schriftenreihe Schiffbau, vol.58, pp.119-163, 1959.

S. Zhu, X. Hu, and Q. Wu, A level set method for shape optimization in semilinear elliptic problems, Journal of Computational Physics, vol.355, issue.9, pp.104-120, 2018.

, Le corps, considéré lisse avance à vitesse constante, sous la surface libre d'un fluide qui est supposé parfait et incompressible. La résistance de vague est la trainée, c'est-à-dire la composante horizontale de la force exercée par le fluide sur l'obstacle. Nous utilisons les équations de Neumann-Kelvin 2D, qui s'obtiennent en linéarisant les équations d'Euler irrotationnelles avec surface libre. Le problème de Neumann-Kelvin est formulé comme une équation intégrale de frontière basée sur une solution fondamentale qui intègre la condition linéarisée à la surface libre. Nous utilisons une méthode de descente de gradient pour trouver un minimiseur local du problème de résistance de vague. Un gradient par rapport à la forme est calculé par la méthode de variation de frontières. Nous utilisons une approche level-set pour calculer la résistance de vague et gérer les déplacements de la frontière de l'obstacle, nous calculons la forme d'un objet immergé d'aire donnée qui minimise la résistance de vague

, Mots clés : optimisation de forme, résistance de vague, problème de Neumann-Kelvin, équa-tion intégrale de frontière, méthode level-set