A numerical method for shape optimization of surface ships is presented. The classical potential flow theory is used, and the free surface boundary conditions are linearized using Dawson's method (see Nakos, D., and Sclavounos, P., "Ship Motions by a Three-Dimensional Rankine Panel Method," 18th Naval Hydrodynamic Symposium, National Academy Press, Washington, DC, 1990, pp. 21-40). Objective functional for wave resistance minimization and inverse problems are considered. An important contribution of this work is the formulation of a continuous adjoint approach for computing the gradients of these objective functionals. The potential flow problem is solved with an existing panel code (SWAN-v2.2). Like the velocity potential function, the adjoint function is governed by Laplace's equation; however, the adjoint radiation condition demands that waves may exist only upstream. The adjoint problem is also solved using the same code (SWAN-v2.2) after some modifications are introduced to handle the respective boundary conditions. Geometric characteristics, wave resistance, and surface wave patterns of optimized hull forms are presented.
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