Shape optimization approaches to free-surface problems

摘要

Three different reformulations of a free-surface problem as shape optimization problems are considered. These give rise to three different cost functionals that apparently have not been exploited in literature. The shape derivatives of the cost functionals are explicitly determined. The gradient information is combined with the boundary variation method in a preconditioned steepest descent algorithm to solve the shape optimization problems. Numerical results that compare the performance of the proposed cost functionals are presented.