On the use of consistent approximations in boundary element-based shape optimization in the presence of uncertainty

This work addresses certain aspects of shape optimization for linearly elastic systems in the presence of uncertainty. The goal is to formulate and test a set of computationally tractable methods for incorporating uncertainty in the system. The boundary element method is employed in solving the underlying elasticity equations. The resulting minimax problem is studied in the context of the so-called consistent approximations, which allow for adaptive control of the discretization error during the iterative optimization process.