Gradient-based shape optimization of 2D wave barriers using the Boundary Element Method and the Finite Element Method

Abstract

This report is concerned with the gradient-based shape optimization of two dimensional wave barriers using the Boundary Element Method (BEM) and the Finite Element Method (FEM) in the time harmonic domain. The advantages and disadvantages of both numeri- cal methods are widely known, and the problem at hand is one of those problems where they complement very well. The main focus is on the development of the formulation required for the calculation of shape sensitivities, which is usually the costlier stage of a gradient-based shape optimization. Shape sensitivities are calculated using a Direct Dif- ferentiation Method (DDM) rather than an Adjoint Variable Method (AVM) because a small number of design variables is considered. For the sake of completeness and use- fulness, the formulation is described in such a level of detail that its implementation is relatively straightforward. From the FEM point of view, the formulation is developed for wave propagation through isotropic elastic solids. From the BEM point of view, the formulation is developed for wave propagation through inviscid fluids, and anti-plane and in-plane wave propagation through isotropic elastic solids. An entire chapter is devoted to the optimization of wave barriers, where the developments of the present work are ap- plied to the optimization of a simple wave barrier. The studied problem exploit partially the BEM–FEM coupling as it can also be solved by using a BEM–BEM model. How- ever, it serves as an application of the methodology, which will remain valid for future developments based on this work.