Large-Scale Three-Dimensional Acoustic Horn Optimization

Abstract. We consider techniques that enable large-scale gradient-based shape optimization of wave-guiding devices in the context of 3D time-domain simulations. The approach relies on a memory efficient boundary representation of the shape gradient together with primal and adjoint solvers semi-automatically generated by the FEniCS framework. The hyperbolic character of the governing linear wave equation, written as a first-order system, is exploited through systematic use of the characteristic decomposition both to define the objective function and to obtain stable numerical fluxes in the Discontinuous Galerkin spatial discretization. The methodology is successfully used to optimize the shape of midrange acoustic horns for maximum transmission efficiency.