Shape optimization of an acoustic horn Original Research Article

The shape of an acoustic horn is optimized with respect to its ability to provide impedance matching to the surrounding air. The resulting minimization problem is solved using a BFGS quasi-Newton algorithm. The wave propagation is modeled by a finite-element approximation of the Helmholtz equation, and the necessary objective-function gradient is calculated from the solution of the associated adjoint equation. Local solutions to the optimization problem, corresponding to irregular horn contours, are avoided by using a filtering technique that applies smoothing to the design updates and the gradient. The method converges fast to a smooth solution, and the resulting horn has good impedance properties throughout the entire frequency band of interest.