Structural optimization of an acoustic horn

The objective of the present article is to find an optimal design of an acoustic horn in the case that the magnitude of the reflection wave integrated over the inflow boundary is to be minimized meanwhile the Helmholtz equation models the wave propagation. In contrast to the current approaches such as gradient-based optimization algorithms, we employ here a non-iterative method based on measure theory which dose not require any information of gradients and the differentiability of objective function in the optimization problem is not as a rule. Implementation of our fast convergence approach shows that the resulting horns, not only for single frequency optimization but also for a band of frequencies, are very efficient.