On the impact of the shape of the artificial boundary in exterior Helmholtz problems
* Presenting author
Acoustical problems can be investigated numerically in the frequency domain by solving the Helmholtz equation with the Finite element method (FEM). In exterior problems we approximate the radiation condition by truncating the considered domain with an artificial absorbing boundary. Popular choices include absorbing boundary conditions (ABC) or absorbing layers (PML), where the implementation of the latter is usually more involved. Both methods have the disadvantage (although for PML this is less significant), that they still reflect small parts of the wave if the domain is discretized for numerical computation. This reflection error is typically small for normal (0 degrees) incidence but increases with larger incidence angles.In this numerical study we consider a model problem in two dimensions. For various ABCs we study the impact of changing the shape of the artificial boundary on the reflection error and the accuracy of the numerical simulations.The outcome of numerical simulations for different ABCs and methods of shape optimization will be discussed in detail.