Domain Optimization for an Acoustic Waveguide Scattering Problem
We consider a domain optimization problem of an unbounded domain, which models scattering of a time-harmonic acoustic wave at the junction of two closed waveguides. Solutions of our problem fulfill the Helmholtz equation with a real wavenumber, a modal radiation condition and homogeneous Dirichlet boundary conditions. We derive an a-priori bound for the solution on a certain class of domains (which is compact in the Hausdorff metric topology) and show that within this class the solution depends H{sup 1}-continuously on the domain. Furthermore, we show some numerical examples to illustrate our results, which were calculated using the domain (or shape) derivative of our problem.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗