Applied Mathematics & Optimization

, Volume 72, Issue 1, pp 101–146

Domain Optimization for an Acoustic Waveguide Scattering Problem


DOI: 10.1007/s00245-014-9273-1

Cite this article as:
Ott, J. Appl Math Optim (2015) 72: 101. doi:10.1007/s00245-014-9273-1


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 \(H^1\)-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.


Helmholtz equation Scattering problem Waveguides Existence of optimal domains 

Mathematics Subject Classification

49J20 35J05 35R35 

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute for Algebra and GeometryKarlsruhe Institute for TechnologyKarlsruheGermany