Domain Optimization for an Acoustic Waveguide Scattering Problem

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 $$H^1$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Domain Optimization for an Acoustic Waveguide Scattering Problem

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Publisher
Springer US
Copyright
Copyright © 2014 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-014-9273-1
Publisher site
See Article on Publisher Site

Abstract

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 $$H^1$$ 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.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 15, 2014

References

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