Abstract
The concept of topological sensitivity has been successfully employed as an imaging tool to obtain the correct initial topology and preliminary geometry of hidden obstacles for a variety of inverse scattering problems. In this paper, we extend these ideas to acoustic scattering involving transient waveforms and penetrable obstacles. Through a boundary integral equation framework, we present a derivation of the topological sensitivity for the featured class of problems and illustrate numerically the utility of the proposed method for preliminary geometric reconstruction of penetrable obstacles. For generality, we also cast the topological sensitivity in the so-called adjoint field setting that is amenable to a generic computational treatment using, for example, finite element or finite difference methods.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 821-834 |
| Number of pages | 14 |
| Journal | Wave Motion |
| Volume | 45 |
| Issue number | 6 |
| DOIs | |
| State | Published - Jun 2008 |
Bibliographical note
Funding Information:A. Malcolm thanks the Institute for Mathematics and its Applications at the University of Minnesota where she was a postdoc during much of this work. A. Malcolm also acknowledges the support she received at Utrecht University through the Dutch National Science Foundation Grant No. NWO:VIVI865.03.007. The support provided by the National Science Foundation through Award No. CMS-0324348 to B. Guzina and the University of Minnesota Supercomputing Institute during the course of this investigation is kindly acknowledged.
Keywords
- Acoustic waves
- Inverse scattering
- Topological derivative
- Transient waveforms