On the Spectrum of Volume Integral Operators in Acoustic Scattering

M. Costabel ()
Additional contact information
M. Costabel: Université de Rennes 1, IRMAR

Chapter Chapter 11 in Integral Methods in Science and Engineering, 2015, pp 119-127 from Springer

Abstract: Abstract Volume integral equations have been used as theoretical and numerical tools in scattering theory for a long time. The basic idea of the VIE method in scattering by a penetrable object is to consider the effect of the scatterer as a perturbation of a whole-space constant coefficient problem and to solve the latter by convolution with the whole-space fundamental solution. In acoustic and electromagnetic scattering, this results in strongly singular integral equations that have a non-trivial essential spectrum, in general. Using techniques developed for the case of electromagnetic scattering (see the recent note by M. Costabel, E. Darrigrand and H. Sakly, The essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body. Comptes Rendus Mathématique, 350, 193–197 (2012)), we determine the essential spectrum, hence the well-posedness in the sense of Fredholm, of the volume integral equation in acoustic scattering. It turns out that the question can be reduced to the study of the classical double layer potential boundary integral operator.

Keywords: Volume Integral Equation; Acoustic Scattering; Essential Spectrum (search for similar items in EconPapers)
Date: 2015
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-16727-5_11

Ordering information: This item can be ordered from
http://www.springer.com/9783319167275

DOI: 10.1007/978-3-319-16727-5_11

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().