Numerical computations of interior transmission eigenvalues for scattering objects with cavities. (4th March 2016)

• Record Type: Journal Article
• Authors: Peters, Stefan; Kleefeld, Andreas
• Is Part Of: Inverse problems. Volume 32:Number 4(2016:Apr.)
• Publication Date: 2016-03-04
• Subjects: inside-outside duality -- acoustic scattering -- cavities -- transmission eigenvalues; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/4/045001
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this article we extend the inside-outside duality for acoustic transmission eigenvalue problems by allowing scattering objects that may contain cavities. In this context we provide the functional analytical framework necessary to transfer the techniques that have been used in Kirsch and Lechleiter (2013 Inverse Problems, 29 104011 ) to derive the inside-outside duality. Additionally, extensive numerical results are presented to show that we are able to successfully detect interior transmission eigenvalues with the inside-outside duality approach for a variety of obstacles with and without cavities in three dimensions. In this context, we also discuss the advantages and disadvantages of the inside-outside duality approach from a numerical point of view. Furthermore we derive the integral equations necessary to extend the algorithm in Kleefeld (2013 Inverse Problems, 29 104012 ) to compute highly accurate interior transmission eigenvalues for scattering objects with cavities, which we will then use as reference values to examine the accuracy of the inside-outside duality algorithm.