NDLI: A numerical method to compute interior transmission eigenvalues

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A numerical method to compute interior transmission eigenvalues

Content Provider	Scilit
Author	Kleefeld, Andreas
Copyright Year	2013
Description	Journal: Inverse Problems In this paper the numerical calculation of eigenvalues of the interior transmission problem arising in acoustic scattering for constant contrast in three dimensions is considered. From the computational point of view existing methods are very expensive, and are only able to show the existence of such transmission eigenvalues. Furthermore, they have trouble finding them if two or more eigenvalues are situated closely together. We present a new method based on complex-valued contour integrals and the boundary integral equation method which is able to calculate highly accurate transmission eigenvalues. So far, this is the first paper providing such accurate values for various surfaces different from a sphere in three dimensions. Additionally, the computational cost is even lower than those of existing methods. Furthermore, the algorithm is capable of finding complex-valued eigenvalues for which no numerical results have been reported yet. Until now, the proof of existence of such eigenvalues is still open. Finally, highly accurate eigenvalues of the interior Dirichlet problem are provided and might serve as test cases to check newly derived Faber–Krahn type inequalities for larger transmission eigenvalues that are not yet available.
Related Links	http://iopscience.iop.org/0266-5611/29/10/104012/pdf/0266-5611_29_10_104012.pdf
ISSN	02665611
e-ISSN	13616420
DOI	10.1088/0266-5611/29/10/104012
Journal	Inverse Problems
Issue Number	10
Volume Number	29
Language	English
Publisher	IOP Publishing
Publisher Date	2013-09-18
Access Restriction	Open
Subject Keyword	Journal: Inverse Problems Applied Mathematics Transmission Eigenvalues Integral Equation Complex Valued Highly Accurate
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Signal Processing Mathematical Physics Computer Science Applications

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