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| Conference Presentation (After Call) | FZJ-2018-03205 |
2018
Abstract: Interior transmission eigenvalues play an important role in acoustic scattering theory. However, the numerical calculation of those is a challenging task due to the fact that the problem is non-elliptic and non-self-adjoint. Several new methods have been introduced to find such interior transmission eigenvalues (see for example [1]). One recent method is the inside-outside duality method first introduced by Kirsch and Lechleiter [2]. But, from the computational point of view there are still many issues that have to be addressed to obtain better accuracy.Usually, the surface of the far-field operator is discretized by a fixed number of elements and then the integrand is approximated by constant interpolation (see for example [3]). However, for larger wave numbers the results are insufficient. In [4] it is shown that this approximation can be improved by using either one of the following three methods (a) Gaussian quadrature, (b) spherical t-design, or (c) Lebedev quadrature leading to much better accuracy for the numerical calculation of interior transmission eigenvalues via the inside-outside duality method.References1. A. Kleefeld, A numerical method to compute interior transmission eigenvalues, Inverse Problems, 29, 104012 (2013).2. A. Kirsch and A. Lechleiter, The inside-outside duality method for scattering problems by inhomogeneous media, Inverse Problems, 29, 104011 (2013).3. S. Peters and A. Kleefeld, Numerical computations of interior transmission eigenvalues for scattering objects with cavities, Inverse Problems, 32, 045001 (2016). 4. A. Kleefeld and E. Reichwein, Improvement of the inside-outside duality method, In C. Constanda, M. Dalla Riva, P.D. Lamberti, and P. Musolino (Eds.): Integral Methods in Science and Engineering, Vol. 1, Birkhäuser Basel, 2017.
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