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@INPROCEEDINGS{Kleefeld:847874,
      author       = {Kleefeld, Andreas},
      title        = {{I}mprovement of the inside-outside duality method},
      reportid     = {FZJ-2018-03205},
      year         = {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.},
      month         = {May},
      date          = {2018-05-21},
      organization  = {9th International Conference Inverse
                       Problems: Modeling $\&$ Simulation,
                       Paradise Bay Resort Hotel (Malta), 21
                       May 2018 - 26 May 2018},
      subtyp        = {After Call},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511)},
      pid          = {G:(DE-HGF)POF3-511},
      typ          = {PUB:(DE-HGF)6},
      url          = {https://juser.fz-juelich.de/record/847874},
}