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Essential spectrum of local multi-trace boundary integral operators

Xavier Claeys 1, 2 
2 ALPINES - Algorithms and parallel tools for integrated numerical simulations
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, INSMI - Institut National des Sciences Mathématiques et de leurs Interactions
Abstract : Considering pure transmission scattering problems in piecewise constant media, we derive an exact analytic formula for the spectrum of the corresponding local multi-trace boundary integral operators in the case where the geometrical configuration does not involve any junction point and all wave numbers equal. We deduce from this the essential spectrum in the case where wave numbers vary. Numerical evidences of these theoretical results are also presented.
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Submitted on : Tuesday, January 5, 2016 - 5:59:08 PM
Last modification on : Friday, January 21, 2022 - 3:22:14 AM
Long-term archiving on: : Thursday, April 7, 2016 - 3:40:51 PM


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  • HAL Id : hal-01251212, version 1
  • ARXIV : 1508.00556


Xavier Claeys. Essential spectrum of local multi-trace boundary integral operators. IMA Journal of Applied Mathematics, 2016. ⟨hal-01251212⟩



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