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Effective semi-analytic integration for hypersingular Galerkin boundary integral equations for the Helmholtz equation in 3D

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Abstract

We deal with the Galerkin discretization of the boundary integral equations corresponding to problems with the Helmholtz equation in 3D. Our main result is the semi-analytic integration for the bilinear form induced by the hypersingular operator. Such computations have already been proposed for the bilinear forms induced by the single-layer and the double-layer potential operators in the monograph The Fast Solution of Boundary Integral Equations by O. Steinbach and S. Rjasanow and we base our computations on these results.

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Authors and Affiliations

  1. Department of Applied Mathematics, VŠB-TU Ostrava, 17. listopadu 15/2172, 708 33, Ostrava-Poruba, Czech Republic

    Jan Zapletal & Jiří Bouchala

Authors
  1. Jan Zapletal
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  2. Jiří Bouchala
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Correspondence to Jan Zapletal.

Additional information

This research has been supported by the grant of the Ministry of Education of the Czech Republic No. MSM6198910027, by VŠB-Technical University of Ostrava under the grant SGS SP2013/191, by the European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070) and by the project SPOMECH-Creating a multidisciplinary R&D team for reliable solution of mechanical problems, reg. no. CZ.1.07/2.3.00/20.0070 within the Operational Programme ‘Education for competitiveness’ funded by the Structural Funds of the European Union and the state budget of the Czech Republic.

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Zapletal, J., Bouchala, J. Effective semi-analytic integration for hypersingular Galerkin boundary integral equations for the Helmholtz equation in 3D. Appl Math 59, 527–542 (2014). https://doi.org/10.1007/s10492-014-0070-6

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  • DOI: https://doi.org/10.1007/s10492-014-0070-6

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