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Indirect Methods with Brakhage-Werner Potentials for Helmholtz Transmission Problems

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • María-Luisa Rapún

    (Universidad Pública de Navarra, Dep. Matemática e Informática)

  • Francisco-Javier Sayas

    (Universidad de Zaragoza, Dep. Matemática Aplicada)

Abstract

In this work we propose and analyse numerical methods for Helmholtz transmission problems in two and three dimensions. The methods we analyse use combined single and double layer potentials to represent the interior and exterior solution of the transmission problem. The corresponding boundary integral system includes weakly singular and hypersingular boundary integral operators on the interface. Its invertibility is equivalent to the unique solvability of the transmission problem, since the use of the above mentioned potentials does not introduce spurious eigenmodes in the formulation. We give necessary and sufficient conditions for the convergence of general Petrov-Galerkin schemes for solving the resulting system, providing some concrete methods for the two dimensional case. Some numerical experiments are shown.

Suggested Citation

  • María-Luisa Rapún & Francisco-Javier Sayas, 2006. "Indirect Methods with Brakhage-Werner Potentials for Helmholtz Transmission Problems," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 1146-1154, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_115
    DOI: 10.1007/978-3-540-34288-5_115
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