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A new coupling of mixed finite element and boundary element methods for an exterior Helmholtz problem in the plane

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Abstract

This paper deals with the scattering of time harmonic electromagnetic waves by an infinitely long cylinder containing a non-homogeneous conducting medium. More precisely, we study the transverse magnetic field that solves an interface problem holding between the cross section of the cylinder and the exterior two-dimensional free space. We apply a dual-mixed variational formulation in the obstacle coupled with a boundary integral equation method in the unbounded homogeneous space. A Fredholm alternative is utilized to prove that this continuous formulation is well posed. We define the corresponding discrete scheme by using the lowest order rotated Raviart-Thomas finite elements for the magnetic field and spectral elements for the boundary unknown. Then, we show that the resulting Galerkin scheme is uniquely solvable and convergent, and prove optimal error estimates. Finally, we illustrate our analysis with some results from computational experiments.

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Authors and Affiliations

  1. GI2MA, Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción, Chile

    Gabriel N. Gatica

  2. Departamento de Construcción e Ingeniería de Fabricación, Universidad de Oviedo, Oviedo, Spain

    Antonio Márquez

  3. Departamento de Matemáticas, Facultad de Ciencias, Universidad de Oviedo, Calvo Sotelo s/n, Oviedo, Spain

    Salim Meddahi

Authors
  1. Gabriel N. Gatica
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  2. Antonio Márquez
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  3. Salim Meddahi
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Corresponding author

Correspondence to Gabriel N. Gatica.

Additional information

Communicated by Aihui Zhou.

This research was partially supported by CONICYT-Chile through the FONDAP Program in Applied Mathematics, by the Dirección de Investigación of the Universidad de Concepción through the Advanced Research Groups Program, and by the Ministerio de Educación y Ciencia of Spain, through the project No. MTM2004-05417.

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Gatica, G.N., Márquez, A. & Meddahi, S. A new coupling of mixed finite element and boundary element methods for an exterior Helmholtz problem in the plane. Adv Comput Math 30, 281–301 (2009). https://doi.org/10.1007/s10444-008-9068-5

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  • DOI: https://doi.org/10.1007/s10444-008-9068-5

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