Método de elementos espectrales de galerkin discontinuo para calcular reflexión y transmisión de ondas electromagnéticas

• Autores: Mónica Jhoana Mesa Mazo, César Augusto Acosta Minoli, Hernán Darío Toro Zapata
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 25, Nº. 1, 2018, págs. 41-59
• Idioma: español
• DOI: 10.15517/rmta.v1i25.32231
• Títulos paralelos:
  • Discontinuous galerkin spectral element method to compute reflection and transmission of electromagnetic waves
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• Resumen
  • español

    Este trabajo tiene por objetivo presentar el desarrollo y la validación de un algoritmo de alto orden de precisión, basado en el método de elementos espectrales nodal de Galerkin discontinuo, por su siglas en inglés (DGSEM), para calcular la reflexión y la transmisión de ondas electromagnéticasviajando en dos medios isotrópicos y homogéneos, los cuales se encuentran separados por una interfaz plana vertical con características diferentes de permitividad " y permeabilidad . Para discretizar espacialmente se derivó el método DGSEM sobre las ecuaciones de Maxwell. Posteriormente, se derivó un resolvente de Riemann para calcular el flujo numérico entre los elementos que componen la malla del dominio computacional, para calcular la reflexión y la transmisión de onda en la interfaz, y para introducir las respectivas condiciones de frontera. Finalmente, para discretizar en el tiempo, se utilizó el método de Runge-Kutta explícito de tercer orden de Williamson. Los resultados del algoritmo, en comparación con la solución analítica, demuestran convergencia espectral en el espacio y de tercer orden en el tiempo.

  • English

    Modeling wave reflection and transmission is important for a diversity of applications in physics and engineering. Examples can be found in acoustics and electromagnetism. Computational wave propagation requires high order accuracy both in space and time to get accurate phase and dissipation properties. In this paper we derive and evaluate a high order accurate method based on Discontinuous Galerkin Spectral Element Method (DGSEM) to compute reflection and transmission of electromagnetic waves traveling in two homogeneous and isotropic media, separated by a thin plane interfaz, with different physical properties of permittivity " and permeability . To discretize in Space we used DGSEM over a two dimensional Transverse Electric Maxwell Equations. We derived a Riemann solver to compute the numerical flux between the interfaces of two elements of the computational mesh and to add boundary conditions. To discretize in time we use a third order low storage Runge-Kutta of Williamson. Results when compared with the analytical solution, showedspectral convergence in space and third order convergence in time.

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