Computing Floquet�Bloch modes in biperiodic slabs with boundary elements

• Autores: Johannes Tausch
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 254, Nº 1, 2013 (Ejemplar dedicado a: Nonlinear Elliptic Differential Equations, Bifurcation, Local Dynamics of Parabolic Systems and Numerical Methods), págs. 192-203
• Idioma: inglés
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• Resumen

  • A new variational formulation for the boundary element computation of Floquet�Bloch solutions to the Helmholtz equation is derived. The method is applicable to geometries that are layered in the vertical and biperiodic in two horizontal directions. The discretization leads to a nonlinear Hermitian eigenvalue problem which is solved using a homotopy approach. Numerical examples demonstrate that with the boundary element approach a high accuracy can be achieved with a small number of degrees of freedom in the discretization.