A 3D curvilinear discontinuous Galerkin time-domain solver for nanoscale light–matter interactions

• J. Viquerat ^[1] ; C. Scheid ^[1]
  1. [1] French Institute for Research in Computer Science and Automation

     French Institute for Research in Computer Science and Automation

     Arrondissement de Versailles, Francia

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 289, Nº 1 (1 December 2015), 2015, págs. 37-50
• Idioma: inglés
• DOI: 10.1016/j.cam.2015.03.028
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• Resumen

  • Classical finite element methods rely on tessellations composed of straight-edged elements mapped linearly from a reference element, on domains which physical boundaries and interfaces are indifferently straight or curved. This approximation represents a serious hindrance for high-order methods, since they limit the accuracy of the spatial discretization to second order. Thus, exploiting an enhanced representation of physical geometries is in agreement with the natural procedure of high-order methods, such as the discontinuous Galerkin method. In this framework, we propose and validate an implementation of a high-order mapping for tetrahedra, and then focus on specific photonics and plasmonics setups to assess the gains of the method in terms of memory and performances.