WIAS Preprint No. 1323, (2008)

Numerical simulation of waves in periodic structures


  • Ehrhardt, Matthias
  • Han, Houde
  • Zheng, Chunxiong

2010 Mathematics Subject Classification

  • 35B27 65M99 35Q60 35J05

2008 Physics and Astronomy Classification Scheme

  • 02.70.Bf 31.15.-p 42.82.Et 85.35.-p 85.35.Be


  • periodic media, Helmholtz equation, Schrödinger equation, Dirichlet-to-Neumann maps, Robin-to-Robin maps, band structure, Floquet-Bloch theory, high-order finite elements




In this work we present a new numerical technique for solving periodic structure problems. This new approach possesses several advantages. First, it allows for a fast evaluation of the Robin-to-Robin operator for periodic array problems. Secondly, this computational method can also be used for bi-periodic structure problems with local defects. Our strategy is an improvement of the recently developed recursive doubling process by Yuan and Lu.
In this paper we consider several problems, such as the exterior elliptic problems with strong coercivity, the time-dependent Schrödinger equation and finally the Helmholtz equation with damping.

Appeared in

  • Commun. Comput. Phys., 5 (2009) pp. 849--872.

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