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Preprint 48-2007

Numerical simulation of waves in periodic structures

Source file is available as :   Portable Document Format (PDF)

Author(s) : Matthias Ehrhardt , Houde Han , Chunxiong Zheng

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 48-2007

MSC 2000

35B27 Homogenization; partial differential equations in media with periodic structure
65M99 None of the above, but in this section
35Q60 Equations of electromagnetic theory and optics
35J05 Laplace equation, reduced wave equation , Poisson equation

PACS : 02.70.Bf, 31.15.-p, 42.82.Et, 85.35.-p, 85.35.Be

Abstract :
In this work we present a new numerical technique for solving periodic structure problems. This new approach possess several advantages. First, it allows for a fast evaluation of the Dirichlet-to-Robin operator for periodic array problems. Secondly, this implementational 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 in one and two dimensions and finally the Helmholtz equation.

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

Notes :
submitted to: Communications in Computational Physics

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