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Preprint 27-2007

Exact artificial boundary conditions for problems with periodic structures

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

Author(s) : Matthias Ehrhardt , Zheng Chunxiong

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 27-2007

MSC 2000

65M99 None of the above, but in this section
81-08 Computational methods

Abstract :
Based on the work of Zheng on the artificial boundary condition for the Schrödinger equation with sinusoidal potentials at infinity, an analytical impedance expression is presented for general second order periodic ODE problems and its validity is shown to be strongly supported by numerical evidences. This new expression for the kernel of artificial boundary conditions is then used for computing the bound states of the Schrödinger operator with periodic potentials at infinity. Other potential applications are associated with the exact artificial boundary conditions for some time-dependent problems with periodic structures. As an example, a two-dimensional hyperbolic equation modeling the TE polarization of the electromagnetic field with a periodic dielectric permittivity is considered.

Keywords : artificial boundary conditions, periodic potential, Schrödinger equation, hyperbolic equation

Notes :
submitted to: Journal of Computational Physics

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