Inhalt des Dokuments
Preprint 27-2007
Exact artificial boundary conditions for problems with periodic structures
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