Summary: ZAMM header will be provided by the publisher
Discrete Transparent Boundary Conditions for transient kp­Schr¨odinger
Equations with Application to Quantum­Heterostructures
Andrea Zisowsky1
, Anton Arnold2
, Matthias Ehrhardt1
, and Thomas Koprucki3
1
Institut f¨ur Mathematik, Technische Universit¨at Berlin, Straße des 17. Juni 136, D­10623 Berlin
2
Institut f¨ur Numerische Mathematik, Universit¨at M¨unster, Einsteinstraße 62, D­48149 M¨unster
3
Weierstrass­Institut f¨ur Angewandte Analysis und Stochastik, Mohrenstraße 39, D­10117 Berlin
Key words systems of Schr¨odinger equations, transparent boundary conditions, layered semiconductors, discrete convolu-
tion, sum-of-exponentials, finite difference schemes.
MSC (2000) 65M12, 35Q40, 45K05
This work is concerned with transparent boundary conditions (TBCs) for systems of Schr¨odinger-type equations, namely
the time-dependent kp-Schr¨odinger equations. These TBCs are constructed for the fully discrete scheme (Crank-Nicolson,
finite differences), in order to maintain unconditional stability of the scheme and to avoid numerical reflections. The discrete
transparent boundary conditions (DTBCs) are discrete convolutions in time and are constructed using the Z-transformed

Source: Arnold, Anton - Institut für Analysis und Scientific Computing, Technische Universität Wien

Collections: Mathematics