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Takustrae 7 D-14195 Berlin-Dahlem
 

Summary: Takustraße 7
D-14195 Berlin-Dahlem
Germany
Konrad-Zuse-Zentrum
f¨ur Informationstechnik Berlin
DANIEL RUPRECHT ACHIM SCH ¨ADLE
FRANK SCHMIDT LIN ZSCHIEDRICH
Transparent boundary conditons for
time-dependent problems
ZIB-Report 07-12 (Mai 2007)
TRANSPARENT BOUNDARY CONDITONS FOR
TIME-DEPENDENT PROBLEMS
DANIEL RUPRECHT, ACHIM SCH¨ADLE, FRANK SCHMIDT, AND LIN
ZSCHIEDRICH
Abstract. A new approach to derive transparent boundary conditions (TBCs) for wave,
Schr¨odinger, heat and drift-diffusion equations is presented. It relies on the pole condition and
distinguishes between physical reasonable and unreasonable solutions by the location of the singu-
larities of the spatial Laplace transform of the exterior solution. To obtain a numerical algorithm, a
M¨obius transform is applied to map the Laplace transform onto the unit disc. In the transformed
coordinate the solution is expanded into a power series. Finally, equations for the coefficients of the

  

Source: Andrzejak, Artur - Konrad-Zuse-Zentrum für Informationstechnik Berlin

 

Collections: Computer Technologies and Information Sciences