Transparent boundary conditions for time-dependent problems

Link:
Autor/in:
Verlag/Körperschaft:
Hamburg University of Technology
Erscheinungsjahr:
2008
Medientyp:
Text
Schlagworte:
  • Drift-diffusion equation
  • Klein-gordon equation
  • Nonreflecting boundary condition
  • Pole condition
  • Schrödinger equation
  • Transparent boundary condition
  • Wave equation
  • 510: Mathematik
Beschreibung:
  • A new approach to derive transparent boundary conditions (TBCs) for dispersive wave, Schrödinger, heat, and drift-diffusion equations is presented. It relies on the pole condition and distinguishes between physically reasonable and unreasonable solutions by the location of the singularities of the Laplace transform of the exterior solution. Here the Laplace transform is taken with respect to a generalized radial variable. To obtain a numerical algorithm, a Möbius 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 power series are derived. These are coupled to the equation in the interior and yield transparent boundary conditions. Numerical results are presented in the last section, showing that the error introduced by the new approximate TBCs decays exponentially in the number of coefficients. © 2008 Society for Industrial and Applied Mathematics.
Beziehungen:
DOI 10.1137/070692637
Quellsystem:
TUHH Open Research
Interne Metadaten
Quelldatensatz
oai:tore.tuhh.de:11420/7065