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Transparent boundary conditions for time-dependent problems
Publikationstyp
Journal Article
Date Issued
2008-07-02
Sprache
English
TORE-URI
Volume
30
Issue
5
Start Page
2358
End Page
2385
Citation
SIAM Journal on Scientific Computing 5 (30): 2358-2385 (2007)
Publisher DOI
Scopus ID
Publisher
SIAM
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.
Subjects
Drift-diffusion equation
Klein-gordon equation
Nonreflecting boundary condition
Pole condition
Schrödinger equation
Transparent boundary condition
Wave equation
DDC Class
510: Mathematik