Repository: Freie Universität Berlin, Math Department

Transparent Boundary Conditions for Time-dependent Problems

Ruprecht, D. and Schaedle, A. and Schmidt, F. and Zschiedrich, L. (2008) Transparent Boundary Conditions for Time-dependent Problems. SIAM J. Sci. Comput., 30 (5). pp. 2358-2385. ISSN 1064-8275

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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.

Item Type:Article
Uncontrolled Keywords:Klein-Gordon equation, Schrödinger equation, drift-diffusion equation, nonreflecting boundary condition, pole condition, transparent boundary condition, wave equation
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:541
Deposited By: Ulrike Eickers
Deposited On:14 Jul 2009 12:30
Last Modified:14 Jul 2009 12:59

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