TUHH Open Research (TORE)https://tore.tuhh.deTORE captures, stores, indexes, preserves, and distributes digital research material.Sun, 04 Jun 2023 01:54:53 GMT2023-06-04T01:54:53Z5031- Transparent boundary conditions based on the Pole Condition for time-dependent, two-dimensional problemshttp://hdl.handle.net/11420/10528Title: Transparent boundary conditions based on the Pole Condition for time-dependent, two-dimensional problems
Authors: Ruprecht, Daniel; Schädle, Achim; Schmidt, Frank
Abstract: The pole condition approach for deriving transparent boundary conditions is extended to the time-dependent, two-dimensional case. Non-physical modes of the solution are identified by the position of poles of the solution's spatial Laplace transform in the complex plane. By requiring the Laplace transform to be analytic on some problem dependent complex half-plane, these modes can be suppressed. The resulting algorithm computes a finite number of coefficients of a series expansion of the Laplace transform, thereby providing an approximation to the exact boundary condition. The resulting error decays super-algebraically with the number of coefficients, so relatively few additional degrees of freedom are sufficient to reduce the error to the level of the discretization error in the interior of the computational domain. The approach shows good results for the Schrödinger and the drift-diffusion equation but, in contrast to the one-dimensional case, exhibits instabilities for the wave and Klein-Gordon equation. Numerical examples are shown that demonstrate the good performance in the former and the instabilities in the latter case.
Mon, 01 Jul 2013 00:00:00 GMThttp://hdl.handle.net/11420/105282013-07-01T00:00:00Z
- Optimal parameter choice for the pole conditionhttp://hdl.handle.net/11420/10536Title: Optimal parameter choice for the pole condition
Authors: Ruprecht, Daniel; Schädle, Achim; Schmidt, Frank
Fri, 29 Nov 2013 00:00:00 GMThttp://hdl.handle.net/11420/105362013-11-29T00:00:00Z
- Transparent boundary conditions for time-dependent problemshttp://hdl.handle.net/11420/7065Title: Transparent boundary conditions for time-dependent problems
Authors: Ruprecht, Daniel; Schädle, Achim; Schmidt, Frank; Zschiedrich, Lin
Abstract: 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.
Wed, 02 Jul 2008 00:00:00 GMThttp://hdl.handle.net/11420/70652008-07-02T00:00:00Z