Mathematics – Numerical Analysis
Scientific paper
2012-04-17
Mathematics
Numerical Analysis
Scientific paper
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 Schr\"odinger 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.
Ruprecht Daniel
Schädle Achim
Schmidt Frank
No associations
LandOfFree
Transparent boundary conditions based on the Pole Condition for time-dependent, two-dimensional problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Transparent boundary conditions based on the Pole Condition for time-dependent, two-dimensional problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Transparent boundary conditions based on the Pole Condition for time-dependent, two-dimensional problems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-290100