@article{RuprechtSchaedleSchmidtetal.2008, author = {Ruprecht, Daniel and Sch{\"a}dle, Achim and Schmidt, Frank and Zschiedrich, Lin}, title = {Transparent boundary conditions for time-dependent problems}, volume = {30}, journal = {SIAM J. Sci. Comput.}, number = {5}, doi = {10.1137/070692637}, pages = {2358 -- 2385}, year = {2008}, language = {en} } @inproceedings{SchaedleRuprechtSchmidt2007, author = {Sch{\"a}dle, Achim and Ruprecht, Daniel and Schmidt, Frank}, title = {Transparent boundary conditions - the pole condition approach}, booktitle = {Proceedings of Waves 2007}, editor = {et.al., N. Biggs}, pages = {301 -- 303}, year = {2007}, language = {en} } @article{RuprechtSchaedleSchmidt2013, author = {Ruprecht, Daniel and Sch{\"a}dle, Achim and Schmidt, Frank}, title = {Transparent boundary conditions based on the pole condition for time-dependent, two-dimensional problems}, volume = {29}, journal = {Numerical Methods for Partial Differential Equations}, number = {4}, doi = {10.1002/num.21759}, pages = {1367 -- 1390}, year = {2013}, language = {en} } @misc{RuprechtSchaedleSchmidtetal.2007, author = {Ruprecht, Daniel and Sch{\"a}dle, Achim and Schmidt, Frank and Zschiedrich, Lin}, title = {Transparent boundary conditons for time-dependent problems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9558}, number = {07-12}, year = {2007}, abstract = {A new approach to derive transparent boundary conditions (TBCs) for wave, Schr{\"o}dinger, heat and drift-diffusion equations is presented. It relies on the pole condition and distinguishes between physical reasonable and unreasonable solutions by the location of the singularities of the spatial Laplace transform of the exterior solution. To obtain a numerical algorithm, a M{\"o}bius 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.}, language = {en} }