Ruprecht, D, Schädle, A and Schmidt, F (2013) Transparent boundary conditions based on the pole condition for time-dependent, two-dimensional problems. Numerical Methods for Partial Differential Equations, 29 (4). 1367 - 1390. ISSN 0749-159X
Abstract
The pole condition approach for deriving transparent boundary conditions is extended to the time-dependent, two-dimensional case. Nonphysical 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.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | This is the peer reviewed version of the following article: Ruprecht, D, Schädle, A and Schmidt, F (2013) Transparent boundary conditions based on the pole condition for time-dependent, two-dimensional problems. Numerical Methods for Partial Differential Equations, 29 (4). 1367 - 1390, which has been published in final form at http://dx.doi.org/10.1002/num.21759. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. |
Keywords: | drift diffusion equation; Klein Gordon equation; nonreflecting boundary condition; pole condition; Schrodinger equation; transparent boundary condition; wave equation |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mechanical Engineering (Leeds) > Institute of Engineering Thermofluids, Surfaces & Interfaces (iETSI) (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 10 Nov 2015 10:37 |
Last Modified: | 11 Nov 2015 07:32 |
Published Version: | http://dx.doi.org/10.1002/num.21759 |
Status: | Published |
Publisher: | Wiley |
Identification Number: | 10.1002/num.21759 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:90545 |