Ruprecht, D orcid.org/0000-0003-1904-2473, Schaedle, A, Schmidt, F et al. (1 more author) (2008) Transparent Boundary Conditions for Time-Dependent Problems. SIAM Journal on Scientific Computing, 30 (5). pp. 2358-2385. ISSN 1064-8275
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2008, Society for Industrial and Applied Mathematics. This is an author produced version of a paper published in the SIAM Journal on Scientific Computing. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | transparent boundary condition; nonreflecting boundary condition; pole condition; wave equation; Klein-Gordon equation; Schrodinger equation; drift-diffusion equation |
Dates: |
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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: | 15 Jul 2016 16:00 |
Last Modified: | 25 Oct 2016 06:00 |
Published Version: | http://doi.org/10.1137/070692637 |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics |
Identification Number: | 10.1137/070692637 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:90544 |