Abstract
In this paper, we introduce the results for the Schwarz waveform relaxation (SWR) algorithm applied to a class of non-dissipative reaction diffusion equations. Both the Dirichlet and Robin transmission conditions (TCs) are considered. For the Dirichlet TC, we consider the algorithm for the nonlinear problem \(\partial _{t}u =\mu \partial _{xx}u + f(u)\), in the case of many subdomains.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
D. Bennequin, M.J. Gander, L. Halpern, A homographic best approximation problem with application to optimized schwarz waveform relaxation. Math. Comput. 78, 185–223 (2009)
F. Caetano, M.J. Gander, L. Halpern, J. Szeftel, Schwarz waveform relaxation algorithms for smilinear reaction-diffusion equations. Netw. Heterog. Media 5, 487–505 (2010)
M.J. Gander, A waveform relaxation algorithm with overlapping splitting for reaction diffusion equations. Numer. Linear Algebra Appl. 6, 125–145 (1998)
M.J. Gander, L. Halpern, Optimized schwarz waveform relaxation for advection reaction diffusion problems. SIAM J. Numer. Anal. 45, 666–697 (2007)
M.J. Gander, A.M. Stuart, Space-time continuous analysis of waveform relaxation for the heat equation. SIAM J. Sci. Comput. 19, 2014–2031 (1998)
L. Halpern, Absorbing boundary conditions and optimized schwarz waveform relaxation. Behav. Inf. Technol. 46, 21–34 (2006)
S.L. Wu, Convergence analysis of the schwarz waveform relaxation algorithms for a class of non-dissipative problems. Manuscript (2014)
S.L. Wu, C.M. Huang, T.Z. Huang, Convergence analysis of the overlapping schwarz waveform relaxation algorithm for reaction-diffusion equations with time delay. IMA J. Numer. Anal. 32, 632–671 (2012)
Acknowledgement
The author is very grateful to Prof. Martin J. Gander, for his fund of the DD22 conference, his careful reading and revision of this paper, and his professional instructions in many fields.
This work was supported by the NSF of Science & Technology of Sichuan Province (2014JQ0035), the project of the Key Laboratory of Cambridge and Non-Destructive Inspection of Sichuan Institutes of Higher Education (2013QZY01) and the NSF of China (11301362, 11371157, 91130003).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Wu, SL. (2016). Schwarz Waveform Relaxation for a Class of Non-dissipative Problems. In: Dickopf, T., Gander, M., Halpern, L., Krause, R., Pavarino, L. (eds) Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-319-18827-0_64
Download citation
DOI: https://doi.org/10.1007/978-3-319-18827-0_64
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18826-3
Online ISBN: 978-3-319-18827-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)