Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical Boundary Conditions
We are interested in solving heat equations with nonlinear dynamical boundary conditions by using domain decomposition methods. In the classical framework, one first discretizes the time direction and then solves a sequence of state steady problems by the domain decomposition method. In this paper,...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/474608 |
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| _version_ | 1832566185858695168 |
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| author | Shu-Lin Wu |
| author_facet | Shu-Lin Wu |
| author_sort | Shu-Lin Wu |
| collection | DOAJ |
| description | We are interested in solving heat equations with nonlinear dynamical boundary conditions by using domain decomposition methods. In the classical framework, one first discretizes the time direction and then solves a sequence of state steady problems by the domain decomposition method. In this paper, we consider the heat equations at spacetime continuous level and study a Schwarz waveform relaxation algorithm for parallel computation purpose. We prove the linear convergence of the algorithm on long time intervals and show how the convergence rate depends on the size of overlap and the nonlinearity of the nonlinear boundary functions. Numerical experiments are presented to verify our theoretical conclusions. |
| format | Article |
| id | doaj-art-2a3267bead114e5f9b4d593bc73c4e55 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2a3267bead114e5f9b4d593bc73c4e552025-02-03T01:04:46ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/474608474608Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical Boundary ConditionsShu-Lin Wu0School of Science, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, ChinaWe are interested in solving heat equations with nonlinear dynamical boundary conditions by using domain decomposition methods. In the classical framework, one first discretizes the time direction and then solves a sequence of state steady problems by the domain decomposition method. In this paper, we consider the heat equations at spacetime continuous level and study a Schwarz waveform relaxation algorithm for parallel computation purpose. We prove the linear convergence of the algorithm on long time intervals and show how the convergence rate depends on the size of overlap and the nonlinearity of the nonlinear boundary functions. Numerical experiments are presented to verify our theoretical conclusions.http://dx.doi.org/10.1155/2013/474608 |
| spellingShingle | Shu-Lin Wu Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical Boundary Conditions Abstract and Applied Analysis |
| title | Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical Boundary Conditions |
| title_full | Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical Boundary Conditions |
| title_fullStr | Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical Boundary Conditions |
| title_full_unstemmed | Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical Boundary Conditions |
| title_short | Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical Boundary Conditions |
| title_sort | schwarz waveform relaxation for heat equations with nonlinear dynamical boundary conditions |
| url | http://dx.doi.org/10.1155/2013/474608 |
| work_keys_str_mv | AT shulinwu schwarzwaveformrelaxationforheatequationswithnonlineardynamicalboundaryconditions |