Optimized Schwarz Waveform Relaxation Methods for Advection Reaction Diffusion Problems
We study in this paper a new class of waveform relaxation algorithms for large systems of ordinary differential equations arising from discretizations of partial differential equations of advection reaction diffusion type. We show that the transmission conditions between the subsystems have a tremen...
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| Veröffentlicht in: | SIAM journal on numerical analysis 2007-01, Vol.45 (2), p.666-697 |
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| creator | Gander, M. J. Halpern, L. |
| description | We study in this paper a new class of waveform relaxation algorithms for large systems of ordinary differential equations arising from discretizations of partial differential equations of advection reaction diffusion type. We show that the transmission conditions between the subsystems have a tremendous influence on the convergence speed of the waveform relaxation algorithms, and we identify transmission conditions with optimal performance. Since these optimal transmission conditions are expensive to use, we introduce a class of local transmission conditions of Robin type, which approximate the optimal ones and can be used at the same cost as the classical transmission conditions. We determine the transmission conditions in this class with the best performance of the associated waveform relaxation algorithm. We show that the new algorithm is well posed and converges much faster than the classical one. We illustrate our analysis with numerical experiments. |
| doi_str_mv | 10.1137/050642137 |
| format | Article |
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J. ; Halpern, L.</creator><creatorcontrib>Gander, M. J. ; Halpern, L.</creatorcontrib><description>We study in this paper a new class of waveform relaxation algorithms for large systems of ordinary differential equations arising from discretizations of partial differential equations of advection reaction diffusion type. We show that the transmission conditions between the subsystems have a tremendous influence on the convergence speed of the waveform relaxation algorithms, and we identify transmission conditions with optimal performance. Since these optimal transmission conditions are expensive to use, we introduce a class of local transmission conditions of Robin type, which approximate the optimal ones and can be used at the same cost as the classical transmission conditions. We determine the transmission conditions in this class with the best performance of the associated waveform relaxation algorithm. We show that the new algorithm is well posed and converges much faster than the classical one. 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We determine the transmission conditions in this class with the best performance of the associated waveform relaxation algorithm. We show that the new algorithm is well posed and converges much faster than the classical one. 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| source | SIAM Journals Online; Jstor Complete Legacy; JSTOR Mathematics & Statistics |
| subjects | Advection Algorithms Approximation Boundary conditions Decomposition Experiments Fourier transformations Initial guess Low frequencies Perceptron convergence procedure Spacetime Waveforms |
| title | Optimized Schwarz Waveform Relaxation Methods for Advection Reaction Diffusion Problems |
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