Nonlinear Advection Problems and Overlapping Schwarz Waveform Relaxation
We analyze the convergence behavior of the overlapping Schwarz waveform relaxation algorithm applied to nonlinear advection problems. We show for Burgers' equation that the algorithm converges super-linearly at a rate which is asymptotically comparable to the rate of the algorithm applied to linear advection problems. The convergence rate depends on the overlap and the length of the time interval. We carefully track dependencies on the viscosity parameter and show the robustness of all estimates with respect to this parameter.
KeywordsHeat Kernel Domain Decomposition Domain Decomposition Method Viscosity Parameter Relaxation Algorithm
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- C. Dafermos. Hyperbolic conservation laws in continuum physics. Springer, New York, 2000.Google Scholar
- D. S. Daoud and M. J. Gander. Overlapping Schwarz waveform relaxation for convection reaction diffusion problems. In N. D. et al., editor, 13th International Conference on Domain Decomposition Methods, pages 253–260, 2000.Google Scholar
- V. Dolean, S. Lanteri, and F. Nataf. Convergence analysis of a Schwarz type domain decomposition method for the solution of the Euler equations. Technical Report 3916, INRIA, aopr 2000. URL http://www.inria.fr/RRRT/RR-3916.html.Google Scholar
- M. J. Gander. Analysis of Parallel Algorithms for Time Dependent Partial Differential Equations. PhD thesis, Stanford University, Stanford, CA 94305, USA, September 1997.Google Scholar
- M. J. Gander and C. Rohde. Overlapping Schwarz waveform relaxation for convection dominated nonlinear conservation laws. Technical Report 12, Mathematisches Institut, Albert-Ludwigs-Universitäat Freiburg, 2003.Google Scholar