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A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations

Shi Jin , University of Wisconsin-Madison Jian-Guo Liu Duke University Li Wang University of Wisconsin-Madison

Analysis of PDEs mathscidoc:1702.03045

MATHEMATICS OF COMPUTATION, 82, (282), 749–779, 2013.4
We present a domain decomposition method on a semilinear hyperbolic system with multiple relaxation times. In the region where the relaxation time is small, an asymptotic equilibrium equation can be used for computational efficiency. An interface condition based on the sign of the characteristic speed at the interface is provided to couple the two systems in a domain decomposition setting. A rigorous analysis, based on the Laplace Transform, on the $ L^2$ error estimate is presented for the linear case, which shows how the error of the domain decomposition method depends on the smaller relaxation time, and the boundary and interface layer effects. The given convergence rate is optimal. We present a numerical implementation of this domain decomposition method, and give some numerical results in order to study the performance of this method.
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@inproceedings{shi2013a,
  title={A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations},
  author={Shi Jin, Jian-Guo Liu, and Li Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208222816678072323},
  booktitle={MATHEMATICS OF COMPUTATION},
  volume={82},
  number={282},
  pages={749–779},
  year={2013},
}
Shi Jin, Jian-Guo Liu, and Li Wang. A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations. 2013. Vol. 82. In MATHEMATICS OF COMPUTATION. pp.749–779. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208222816678072323.
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