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

Authors: Shi Jin, Jian-guo Liu and Li Wang
Journal: Math. Comp. 82 (2013), 749-779
MSC (2010): Primary 65M55, 35L50
Published electronically: October 9, 2012
MathSciNet review: 3008837
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Abstract: 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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Additional Information

Shi Jin
Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706

Jian-guo Liu
Affiliation: Department of Physics and Department of Mathematics, Duke University, Durham, North Carolina 27708

Li Wang
Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706

Received by editor(s): February 17, 2011
Received by editor(s) in revised form: October 9, 2011
Published electronically: October 9, 2012
Additional Notes: This research was partially supported by NSF grant No. DMS-0608720, and NSF FRG grant DMS-0757285. The first author was also supported by a Van Vleck Distinguished Research Prize and a Vilas Associate Award from the University of Wisconsin-Madison
The second author research was supported by NSF grant DMS 1011738
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