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

DOI:
https://doi.org/10.1090/S0025-5718-2012-02643-3

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 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

Email:
jin@math.wisc.edu

**Jian-guo Liu**

Affiliation:
Department of Physics and Department of Mathematics, Duke University, Durham, North Carolina 27708

Email:
Jian-Guo.Liu@duke.edu

**Li Wang**

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

Email:
wangli@math.wisc.edu

DOI:
https://doi.org/10.1090/S0025-5718-2012-02643-3

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

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.