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A modified particle method for semilinear hyperbolic systems with oscillatory solutions

Fetecau, R. C. and Hou, T. Y. (2004) A modified particle method for semilinear hyperbolic systems with oscillatory solutions. Methods and Applications of Analysis, 11 (4). pp. 573-604. ISSN 1073-2772. http://resolver.caltech.edu/CaltechAUTHORS:20111013-071805594

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Abstract

We introduce a modified particle method for semi-linear hyperbolic systems with highly oscillatory solutions. The main feature of this modified particle method is that we do not require different families of characteristics to meet at one point. In the modified particle method, we update the ith component of the solution along its own characteristics, and interpolate the other components of the solution from their own characteristic points to the ith characteristic point. We prove the convergence of the modified particle method essentially independent of the small scale for the variable coefficient Carleman model. The same result also applies to the non-resonant Broadwell model. Numerical evidence suggests that the modified particle method also converges essentially independent of the small scale for the original Broadwell model if a cubic spline interpolation is used.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://projecteuclid.org/euclid.maa/1144939948PublisherUNSPECIFIED
Additional Information:© 2004 International Press. Received November 7, 2004; accepted for publication February 2, 2004. The research of T. Hou was supported in part by NSF under the NSF FRG grant DMS-0353838 and ITR Grant ACI-0204932.
Funders:
Funding AgencyGrant Number
NSF Focused Research Groups (FRG)DMS-0353838
NSF- Information Technology Research (ITR)ACI-0204932
Subject Keywords:Particle methods, homogenization, hyperbolic systems
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Zentralblatt MATH identifier 1100.65076
Mathematical Reviews number (MathSciNet)MR2195371
Classification Code:AMS subject classifications: 65M12, 74Q10
Record Number:CaltechAUTHORS:20111013-071805594
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20111013-071805594
Official Citation:A modified particle method for semilinear hyperbolic systems with oscillatory solutions R. C. Fetecau and T. Y. Hou; 573-604
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:27203
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:13 Oct 2011 14:56
Last Modified:26 Dec 2012 14:16

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