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Theoretical and numerical analysis on a thermo-elastic system with discontinuities

Li, Zhilin and Wang, Deshen and Zou, Jun (1998) Theoretical and numerical analysis on a thermo-elastic system with discontinuities. Journal of Computational and Applied Mathematics, 92 (1). pp. 37-58. ISSN 0377-0427. http://resolver.caltech.edu/CaltechAUTHORS:20170409-075602328

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Abstract

A second-order accurate numerical scheme is proposed for a thermo-elastic system which models a bar made of two distinct materials. The physical parameters involved may be discontinuous across the joint of the two materials, where there might be also singular heat and/or force sources. The solution components, the temperature and the displacement, may change rapidly across the joint. By transforming the system into a different one, time-marching schemes can be used for the new system which is well posed. The immersed interface method is employed to deal with the discontinuities of the coefficients and the singular sources. The proposed numerical method can fit both explicit and implicit formulation. For the implicit version, a stable and fast prediction-correction scheme is also developed. Convergence analysis shows that our method is second-order accurate at all grid points in spite of the discontinuities across the interface. Numerical experiments are performed to support the theoretical analysis in this paper.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/S0377-0427(98)00044-2DOIArticle
https://www.sciencedirect.com/science/article/pii/S0377042798000442PublisherArticle
Additional Information:© 1998 Published by Elsevier. Received 16 February 1997; received in revised form 30 October 1997. The author was partially supported by NSF Grant 9626703 and URI grant #N00014092-J-1890 from ARPA at UCLA. The author was partially supported by the Direct Grant of CUHK and Hong Kong RGC grant no. CUHK 338/96E. The authors would like to thank many people at the department of mathematics at UCLA and Mississippi State University for many useful discussions and suggestions.
Funders:
Funding AgencyGrant Number
NSFDMS-9626703
Office of Naval Research (ONR)N00014092-J-1890
Advanced Research Projects Agency (ARPA)UNSPECIFIED
Chinese University of Hong KongUNSPECIFIED
Research Grants Council of Hong KongCUHK 338/96E
Subject Keywords:Mixed type system; Discontinuous coefficients; Dirac delta function; Finite difference; Semi-implicit prediction-correction scheme; Error analysis
Classification Code:AMS classification: 65M06; 65M12; 65N06; 73C35
Record Number:CaltechAUTHORS:20170409-075602328
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170409-075602328
Official Citation:Zhilin Li, Deshen Wang, Jun Zou, Theoretical and numerical analysis on a thermo-elastic system with discontinuities, Journal of Computational and Applied Mathematics, Volume 92, Issue 1, 1998, Pages 37-58, ISSN 0377-0427, https://doi.org/10.1016/S0377-0427(98)00044-2. (http://www.sciencedirect.com/science/article/pii/S0377042798000442)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76445
Collection:CaltechAUTHORS
Deposited By: 1Science Import
Deposited On:04 Apr 2018 17:19
Last Modified:04 Apr 2018 17:19

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