A second-order continuity domain-decomposition technique based on integrated Chebyshev polynomials for two-dimensional elliptic problems

Mai-Duy, Nam and Tran-Cong, Thanh (2008) A second-order continuity domain-decomposition technique based on integrated Chebyshev polynomials for two-dimensional elliptic problems. Applied Mathematical Modelling, 32 (12). pp. 2851-2862. ISSN 0307-904X

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Abstract

This paper presents a second-order continuity
non-overlapping domain decomposition (DD) technique for
numerically solving second-order elliptic problems in
two-dimensional space. The proposed DD technique uses integrated Chebyshev polynomials to represent the solution in subdomains. The constants of integration are utilized to impose continuity of the second-order normal derivative of the solution at the interior points of subdomain interfaces. To also achieve a C2 (C squared) function
at the intersection of interfaces, two additional unknowns are introduced at each intersection point. Numerical results show that the present DD method yields a higher level of accuracy than conventional DD techniques based on differentiated Chebyshev polynomials.

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Item Type:	Article (Commonwealth Reporting Category C)
Refereed:	Yes
Item Status:	Live Archive
Additional Information:	Accepted manuscript deposited in accordance with the copyright policy of the publisher.
Faculty/School / Institute/Centre:	Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering (Up to 30 Jun 2013)
Faculty/School / Institute/Centre:	Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering (Up to 30 Jun 2013)
Date Deposited:	21 May 2009 21:13
Last Modified:	02 Jul 2013 23:08
Uncontrolled Keywords:	non-overlapping domain decomposition; second order continuity; collocation point; integrated Chebyshev polynomials; second-order elliptic problems
Fields of Research (2008):	01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations 09 Engineering > 0915 Interdisciplinary Engineering > 091504 Fluidisation and Fluid Mechanics 01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
Socio-Economic Objectives (2008):	E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI:	https://doi.org/10.1016/j.apm.2007.10.003
URI:	http://eprints.usq.edu.au/id/eprint/4570

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