A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains

Mai-Duy, Nam and See, Howard and Tran-Cong, Thanh (2009) A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains. Applied Mathematical Modelling, 33 (1). pp. 284-299. ISSN 0307-904X

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Abstract

In this paper, an integral collocation approach based on Chebyshev polynomials for numerically solving biharmonic equations [N. Mai-Duy, R.I. Tanner, A spectral collocation method based on integrated Chebyshev polynomials for biharmonic boundary-value problems, J. Comput. Appl. Math. 201 (1) (2007) 30–47] is further developed for the case of irregularly shaped domains. The problem domain is embedded in a domain of regular shape, which facilitates the use of tensor product grids. Two relevant important issues, namely the description of the boundary of the domain on a tensor product grid and the imposition of double boundary conditions, are handled effectively by means of integration constants. Several schemes of the integral collocation formulation are proposed, and their performances are numerically investigated through the interpolation of a function and the solution of 1D and 2D biharmonic problems. Results obtained show that they yield spectral accuracy.


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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 (Elsevier).
Depositing User: Dr Nam Mai-Duy
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 08 Jan 2010 23:30
Last Modified: 02 Jul 2013 23:34
Uncontrolled Keywords: integral collocation formulation; biharmonic problems; complex geometries; fictitious domains; Chebyshev polynomials
Fields of Research (FOR2008): 01 Mathematical Sciences > 0101 Pure Mathematics > 010106 Lie Groups, Harmonic and Fourier Analysis
01 Mathematical Sciences > 0101 Pure Mathematics > 010102 Algebraic and Differential Geometry
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: doi: 10.1016/j.apm.2007.11.002
URI: http://eprints.usq.edu.au/id/eprint/6500

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