An integral-collocation-based fictitious-domain technique for solving elliptic problems

Mai-Duy, Nam and See, Howard and Tran-Cong, Thanh (2008) An integral-collocation-based fictitious-domain technique for solving elliptic problems. Communications in Numerical Methods in Engineering, 24 (11). pp. 1291-1314. ISSN 1069-8299

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Abstract

This paper presents a new fictitious-domain technique for numerically solving elliptic second-order partial-differential equations (PDEs) in complex geometries. The proposed technique is based on the use of integral collocation schemes and Chebyshev polynomials. The boundary conditions on the actual boundary are implemented by means of integration constants. The method works for both Dirichlet and Neumann boundary conditions. Several test problems are considered to verify the technique. Numerical results show that the present method yields spectral accuracy for smooth (analytic) problems.


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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.
Depositing User: Dr Nam Mai-Duy
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 22 May 2009 02:30
Last Modified: 10 Oct 2014 05:57
Uncontrolled Keywords: fictitious domains; point collocation techniques; integrated Chebyshev polynomials; elliptic problems
Fields of Research (FOR2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
09 Engineering > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics
Identification Number or DOI: doi: 10.1002/cnm.1033
URI: http://eprints.usq.edu.au/id/eprint/4900

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