Mai-Duy, N. and Tanner, R. I. (2007) A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs. International Journal of Numerical Methods for Heat and Fluid Flow, 17 (2). pp. 165-186. ISSN 0961-5539
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Purpose -- To present a new collocation method for
numerically solving partial differential equations (PDEs) in rectangular domains.
Design/methodology/approach -- The proposed method is
based on a Cartesian grid and a one-dimensional
integrated-radial-basis-function (1D-IRBF) scheme. The employment of integration to construct the RBF approximations representing the field variables facilitates a fast convergence rate, while the use of a 1D interpolation scheme leads to considerable economy in forming the system matrix and improvement in the condition number of RBF matrices over a 2D interpolation scheme.
Findings -- The proposed method is verified by considering several test problems governed by second- and fourth-order PDEs; very accurate solutions are achieved using relatively coarse grids.
Research limitations/implications -- Only 1D and 2D
formulations are presented, but we believe that extension to 3D problems can be carried out straightforwardly. Further development is needed for the case of non-rectangular domains.
Originality/value -- The contribution of this paper is a
new effective collocation formulation based on RBFs for solving PDEs.
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|Item Type:||Article (Commonwealth Reporting Category C)|
|Item Status:||Live Archive|
|Additional Information (displayed to public):||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:||10 Feb 2008 23:31|
|Last Modified:||02 Jul 2013 22:54|
|Uncontrolled Keywords:||integrated radial basis function; collocation method; Cartesian grid; multiple boundary conditions|
|Fields of Research (FoR):||01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
09 Engineering > 0915 Interdisciplinary Engineering > 091501 Computational Fluid Dynamics
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
|Socio-Economic Objective (SEO):||E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering|
|Identification Number or DOI:||doi: 10.1108/09615530710723948|
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