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A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform

Published online by Cambridge University Press:  03 June 2015

A. Tadeu ,
C. S. Chen ,
J. António  and
Nuno Simões
A. Tadeu*
Affiliation:
Department of Civil Engineering, Faculty of Sciences and Technology, University of Coimbra, Polo II-Pinhal de Marrocos, 3030-290 Coimbra, Portugal
C. S. Chen*
Affiliation:
Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS 39406, USA
J. António
Affiliation:
Department of Civil Engineering, Faculty of Sciences and Technology, University of Coimbra, Polo II-Pinhal de Marrocos, 3030-290 Coimbra, Portugal
Nuno Simões
Affiliation:
Department of Civil Engineering, Faculty of Sciences and Technology, University of Coimbra, Polo II-Pinhal de Marrocos, 3030-290 Coimbra, Portugal
*
URL:http://www.math.usm.edu/cschen/, Email: tadeu@dec.uc.pt
Corresponding author. Email: cs.chen@usm.edu
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Abstract

Fourier transform is applied to remove the time-dependent variable in the diffusion equation. Under non-harmonic initial conditions this gives rise to a non-homogeneous Helmholtz equation, which is solved by the method of fundamental solutions and the method of particular solutions. The particular solution of Helmholtz equation is available as shown in [4, 15]. The approximate solution in frequency domain is then inverted numerically using the inverse Fourier transform algorithm. Complex frequencies are used in order to avoid aliasing phenomena and to allow the computation of the static response. Two numerical examples are given to illustrate the effectiveness of the proposed approach for solving 2-D diffusion equations.

Keywords

65Y0435K05Transient heat transfermeshless methodsmethod of particular solutionsmethod of fundamental solutionsfrequency domainFourier transform
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 5 , October 2011 , pp. 572 - 585
Copyright
Copyright © Global-Science Press 2011

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