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Volume 3, Issue 5
A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform

A. Tadeu, C. S. Chen, J. Antόnio & Nuno Simões

Adv. Appl. Math. Mech., 3 (2011), pp. 572-585.

Published online: 2011-03

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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

Transient heat transfer, meshless methods, method of particular solutions, method of fundamental solutions, frequency domain, Fourier transform.

  • AMS Subject Headings

65Y04, 35K05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-3-572, author = {A. and Tadeu and and 20340 and and A. Tadeu and C. S. and Chen and and 20341 and and C. S. Chen and J. and Antόnio and and 20342 and and J. Antόnio and Nuno and Simões and and 20344 and and Nuno Simões}, title = {A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2011}, volume = {3}, number = {5}, pages = {572--585}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1039}, url = {http://global-sci.org/intro/article_detail/aamm/183.html} }
TY - JOUR T1 - A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform AU - Tadeu , A. AU - Chen , C. S. AU - Antόnio , J. AU - Simões , Nuno JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 572 EP - 585 PY - 2011 DA - 2011/03 SN - 3 DO - http://doi.org/10.4208/aamm.10-m1039 UR - https://global-sci.org/intro/article_detail/aamm/183.html KW - Transient heat transfer, meshless methods, method of particular solutions, method of fundamental solutions, frequency domain, Fourier transform. AB -

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.

A. Tadeu, C. S. Chen, J. Antόnio & Nuno Simões. (1970). A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform. Advances in Applied Mathematics and Mechanics. 3 (5). 572-585. doi:10.4208/aamm.10-m1039
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