#### Title

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

#### Document Type

Article

#### Publication Date

10-1-2011

#### Department

Mathematics

#### School

Mathematics and Natural Sciences

#### 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.

#### Publication Title

Advances in Applied Mathematics and Mechanics

#### Volume

3

#### Issue

5

#### First Page

572

#### Last Page

585

#### Recommended Citation

Tadeu, A.,
Chen, C.,
António, J.,
Simões, N.
(2011). A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform. *Advances in Applied Mathematics and Mechanics, 3*(5), 572-585.

Available at: https://aquila.usm.edu/fac_pubs/352