Commun. Comput. Phys.,
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Volume 4.


The Method of Fundamental Solutions for Steady-State Heat Conduction in Nonlinear Materials

A. Karageorghis 1*, D. Lesnic 2

1 Department of Mathematics and Statistics, University of Cyprus, 1678 Nicosia, Cyprus.
2 Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK.

Received 19 October 2007; Accepted (in revised version) 21 February 2008
Available online 29 May 2008

Abstract

The steady-state heat conduction in heat conductors with temperature dependent thermal conductivity and mixed boundary conditions involving radiation is investigated using the method of fundamental solutions. Various computational issues related to the method are addressed and numerical results are presented and discussed for problems in two and three dimensions.

AMS subject classifications: 65N35, 65N38, 65H10

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Key words: Nonlinear heat conduction, radiation, method of fundamental solutions.

*Corresponding author.
Email: andreask@ucy.ac.cy (A. Karageorghis), amt5ld@maths.leeds.ac.uk (D. Lesnic)
 

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