A method of fundamental solutions for two-dimensional heat conduction

Abstract

We investigate an application of the method of fundamental solutions (MFS) to heat conduction in two-dimensional bodies, where the thermal diffusivity is piecewise constant. We extend the MFS proposed in Johansson and Lesnic [A method of fundamental solutions for transient heat conduction, Eng. Anal. Bound. Elem. 32 (2008), pp. 697–703] for one-dimensional heat conduction with the sources placed outside the space domain of interest, to the two-dimensional setting. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be obtained efficiently with small computational cost.

Keywords:

• heat conduction
• method of fundamental solutions

2000 AMS Subject Classifications :

• 35K05
• 35A35
• 65N35

Acknowledgements

The authors would like to thank the referees for their suggestions. The third author acknowledges financial support from EPSRC in the form of a Doctoral Training Grant (DTG).