A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems

Abstract

We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric and axisymmetric backward heat conduction problem (BHCP) in a solid or hollow cylinder. In the BHCP, the initial temperature is to be determined from the temperature measurements at a later time. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach [B.T. Johansson and D. Lesnic, A method of fundamental solutions for transient heat conduction, Eng. Anal. Boundary Elements 32 (2008), pp. 697–703] for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.

Keywords:

• heat conduction
• method of fundamental solutions (MFS)
• axisymmetric heat equation
• radially symmetric heat equation
• backward inverse problem

Keywords:

• 35K05
• 35A35
• 65N35

Acknowledgements

The authors thank the referees for their suggestions. The third author thanks the financial support received from the EPSRC.