Source strength identification problem for the three-dimensional inverse heat conduction equations

ABSTRACT

In this paper, we consider the source strength identification problem for the three-dimensional inverse heat conduction equations. The problem is to determine an unknown heat source strength from the measurement data for a specified location. In this process, the direct problem is solved by applying the Green’s function method. Then, this problem can be converted into a Volterra integral equation of the first kind. Further, the Tikhonov and truncated singular value decomposition regularization methods are developed to identify the unknown source strength based on the discrepancy principle for choosing the regularization parameter. Finally, numerical examples are presented to show the feasibility and efficiency of the proposed method.

KEYWORDS:

• Inverse heat conduction problem
• source strength
• integral equation
• regularization

SUBJECT CLASSIFICATIONS CODE:

• 35K05
• 35R30
• 45Q05

Acknowledgements

We would like to thank the referees for constructive suggestions and comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the Natural Science Basic Research Plan in Shaanxi Province of China [grant number 2019JM-284].