A boundary element method for a multi-dimensional inverse heat conduction problem

Abstract

In this paper, we investigate a variational method for a multi-dimensional inverse heat conduction problem in Lipschitz domains. We regularize the problem by using the boundary element method coupled with the conjugate gradient method. We prove the convergence of this scheme with and without Tikhonov regularization. Numerical examples are given to show the efficiency of the scheme.

Keywords:

• inverse heat conduction problem
• ill-posed problem
• boundary element method
• Lipschitz domain
• conjugate gradient method
• Tikhonov regularization

2000 AMS Subject Classification :

• 65M32
• 65M30
• 65M38

Acknowledgements

This research was supported by a Marie Curie International Incoming Fellowship within the 7th European Community Framework Programme and, partially, by a Vietnam NAFOSTED Grant.