An iterative bem for the cauchy steady state heat conduction problem in an anisotropic medium with unknown thermal conductivity tensor

Abstract

In this paper we propose an alternating iterative boundary element method (BEM) to simultaneously predict the unknown conductivity coefficients and the unknown boundary data for a Cauchy steady state heat conduction problem in an anisotropic medium. This complex ill-posed problem is obtained by combining a Cauchy inverse thermal problem with a parameter estimation problem. The numerical algorithm is based on an iterative (BEM) combined with a least squares technique. The numerical results obtained confirm that provided that an appropriate stopping regularization criterion is imposed, the iterative BEM produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data. An efficient stopping regularization criterion to cease the iterative process is proposed and a variable relaxation factor is used to increase the rate of convergence of the algorithm.

Keywords:

• Boundary element method
• Iterative techniques
• Cauchy problem
• Anisotropic medium
• Thermal conductivity tensor
• Heat conduction

^*Corresponding author. Fax: [phone]

^*Corresponding author. Fax: [phone]

Notes

^*Corresponding author. Fax: [phone]