Adaptive wavelet methods and sparsity reconstruction for inverse heat conduction problems

作者：Bonesky Thomas; Dahlke Stephan^*; Maass Peter; Raasch Thorsten

来源：Advances in Computational Mathematics, 2010, 33(4): 385-411.

DOI：10.1007/s10444-010-9147-2

• Regularization of ill-posed problems
• Sparsity
• Adaptive numerical schemes
• Parabolic partial differential equations
• Iterated soft shrinkage

This paper is concerned with the numerical treatment of inverse heat conduction problems. In particular, we combine recent results on the regularization of ill-posed problems by iterated soft shrinkage with adaptive wavelet algorithms for the forward problem. The analysis is applied to an inverse parabolic problem that stems from the industrial process of melting iron ore in a steel furnace. Some numerical experiments that confirm the applicability of our approach are presented.

• 出版日期2010-11