Determination of a spacewise dependent heat source

By T. Johansson, Daniel Lesnic. 2007

179 citations recorded by the source corpus.

This paper investigates the inverse problem of determining a spacewise dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from a supplementary temperature measurement at a given single instant of time. The spacewise dependent temperature measurement ensures that the inverse problem has a unique solution, but this solution is unstable, hence the problem is ill-posed. For this inverse problem, we propose an iterative algorithm based on a sequence of well-posed direct problems which are solved at each iteration step using the boundary element method (BEM). The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for various typical benchmark test examples which have the input measured data perturbed by increasing amounts of random noise.

Subfields: Aerospace Engineering, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e81fca765fd349c56ee342ecbabbf0ff0a560a6e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Aerospace Engineering

1. C. Fu
2. Fan Yang
3. B. Johansson
4. Daniel Lesnic
5. Liang Yan
6. Fangfang Dou

In Computational Mechanics

1. C. Fu
2. Fan Yang
3. B. Johansson
4. Daniel Lesnic
5. Fangfang Dou
6. Liang Yan
7. Ting Wei

In Mathematical Physics

1. C. Fu
2. Fan Yang
3. B. Johansson
4. Daniel Lesnic
5. Ting Wei
6. Hai-Hua Qin
7. Liviu Marin
8. Fangfang Dou

Citations in the corpus

• A procedure for determining a spacewise dependent heat source and the initial temperature (2008, methodology): “Under these conditions, the operator L generates a C0 (continuous) contraction semi-group {G(t)}t2Rþ in L (2)( ) with DðLÞ 1⁄4 fu : u 2 H(1)0ð Þ, Lu 2 L(2)ð Þg a dense set of its domain, see [8].”
• A simplified Tikhonov regularization method for determining the heat source (2010, methodology): “In [5,6], the authors determined the heat source dependent on one variable in a bounded domain by the boundary-element method and an iterative algorithm.”