Determination of a spacewise dependent heat source

Tomas Johansson, Daniel Lesnic

    Research output: Contribution to journalArticlepeer-review


    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.
    Original languageEnglish
    Pages (from-to)66-80
    Number of pages15
    JournalJournal of Computational and Applied Mathematics
    Issue number1
    Early online date4 Dec 2006
    Publication statusPublished - 1 Dec 2007


    • boundary element method
    • discrepancy principle
    • heat source
    • inverse problem
    • iterative regularization
    • parabolic heat equation.


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