Splitting-based conjugate gradient method for a multi-dimensional linear inverse heat conduction problem

Dinh Nho Hào, Nguyen Trung Thành, Hichem Sahli

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

In this paper we consider a multi-dimensional inverse heat conduction problem with time-dependent coefficients in a box, which is well-known to be severely ill-posed, by a variational method. The gradient of the functional to be minimized is obtained by the aid of an adjoint problem, and the conjugate gradient method with a stopping rule is then applied to this ill-posed optimization problem. To enhance the stability and the accuracy of the numerical solution to the problem, we apply this scheme to the discretized inverse problem rather than to the continuous one. The difficulties with large dimensions of discretized problems are overcome by a splitting method which only requires the solution of easy-to-solve one-dimensional problems. The numerical results provided by our method are very good and the techniques seem to be very promising.

Original languageEnglish (US)
Pages (from-to)361-377
Number of pages17
JournalJournal of Computational and Applied Mathematics
Volume232
Issue number2
DOIs
StatePublished - Oct 15 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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