An Inverse Problem in Estimating the Time Dependent Source Term and Initial Temperature Simultaneously by the Polynomial Regression and Conjugate Gradient Method

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Coskun A.

FILOMAT, cilt.34, sa.10, ss.3507-3516, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 10
  • Basım Tarihi: 2020
  • Doi Numarası: 10.2298/fil2010507c
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.3507-3516
  • Anahtar Kelimeler: Inverse source problem, parabolic problem, Tikhonov functional, polynomial regression, conjugate gradient method, RIGHT-HAND SIDE, NUMERICAL-METHOD, EQUATION, IDENTIFICATION
  • Kocaeli Üniversitesi Adresli: Evet

Özet

From the final and interior temperature measurements identifying the source term with initial temperature simultaneously is an inverse heat conduction problem which is a kind of ill-posed. The optimal control framework has been found to be effective in dealing with these problems. However, they require to find the gradient information. This idea has been employed in this research. We derive the gradient of Tikhonov functional and establish the stability of the minimizer from the necessary condition. The stability and effectiveness of evolutionary algorithm are presented for various test examples.