nach oben

Journal of Applied Mathematics and Computing

Erschienen in:

22.10.2019 | Original Research

Two-dimensional inverse heat conduction problem in a quarter plane: integral approach

verfasst von: Anis Bel Hadj Hassin, Lahcène Chorfi

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2020

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

We consider a two-dimensional inverse heat conduction problem in the region \(\lbrace x>0, y >0 \rbrace \) with infinite boundary which consists to reconstruct the boundary condition \(f(y,t)=u(0,y,t)\) on one side from the measured temperature \(g(y,t)=u(1,y,t)\) on accessible interior region. The numerical solution of the direct problem is computed by a boundary integral equation method. The inverse problem is equivalent to an ill-posed integral equation. For its approximation we use the regularization of Tikhonov after the mollification of the noised data \(g_\delta \) of exact data g. We show some numerical examples to illustrate the validity of the method.

Vorheriger Artikel Nonhomogeneous backward heat conduction problem: Compact filter regularization and error estimates

Nächster Artikel On -valued automata: an operator oriented view

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Busby, H.R., Trujillo, D.M.: Numerical solution to a two-dimensional inverse heat conduction problem. Int. J. Numer. Methods Eng. 21, 349–359 (1985)MATHCrossRef

Chapko, R.: On the numerical solution of direct and inverse problems for the heat equation in a semi-infinite region. J. Comput. Appl. Math. 108, 41–55 (1999)MathSciNetMATHCrossRef

Chorfi, L., Alem, L.: Stable algorithm for identifying a source in the heat equation. Electron. J. Differ. Equ. 267, 1–14 (2015)MathSciNetMATH

Costabel, M.: Boundary integral operators for the heat equation. Integral Equ. Oper. Theory 13(4), 498–552 (1990) MathSciNetMATHCrossRef

Eldén, L., Berntsson, F., Reginska, T.: Wavelet and Fourier methods for solving the sideways heat equation. SIAM J. Sci. Comput. 21(6), 2187–2205 (2000)MathSciNetMATHCrossRef

Engl, H.W., Langthaler, T.: Numerical solution of an inverse problem connected with continuous casting of steel. Z. Oper. Res. 9(6), B185–B199 (1985)MATH

Frankel, J.I.: Residual-minimization least-squares method for inverse heat conduction. Comput. Math. Appl. 32(4), 117–130 (1996)MathSciNetMATHCrossRef

Groetsch, C.W.: The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind. Pitman (Advanced Publishing Program), Boston (1984) MATH

Guo, L., Murio, D.: A mollified space-marching finite-different algorithm for the two-dimensional inverse heat conduction problem with slab symmetry. Inverse Probl. 7(2), 247 (2011)MATHCrossRef

10.

Garshasbi, M., Hassani, F.: Boundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method. Bull. Iran. Math. Soc. 42(5), 1039–1057 (2016)MathSciNetMATH

11.

Guenther, R., Lee, J.: Differential Equations of Mathematical Physics and Integral Equations. Dover, New York (1988)

12.

Häo, D.N.: A mollification method for ill-posed problems. Numer. Math. 68, 469–506 (1994)MathSciNetMATHCrossRef

13.

Hansen, P.C.: Regularization tools version 4.0 for Matlab 7.3. Numer. Algorithms 46(2), 189–194 (2007)MathSciNetMATHCrossRef

14.

Hsiao, G.C., Saranen, J.: Boundary integral solution of the two-dimensional heat equation. Math. Methods Appl. Sci. 16(2), 87–114 (1993)MathSciNetMATHCrossRef

15.

Jonas, P., Louis, A.K.: Approximate inverse for a one-dimensional inverse heat conduction problem. Inverse Probl. 16(1), 175 (2000)MathSciNetMATHCrossRef

16.

Jia, X.Z., Wang, Y.B.: A boundary integral method for solving inverse heat conduction problem. J. Inverse Ill Posed Probl. 14(4), 375–384 (2006)MathSciNetMATHCrossRef

17.

Kaiser, Th, Troltzsch, F.: An inverse problem arising in the steel cooling process. Wiss. Z. Tech. Univ. Karl Marx Stadt 29(2), 212–218 (1987)MathSciNetMATH

18.

Kirsch, A.: An Introduction to the Mathematical Theory of Inverse Problems, vol. 20. Springer, Berlin (2011)MATHCrossRef

19.

Lamm, P.K.: A Survey of Regularization Methods for First-kind Volterra Equations. Surveys on Solution Methods for Inverse Problems, pp. 53–82. Springer, Berlin (2000)MATHCrossRef

20.

Liu, Y., Murio, D.A.: Numerical experiments in 2-D IHCP on bounded domains Part I: The “interior” cube problem. Comput. Math. Appl. 31(1), 15–32 (1996)MathSciNetMATHCrossRef

21.

Lesnic, D., Elliott, L., Ingham, D.B.: Application of the boundary element method to inverse heat conduction problems. Int. J. Heat Mass Transf. 39(7), 1503–1517 (1996)MATHCrossRef

22.

Murio, D.A.: The Mollification Method and the Numerical Solution of Ill-Posed Problems. Wiley, New York (2011)

23.

Piessens, R., Verbaeten, P.: Numerical solution of the Abel integral equation. BIT Numer. Math. 13(4), 451–457 (1973)MathSciNetMATHCrossRef

24.

Qian, Z., Fu, C.-L.: Regularization strategies for a two-dimensional inverse heat conduction problem. Inverse Probl. 23(3), 1053–1068 (2007)MathSciNetMATHCrossRef

25.

Reinhardt, H.-J.: A numerical method for the solution of two-dimensional inverse heat conduction problems. Int. J. Numer. Methods Eng. 32(2), 363–383 (1991)MATHCrossRef

26.

Weir, G.J.: Surface mounted heat flux sensors. ANZIAM J. 7(3), 281–294 (1986)MathSciNetMATH

27.

Wirgin, A.: The inverse crime. arXiv preprint arXiv:math/0401050 (2004)

Titel: Two-dimensional inverse heat conduction problem in a quarter plane: integral approach
verfasst von: Anis Bel Hadj Hassin
Lahcène Chorfi
Publikationsdatum: 22.10.2019
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2020
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-019-01297-4

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 1-2/2020

Global behavior of a rational second order difference equation

A two-step improved Newton method to solve convex unconstrained optimization problems

A new algorithm for solving multi-valued variational inequality problems

Mathematical modeling and dynamic analysis of anti-tumor immune response

Novel numerical method of the fractional cable equation

Non-interior-point smoothing Newton method for CP revisited and its application to support vector machines