355
Views
12
CrossRef citations to date
0
Altmetric
Original Articles

Different finite element approaches for inverse heat conduction problems

&
Pages 3-17 | Received 15 Oct 2008, Accepted 15 Apr 2009, Published online: 08 Oct 2009

References

  • Reddy, JN, and Gartling, DK, 1994. The Finite Element Method in Heat Transfer and Fluid Dynamics. London: CRC Press; 1994.
  • Lewis, RW, Morgan, K, Thomas, HR, and Seetharamu, KN, 1995. The Finite Element Method in Heat Transfer Analysis. New York: John Wiley and Sons; 1995.
  • Bergheau, J-M, and Fortunier, FR, 2008. Finite Element Simulation of Heat Transfer. New York: ISTE Ltd and John Wiley & Sons Inc.; 2008.
  • Mukaddes, AMM, Shioza, R, and Ogino, M, 2006. Parallel finite element analysis of a non-steady heat conductive problem, Int. J. Theoret. Appl. Mech. 1 (1) (2006), pp. 51–61.
  • Ling, X, and Atluri, SN, 2006. Stability analysis for inverse heat conduction problems, Comput. Modeling Eng. Sci. (CMES) 13 (3) (2006), pp. 219–228.
  • Grysa, K, Ciałkowski, MJ, and Kamiński, H, 1981. An inverse temperature field in the theory of thermal stresses, Nucl. Eng. Design 64 (2) (1981), pp. 169–184.
  • Grysa, K, 1989. On the exact and approximate methods of solving inverse problems of temperature fields. Poznań: Rozprawy, Politechnika Poznańska, 204; 1989, (in Polish).
  • Hensel, EC, and Hills, RG, A space marching finite difference algorithm for the one dimensional inverse conduction heat transfer problem, ASME Paper, No. 84-HT-48, 1984.
  • Hore, PS, Kruttz, GW, and Schoenhals, RJ, Application of the finite element method to the inverse heat conduction problem, ASME Paper, No. 77-WA/TM-4, 1977.
  • Bass, B, 1980. Application of the finite element method to the nonlinear inverse heat conduction problem using Beck's second method, Trans. ASME 102 (1980), pp. 168–176.
  • Tikhonov, AN, and Arsenin, VY, 1977. Solution of Ill-posed Problems. Washington, DC: Wiley & Sons; 1977.
  • Alifanov, OM, 1994. Inverse Heat Transfer Problems. New York: Springer-Verlag; 1994.
  • Jirousek, J, 1978. Basis for development of large finite elements locally satisfying all field equations, Comp. Meth. Appl. Eng. 14 (1978), pp. 65–92.
  • Jirousek, J, and Wróblewski, A, 1996. T-elements: State of the art and future trends, Arch. Comp. Meth. Eng. 3 (1996), pp. 323–434.
  • Qin, Q-H, 2000. The Trefftz Finite and Boundary Element Method. Southampton: WIT Press; 2000.
  • Stein, E, 1973. "Die kombination des modifizierten Treffzschen Verfahrens mit der Methode der Finite Elemente". In: Buck, K, Scharpf, D, Stein, E, and Wunderlich, W, eds. Finite Elemente in der Statik. Berlin: Wilhelm Ernst & Sohn; 1973. pp. 172–185.
  • Ruoff, G, 1973. "Die praktische Berechnung der Kopplungsmatrizen bei der Kombination dder Treffzschen Methode und der Methode der Finiten Elemente bei flachen Schalen". In: Buck, K, Scharpf, D, Stein, E, and Wunderlich, W, eds. Finite Elemente in der Statik. Berlin: Wilhelm Ernst & Sohn; 1973. pp. 242–259.
  • Wood, WI, and Lewis, RW, 1975. A comparison of time marching schemes for the transient heat conduction equation, Int. J. Numer. Meth. Eng. 9 (1975), pp. 679–689.
  • Futakiewicz, S, 1999. "Heat functions method for solving direct and inverse heat conduction problems". In: Ph.D. thesis. Poznań: Politechnika Poznańska; 1999, (in Polish).
  • Hożejowski, L, 1999. "Heat polynomials and their applications for solving direct and inverse problems of heat conduction". In: Ph.D. thesis. Kielce: Politechnika Świe¸tokrzyska; 1999, (in Polish).
  • Ciałkowski, MJ, and Fra¸ckowiak, A, 2001. Solution of the stationary 2D inverse heat conduction problem by Trefftz method, J. Thermal Sci. 11 (2) (2001), pp. 148–162.
  • Ciałkowski, MJ, 2001. New type of basic functions of FEM in application to solution of inverse heat conduction problem, J. Thermal Sci. 11 (2) (2001), pp. 163–171.
  • Ciałkowski, MJ, Fra¸ckowiak, A, and Grysa, K, 2007. Solution of a stationary inverse heat conduction problem by means of Trefftz non-continuous method, Int. J. Heat Mass Transfer 50 (11–12) (2007), pp. 2170–2181.
  • Sladek, J, Sladek, V, and Hon, YC, 2006. Inverse heat conduction problems by meshless local Petrov–Galerkin method, Eng. Anal. Boundary Elements 30 (2006), pp. 650–661.
  • Ciałkowski, MJ, Fra¸ckowiak, A, and Grysa, K, 2007. Physical regularization for inverse problems of stationary heat conduction, J. Inv. Ill-Posed Problems 15 (4) (2007), pp. 347–364.
  • Grysa, K, 2003. Heat polynomials and their applications, Arch. Thermodynamics 24 (2) (2003), pp. 107–124.
  • Macia¸g, A, and Wauer, J, 2005. Wave polynomials for solving different types of two-dimensional wave equations, Comput. Assisted Mech. Eng. Sci. 12 (2005), pp. 87–102.
  • Macia¸g, A, 2007. Wave polynomials in elasticity problems, Eng. Trans. 55 (2) (2007), pp. 129–153.
  • Hon, YC, and Wei, T, 2004. A fundamental solution method for inverse heat conduction problem, Eng. Anal. Boundary Elements 28 (2004), pp. 489–495.
  • Hon, YC, and Wei, T, 2005. The method of fundamental solutions for solving multidimensional inverse heat conduction problems, Comput. Modeling Eng. Sci. (CMES) 7 (2005), pp. 119–132.
  • Huang, CH, and Chen, CW, 1998. A boundary-element-based inverse problem of estimating boundary conditions in an irregular domain with statistical analysis, Numerical Heat Transfer, Part B 33 (1998), pp. 251–268.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.