A Sequential Gradient Method for the Inverse Heat Conduction Problem (IHCP)

Author:

Dowding K. J.1,Beck J. V.1

Affiliation:

1. Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824

Abstract

A sequential-in-time implementation is proposed for a conjugate gradient method using an adjoint equation approach to solve the inverse heat conduction problem (IHCP). Because the IHCP is generally ill-posed, Tikhonov regularization is included to stabilize the solution and allow for the inclusion of prior information. Aspects of the sequential gradient method are discussed and examined. Simulated one and two-dimensional test cases are evaluated to study the sequential implementation. Numerical solutions are obtained using a finite difference procedure. Results indicate the sequential implementation has accuracy comparable to the standard whole-domain solution, but in certain cases requires significantly more computational time. Benefits of the on-line nature of a sequential method may outweigh the additional computational requirements. Methods to improve the computational requirements, which make the method competitive with a whole domain solution, are given.

Publisher

ASME International

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics,General Materials Science

Reference21 articles.

1. Alifanov, O. M., Artyukhin, E. A., and Rumyantsev, S. V., 1996, Extreme Methods for Solving III-Posed Problems with Applications to Inverse Heat Transfer Problems, Begell House, New York.

2. Alifanov, O. M., 1994, Inverse Heat Transfer Problems, Springer-Verlag, New York.

3. Alifanov O. M. , and EgorovYu. V., 1985, “Algorithms and Results of Solving the Inverse Heat Conduction Problem in a Two-Dimensional Formulation,” Journal of Engineering Physics, Vol. 48, No. 4, pp. 489–496.

4. Alifanov O. M. , and KerovN. V., 1981, “Determination of External Thermal Load Parameters by Solving the Two-Dimensional Inverse Heat Conduction Problem,” Journal of Engineering Physics, Vol. 41, No. 4, pp. 1049–1053.

5. Artyukhin, E. A., and Gedzhadze, I. Yu., 1994, “Sequential Regularization Solution of a Boundary Inverse Heat Conduction Problem,” 2nd Joint Russian-America Workshop on Inverse Problems in Engineering, Aug., St. Petersberg, Russia.

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