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.
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A Sequential Gradient Method for the Inverse Heat Conduction Problem (IHCP)
K. J. Dowding,
K. J. Dowding
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824
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J. V. Beck
J. V. Beck
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824
Search for other works by this author on:
K. J. Dowding
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824
J. V. Beck
Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824
J. Heat Transfer. May 1999, 121(2): 300-306 (7 pages)
Published Online: May 1, 1999
Article history
Received:
July 9, 1997
Revised:
December 8, 1998
Online:
December 5, 2007
Citation
Dowding, K. J., and Beck, J. V. (May 1, 1999). "A Sequential Gradient Method for the Inverse Heat Conduction Problem (IHCP)." ASME. J. Heat Transfer. May 1999; 121(2): 300–306. https://doi.org/10.1115/1.2825980
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