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TECHNICAL PAPERS: Conduction Heat Transfer

The Steady Inverse Heat Conduction Problem: A Comparison of Methods With Parameter Selection

[+] Author and Article Information
Robert Throne

Department of Electrical Engineering, University of Nebraska, Lincoln, NE 68588e-mail: rthrone1@unl.edu

Lorraine Olson

Department of Mechanical Engineering and Department of Engineering Mechanics, University of Nebraska, Lincoln, NE 68588

J. Heat Transfer 123(4), 633-644 (Feb 01, 2001) (12 pages) doi:10.1115/1.1372193 History: Received February 18, 2000; Revised February 01, 2001
Copyright © 2001 by ASME
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References

Olson,  L. G., and Throne,  R. D., 2000, “A Comparison of the Generalized Eigensystem, Truncated Singular Value Decomposition, and Tikhonov Regularization for the Steady Inverse Heat Conduction Problem,” Inverse Problems in Engineering, 8, pp. 193–227.
Throne,  R., and Olson,  L., 1994, “A Generalized Eigensystem Approach to the Inverse Problem of Electrocardiography,” IEEE Trans. Biomed. Eng., 41, pp. 592–600.
Throne,  R. D., and Olson,  L. G., 1995, “The Effects of Errors in Assumed Conductivities and Geometry on Numerical Solutions to the Inverse Problem of Electrocardiography,” IEEE Trans. Biomed. Eng., 42, pp. 1192–1200.
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Throne,  R. D., Olson,  L. G., and Hrabik,  T. J., 1999, “A Comparison of Higher-Order Generalized Eigensystem Techniques and Tikhonov Regularization for the Inverse Problem of Electrocardiography,” Inverse Problems in Engineering, 7, pp. 143–193.
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Figures

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Typical geometry for inverse boundary value problem in steady heat conduction
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First cluster for the GESL method for the square with holes geometry
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Second cluster for the GESL method for the square with holes geometry
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Third cluster for the GESL method for the square with holes geometry
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L-curve used for identifying appropriate t values for zero order Tikhonov regularization
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L-curve used for identifying appropriate Nclusters values for GESL
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Geometry and finite element mesh for annulus test case. (Inner circle has radius 0.5, outer circle has radius 1.0.)
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Forward computed temperature contours for second annulus test case. (Temperature is zero on inner boundary; contour level intervals are 0.1.)
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Geometry and finite element mesh for square with holes. The outer square is 1.0×1.0. The first inner rectangle is centered at (0.275,0.375) and is 0.15×0.25. The second inner rectangle is centered at (0.65,0.65) and is 0.2×0.2. The radii of the corners on the inner rectangles is 0.01.
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Temperature contours for first square with holes test case. (Temperature is 1.0 on inner boundaries, 0.0 on outer boundary. Contours are at temperature intervals of 0.1.)
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Temperature contours for second square with holes test case: (a) “true” forward computed solution; (b) a GESL inverse solution when 5 percent noise is added to the outer temperatures and fluxes; and (c) a zero-order Tikhonov inverse solution when 5 percent noise is added to the outer temperatures and fluxes. (Temperature contours at 0.0, 0.1,[[ellipsis]]1.0.)
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Temperature contours for third square with holes test case. (Minimum temperature 0.69, maximum temperature 4.84. Contour 1:1.11 2:1.52 3:1.94 4:2.35 5:2.77 6:3.18 7:3.60 8:4.01 9:4.43).

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