Abstract
This note is concerned with the evaluation of the unknown diffusion coefficient in a steady-state heat conduction problem. The proposed method is iterative and, starting with an initial guess, updates the assumed value at every iteration. The updating stage is achieved by generating a set of functions that satisfy some of the required boundary conditions. The correction to the assumed value is then computed by imposing the remaining boundary conditions. Numerical examples are used to study the applicability of this method.
Issue Section:
Research Papers
References
1.
Calderon
, A. P.
, 2006
, “On an Inverse Boundary Value Problem
,” Comput. Appl. Math.
, 25
(2–3
), pp. 133
–138
.2.
Holder
, D. S.
, 2005
, Electrical Impedance Tomography: Methods, History and Applications
, Institute of Physics, Philadephia, PA.3.
Mansouri
, W.
, Baranger
, T.
, Ameur
, H.
, and Tlatli
, N.
, 2016
, “Identification of Injection and Extraction Wells From Overspecified Boundary Data
,” Inverse Probl. Sci. Eng.
, 25
(8
), pp. 1091
–1111
.4.
Zou
, Y.
, and Guo
, Z.
, 2003
, “A Review of Electrical Impedance Techniques for Breast Cancer Detection
,” Med. Eng. Phys.
, 25
(2
), pp. 79
–90
.5.
van den Doel
, K.
, and Ascher
, U.
, 2006
, “On Level Set Regularization for Highly Ill-Posed Distributed Parameter Estimation Problems
,” J. Comput. Phys.
, 216
(2
), pp. 707
–723
.6.
Roininen
, L.
, Huttunen
, J. M. J.
, and Lasanen
, S.
, 2014
, “Whittle-Matérn Priors for Bayesian Statistical Inversion With Applications in Electrical Impedance Tomography
,” Inverse Probl. Imaging
, 8
(2
), p. 561
.7.
Wang
, M.
, 2002
, “Inverse Solutions for Electrical Impedance Tomography Based on Conjugate Gradients Methods
,” Meas. Sci. Technol.
, 13
(1
), p. 101
.8.
Brandstätter
, B.
, Hollaus
, K.
, Hutten
, H.
, Mayer
, M.
, Merwa
, R.
, and Scharfetter
, H.
, 2003
, “Direct Estimation of Cole Parameters in Multifrequency Eit Using a Regularized Gauss-Newton Method
,” Physiol. Meas.
, 24
(2
), p. 437
.9.
Sun
, B.
, Yue
, S.
, Cui
, Z.
, and Wang
, H.
, 2015
, “A New Linear Back Projection Algorithm to Electrical Tomography Based on Measuring Data Decomposition
,” Meas. Sci. Technol.
, 26
(12
), p. 125402
.10.
Tadi
, M.
, 2017
, “On Elliptic Inverse Heat Conduction Problems
,” ASME J. Heat Transfer
, 8
(7
), p. 139
.11.
Wang
, Y.
, and Tadi
, M.
, 2017
, “On Evaluation of the Initial Condition for a Parabolic System
,” Int. J. Heat Mass Transfer
, 115
, pp. 424
–427
.Copyright © 2019 by ASME
You do not currently have access to this content.
