Abstract
This paper is concerned with a geometrical identification of corrosion shape in the thermal testing of materials. To estimate the corrosion shape of materials, we formulate a parameter estimation problem using temperature data from the front surface of materials. We propose a new estimation algorithm based on the time-dependent boundary integral equation method. Summaries of computational experiments by the proposed method are given.
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References
H. T. Banks and F. Kojima, Approximation techniques for domain identification in two-dimensional parabolic systems under boundary observations, Proc. 20th IEEE CDC Conference, Los Angeles, Dec. 9–11, 1987, pp. 1411–1416.
H. T. Banks and F. Kojima, Boundary identification for 2-D parabolic systems arising in thermal testing of materials, Proc. 21th IEEE CDC Conference, Austin, T., Dec. 7–9, 1988, pp. 1678–1683.
H. T. Banks and F. Kojima, Boundary shape identification problems in two-dimensional domains related to thermal testing of materials, Quart. Appl. Math. 47 (1989), 273–293.
H. T. Banks, F. Kojima and W. P. Winfree, Boundary estimation problems arising in thermal tomography, ICASE Report 89–44, NASA Langley Research Center, November, 1989; To appear in Inverse Problems.
C. A. Brrebia, J. C. F. Telles and L. C. Wrobel, Boundary Element Techniques, Theory and Applications in Engineering, Springer, New York, 1984.
D. M. Heath, C. S. Welch and W. P. Winfree, Quantitative thermal diffusivity measurements of composites, Review of Progress in Quantitative Nondestructive Evaluation, vol. 5B, Plenum Publ., 1986, pp.1125–1132.
F. Kojima, Shape identification technique for a 2-D elliptic system by boundary integral equation method, Proc. of the 5th Symp. on Control of Distributed Parameter Systems, Perpignan, France, July 1989.
D. N. Arnold and W. L. Wendland, On the asymptotic convergence of collocation methods, Math. Comp. 41 (1983), 349–381.
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© 1991 Springer Basel AG
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Kojima, F. (1991). A computational method for thermal tomography by time dependent boundary integral equation method. In: Desch, W., Kappel, F., Kunisch, K. (eds) Estimation and Control of Distributed Parameter Systems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 100. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6418-3_15
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DOI: https://doi.org/10.1007/978-3-0348-6418-3_15
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-2676-0
Online ISBN: 978-3-0348-6418-3
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