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Identification of Microscopic Flaws Arising in Thermal Tomography by Domain Decomposition Method

  • Fumio Kojima
Part of the Progress in Systems and Control Theory book series (PSCT, volume 11)

Abstract

Recently, interest in computed thermal tomography has grown, particularly for application to the detection of corrosions or microcrack cLusters which often occur in passenger airplanes or space flight systems. The purpose of the method is to detect cracks inside a material rapidly and nondestructively by analyzing thermogra.phical data collected from the front surface of the material. Figure 1.1 ilLustrates this thermal technique using the infrared imaging. As depicted in, adding the heat source to the front, such as a laser beam, the thermographical data can be recorded by the infrared camera. Mathematically, to estimate the structural information with the thermal data can be formulated as a geometrical heat inverse problem. Previous efforts on the the inverse formulation of 2-D thermal tomography have been discussed in [1] [2] using the so-called “method of mapping”. The efficacy of the algorithm proposed in [1] and [2] has been supported by various kinds of simulation and laboratory data. However, for practical use of our inverse algorithm, we further pay our attention to the following points. The objects which we have to inspect are generally complicated. Hence a simple mapping technique applied in the previous reports is not always sufficient to the practical use. Moreover, in large and complicated objects such as passenger airplanes, rapid inspections are definitely required. The fast and compact algorithm is highly desirable for practical application. Taking into account these, we propose a new method using the domain decomposition approach. The domain decomposition method is very classical tool for solving elliptic partial differential equations. Recently there has been a strong revival of the interest in this method due to its potential in highly parallel computing environments. Our aim of this paper is to show the applicability of the inverse approach based on the domain decomposition method to the practical thermal technique.

Keywords

Domain Decomposition Front Surface Thermal Tomography Domain Decomposition Method Elliptic Partial Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    H.T. Banks and F. Kojima, “Boundary Shape Identification Problems in Two-Dimensional Domains Related to Thermal Testing of Materials,” Quart. Appl. Math., v. 47, 1989, pp. 273–293.Google Scholar
  2. 2.
    H.T. Banks and F. Kojima, “Boundary Estimation Problems Arising in Thermal Tomography,” ICA SE Report No. 89–44, NASA Langley Research Center, November 1989: To appear in Inverse Problems. Google Scholar
  3. 3.
    P.E. Bjorstad and O.B. Widlund, “Iterative Methods for the SoLution of Elliptic Problems on Regions Partitioned into Substructures,” SIAM J. Numer. Anal., v. 23, 1986, pp. 1097–1120.CrossRefGoogle Scholar
  4. 4.
    T.F. Chan and D. Goovaerts, “Schwarz = Schur: Overlapping versus Nonoverlapping Domain Decomposition,” to appear in SIAM J. Math. Anal. Google Scholar
  5. 5.
    J.E. Dennis Jr. and R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equation, Prentice-Hall, Englewood Ciffs, N,J, 1983.Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Fumio Kojima
    • 1
  1. 1.Center for Applied Mathematical SciencesUniversity of Southern CaliforniaLos AngelesUSA

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