Proceedings of the 5th International Conference on Inverse Problems in Engineering: Theory and Prac- tice, Cambridge, UK, 11-15th July 2005 COMPARISON OF A GENETIC ALGORITHM AND A GRADIENT BASED OPTI- MISATION TECHNIQUE FOR A THREE-DIMENSIONAL BOUNDARY DETECTION PROBLEM
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چکیده
In this paper we consider the determination of the shape of an unkown portion of the boundary of a three-dimensional solution domain from Cauchy data on the remaining portion of the boundary. This problem arises in the study of quantitative non-destructive evaluation of corrosion in materials in which boundary measurements of currents and voltages are used to determine the material loss caused by corrosion. The domain identification problem is considered as a variational problem to minimize a defect functional, which utilises some additional data on certain known parts of the boundary. A sequential quadratic programming (SQP) optimisation algorithm and a real coded genetic algorithm (GA) are used in order to minimise the objective functional. The unknown boundary is parameterized using B-splines. The Laplace equation is discretised using the method of fundamental solutions (MFS). Numerical results are presented and discussed for several test examples.
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تاریخ انتشار 2005