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Comparison of a genetic algorithm and a gradient based optimisation technique for the detection of subsurface inclusions. (English) Zbl 1106.35137
Summary: An inverse problem is considered to identify the geometry of discontinuities in a conductive material $$\Omega\subset \mathbb R^2$$ with anisotropic conductivity $$(I+(K-I)\chi D$$ from Cauchy data measurements taken on the boundary $$\partial\Omega$$, where $$D\subset\Omega$$, $$K$$ is a symmetric and positive definite tensor not equal to the identity tensor and $$\chi D$$ is the characteristic function of the domain $$D$$. In this study we use a real coded genetic algorithm in conjunction with a boundary element method to detect an anisotropic inclusion $$D$$, such as a circle, by a single boundary measurement. Numerical results are presented for both isotropic and anisotropic inclusions. The results obtained using the genetic algorithm are compared with the results obtained using a gradient based method. The genetic algorithm based method developed in this paper is found to be a robust, efficient method for detecting the size and location of subsurface inclusions.
##### MSC:
 35R30 Inverse problems for PDEs 65N21 Numerical methods for inverse problems for boundary value problems involving PDEs 65N38 Boundary element methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations
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