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    Solving the Inverse Problems of Laplace Equation to Determine the Robin Coefficient/Cracks' Position Inside a Disk

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 1-28, 2009, DOI:10.3970/cmes.2009.040.001

    Abstract We consider an inverse problem of Laplace equation by recoverning boundary value on the inner circle of a two-dimensional annulus from the overdetermined data on the outer circle. The numerical results can be used to determine the Robin coefficient or crack's position inside a disk from the measurements of Cauchy data on the outer boundary. The Fourier series is used to formulate the first kind Fredholm integral equation for the unknown data f(θ) on the inner circle. Then we consider a Lavrentiev regularization, by adding an extra term αf(θ) to obtain the second kind Fredholm integral More >

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