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The reciprocity gap method for a cavity in an inhomogeneous medium

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  • We consider an interior inverse medium problem of reconstructing the shape of a cavity. Both the measurement locations and point sources are inside the cavity. Due to the lack of a priori knowledge of physical prosperities of the medium inside the cavity and to avoid the computation of background Green's functions, the reciprocity gap method is employed. We prove the related theory and present some numerical examples for validation.
    Mathematics Subject Classification: Primary: 78A46, 31A10; Secondary: 45Q05.

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