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A convexification-based numerical method for a coefficient inverse problem for a parabolic PDE is presented. The key element of this method is the presence of the so-called Carleman weight function in the numerical scheme. Convergence analysis ensures the global convergence of this method, as opposed to the local convergence of the conventional least squares minimization techniques. Numerical results demonstrate a good performance. [ABSTRACT FROM AUTHOR]

We consider approximate cloaking from a regularization viewpoint introduced in Kohn et al (2008 Inverse Problems 24 015016) for EIT and further investigated in Kohn et al (2010 Commun. Pure Appl. Math. 63 0973-1016) and Liu (2009 Inverse Problems 25 045006) for the Helmholtz equation. The cloaking schemes given by Kohn et al and Liu are shown to be (optimally) within | ln ρ|-1 in 2D and ρ in 3D of perfect cloaking, where ρ denotes the regularization parameter. In this paper, we show that by employing a soundhard layer right outside the cloaked region, one could (optimally) achieve ρN in RN, N ≥ 2, which significantly enhances the near-cloak. We then develop a cloaking scheme by making use of a lossy layer with well-chosen parameters. The lossy-layer cloaking scheme is shown to possess the same cloaking performance as the one with a sound-hard layer. Moreover, it is shown that the lossy layer could be taken as a finite realization of the sound-hard layer. Numerical experiments are also presented to assess the cloaking performances of all the cloaking schemes for comparisons. [ABSTRACT FROM AUTHOR]