Reconstruction algorithms of an inverse geometric problem for the modified Helmholtz equation
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In this paper, we consider an inverse geometric problem for the modified Helmholtz equation from measurements of the potential taken on the boundary of the geometrical domain. Our goal is to seek reconstruction algorithms to detect the number, the location, the size and the shape of unknown obstacles from Cauchy data on the external boundary. This problem is ill-posed and nonlinear, thus we should employ regularization techniques in our proposed algorithms. We give several numerical examples to demonstrate the stability of numerical algorithms.
KeywordsTrust-region-reflective optimization algorithm Levenberg–Marquardt algorithm Modified Helmholtz equation Ill-posed problem
Mathematics Subject Classification65N20 65N21
The research of Ji-Chuan Liu was supported by the NSF of China (11601512, 11326236, 11501562) and the Fundamental Research Funds for the Central Universities (2014QNA57).