A new coupled complex boundary method (CCBM) for an inverse obstacle problem

نویسندگان

چکیده

<p style='text-indent:20px;'>In the present work we introduce and study a new method for solving inverse obstacle problem. It consists in identifying perfectly conducting inclusion <inline-formula><tex-math id="M1">\begin{document}$ \omega $\end{document}</tex-math></inline-formula> contained larger bounded domain id="M2">\begin{document}$ \Omega via boundary measurements on id="M3">\begin{document}$ \partial $\end{document}</tex-math></inline-formula>. In order to solve this problem, use coupled complex (CCBM), originaly proposed [<xref ref-type="bibr" rid="b16">16</xref>]. The transforms our problem with Robin condition coupling Dirichlet Neumann data. Then, optimize shape cost function constructed by imaginary part of solution whole determine id="M4">\begin{document}$ Thanks tools optimization, prove existence derivative state respect id="M5">\begin{document}$ We characterize gradient functional make numerical resolution. then investigate stability optimization explain why is severely ill-posed proving compactness Hessian at critical shape. Finally, some results are presented compared classical methods.</p>

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ژورنال

عنوان ژورنال: Discrete and Continuous Dynamical Systems - Series S

سال: 2022

ISSN: ['1937-1632', '1937-1179']

DOI: https://doi.org/10.3934/dcdss.2021069