Geodesic
Algorithm for searching inhomogeneities in inverse nonlinear diffraction problems
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 166 (2024) no. 3, pp. 395-406 Cet article a éte moissonné depuis la source Math-Net.Ru

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This study aims to solve the inverse problem for determining the heterogeneity of an object. The scattered field was measured outside its boundaries at a set of observation points. Both the radiation source and observation points were assumed to be located outside the object. The scattered field was modeled by solving the direct problem. The inverse problem was solved using a two-step method. Nonlinearities of various types were considered. When introducing the computational grid, the generalized grid method was applied. A numerical method for solving the problem was proposed and implemented. The numerical results obtained illustrate how the problem is solved for specified experimental data.
Keywords: two-step method, integral equation, nonlinear diffraction problem, collocation method, numerical method. 
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     author = {A. O. Lapich and M. Y. Medvedik},
     title = {Algorithm for searching inhomogeneities in inverse nonlinear diffraction problems},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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     year = {2024},
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     url = {http://geodesic.mathdoc.fr/item/UZKU_2024_166_3_a8/}
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A. O. Lapich; M. Y. Medvedik. Algorithm for searching inhomogeneities in inverse nonlinear diffraction problems. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 166 (2024) no. 3, pp. 395-406. http://geodesic.mathdoc.fr/item/UZKU_2024_166_3_a8/

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