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Просмотр Публикации по Ключевые слова "3D inverse problem for determining inhomogeneities"

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    Computing Magnifier for Refining the Position and Shape of Three-Dimensional Objects in Acoustic Sensing
    (2022) Bakushinsky, A. B.; Leonov, A. S.; Леонов, Александр Сергеевич
    Abstract: A computational procedure is proposed for refining the position and shape of three-dimensional acoustic inhomogeneities during the sound probing of a medium. The procedure, called a computing magnifier, is based on a high-speed algorithm for solving the inverse problem of acoustic sounding in areas of a special structure (three-dimensional space, cylindrical area, etc.) with a complex wave field amplitude as the data recorded in a thin layer. The algorithm was proposed and studied by the authors in their previous works. The computational magnifying procedure consists of quickly solving the inverse problem using this algorithm on the initial grid in the original 3D region, narrowing the original region to a nested smaller new region containing inhomogeneities, and then solving the inverse problem in this new region on a new grid with the same or even with fewer nodes. By repeating this procedure several times, we can significantly refine the position and shape of the studied inhomogeneities, as if enlarging them. The computational magnifying procedure works much faster than solving the inverse problem on adaptively refined 3D grids in the original area. This makes it easy to implement the procedure on personal computers (PCs) with average performance. A method for the numerical estimation of the quality of refining the position and shape of the studied inhomogeneities based on the use of histograms is proposed. A number of numerical model experiments on a PC on the use of a computing magnifier in a cylindrical region are presented. They include analysis of the quality of the position and shape of the refinement using histograms when solving an inverse problem with accurate and noisy data, the effect of averaging noisy data for determining the position and shape, experiments to assess the resolution of the computing magnifier, etc. The running time of the computing magnifier in each of these three-dimensional numerical experiments is about 10 s. © 2022, Pleiades Publishing, Ltd.