NUMERICAL COMPARISON OF ITERATIVE AND FUNCTIONAL-ANALYTICAL ALGORITHMS FOR INVERSE ACOUSTIC SCATTERING
نویسندگان
چکیده
In this work the numerical solution of acoustic tomography problem based on iterative and functional-analytical algorithms is considered. The mathematical properties these were previously described in works R.G.Novikov for case Schr\"odinger equation. present work, two-dimensional scalar Helmholtz equation, efficiency algorithm reconstruction middle strength scatterers advantages approach recovering strong are demonstrated. A filtering procedure considered space wave vectors, which additionally increases convergence algorithm. Reconstruction results sound speed perturbations demonstrate comparable noise immunity resolution when reconstructing scatterers. comparative investigation inverse scattering problems implemented first time.
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Since supp f ⊂ Ω, uθ satisfies the plain Helmholtz equation with constant wavenumber outside of Ω, the radiation condition and uθ|∂Ω = gθ. So by solving the exterior problem of the Helmholtz equation (analytically if Ω is a circle), uθ can be computed everywhere outside of Ω without prior knowledge of f . In particular, we can compute h = ∂uθ ∂ν on ∂Ω. Thus, our original problem can be rewritte...
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ژورنال
عنوان ژورنال: Eurasian journal of mathematical and computer applications
سال: 2022
ISSN: ['2306-6172', '2308-9822']
DOI: https://doi.org/10.32523/2306-6172-2022-10-1-79-99