A numerical study of super-resolution through fast 3D wideband algorithm for scattering in highly-heterogeneous media |
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| Affiliation: | 1. Reservoir Labs, New York City, NY, United States;2. Division of Computer, Electrical and Mathematical Science and Engineering, King Abdullah University of Science and Technology, Thuwal, 23955-2900, Saudi Arabia;3. Department of Mathematics, Stanford University, United States;4. Laboratoire de Probabilités et Modèles Aléatoires, Université Paris Diderot, France;5. Institute for Computational and Mathematical Engineering, Stanford University, United States;6. Mechanical Engineering Department, Stanford University, CA, United States;1. Kuang-Chi Institute of Advanced Technology, Shenzhen, 518057, China;2. Donbass State Engineering Academy, 84303, Kramatorsk, Donetsk, Ukraine;1. Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa ON K1N 6N5, Canada;2. Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, CY 1678 Nicosia, Cyprus;3. Department of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia;1. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu, China;2. LSEC, Institute of Computational Mathematics and Scientific Engineering Computing, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China;3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China;4. School of Mathematical Sciences, Ocean University of China, Qingdao, Shandong, China;1. Institut für Mathematik, University Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland;2. Institute of Applied Mechanics, Graz University of Technology, 8010 Graz, Austria |
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| Abstract: | We present a wideband fast algorithm capable of accurately computing the full numerical solution of the problem of acoustic scattering of waves by multiple finite-sized bodies such as spherical scatterers in three dimensions. By full solution, we mean that no assumption (e.g. Rayleigh scattering, geometrical optics, weak scattering, Born single scattering, etc.) is necessary regarding the properties of the scatterers, their distribution or the background medium. The algorithm is also fast in the sense that it scales linearly with the number of unknowns. We use this algorithm to study the phenomenon of super-resolution in time-reversal refocusing in highly-scattering media recently observed experimentally (Lemoult et al., 2011), and provide numerical arguments towards the fact that such a phenomenon can be explained through a homogenization theory. |
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| Keywords: | Fast multipole method Multiple scattering Waves in inhomogeneous media Super-resolution Homogenization |
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