Numerical solution of the problem of computational time reversal in a quadrant |
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Authors: | Michael V Klibanov Sergey I Kabanikhin Dmitrii V Nechaev |
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Institution: |
a Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC, USA
b Sobolev Institute of Mathematics, Prospect Acad. Koptyuga 2, Novosibirsk, Russia
c Lavrent'ev Institute of Hydrodynamics, Prospect Acad. Lavrent'eva 15, Novosibirsk, Russia |
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Abstract: | The problem of computational time reversal is posed as the inverse problem of the determination of an unknown initial condition with a finite support in a hyperbolic equation, given the Cauchy data at the lateral surface. Two such two-dimensional inverse problems are solved numerically in the case when the domain is a quadrant and the Cauchy data are given at finite parts of the coordinate axes. The previously obtained Lipschitz stability estimate implies refocusing of the time-reversed wave field in the case of a small amount of noise in the data. It also indicates the possibility of good performance of a proper numerical method. Such performance is demonstrated in this paper for a particular problem and a particular numerical method. |
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