Numerical solution of an inverse problem of coefficient recovering for a wave equation by a stochastic projection methods

Kabanikhin Sergey I. (), Sabelfeld Karl K. (), Novikov Nikita S. () and Shishlenin Maxim A. ()
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Kabanikhin Sergey I.: Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Prospect Akademika Lavrentjeva, 6, and Novosibirsk State University, Pirogova St., 2, 630090, Novosibirsk, Russia
Sabelfeld Karl K.: Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Prospect Akademika Lavrentjeva, 6, and Novosibirsk State University, Pirogova St., 2, 630090, Novosibirsk, Russia
Novikov Nikita S.: Novosibirsk State University, Pirogova St., 2, 630090, Novosibirsk, Russia
Shishlenin Maxim A.: Sobolev Institute of Mathematics SB RAS, Akad. Koptyug avenue, 4, and Novosibirsk State University, Pirogova St., 2, 630090, Novosibirsk, Russia

Monte Carlo Methods and Applications, 2015, vol. 21, issue 3, 189-203

Abstract: An inverse problem of reconstructing the two-dimensional coefficient of the wave equation is solved by a stochastic projection method. We apply the Gel'fand–Levitan approach to reduce the nonlinear inverse problem to a family of linear integral equations. The stochastic projection method is applied to solve the relevant linear system. We analyze the structure of the problem to increase the efficiency of the method by constructing an improved initial approximation. A smoothing spline is used to treat the random errors of the method. The method has low cost and memory requirements. Results of numerical calculations are presented.

Keywords: Wave equation; inverse problems; Gel'fand–Levitan equations; Monte Carlo methods; stochastic projection algorithm (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1515/mcma-2015-0103

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