A Numerical Method for Reconstructing the Coefficient in a Wave Equation
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AbstractWe present a numerical method for reconstructing the coefficient in a wave equation from a single measurement of partial Dirichlet boundary data. The original inverse problem is converted to a nonlinear integral differential equation, which is solved by an iterative method. At each iteration, one linear second-order elliptic problem is solved to update the reconstruction of the coefficient, then the reconstructed coefficient is used to solve the forward problem to obtain the new data for the next iteration. The initial guess of the iterative method is provided by an approximate model. This model extends the approximate globally convergent method proposed by Beilina and Klibanov, which has been well developed for the determination of the coefficient in a special wave equation. Numerical experiments are presented to demonstrate the stability and robustness of the proposed method with noisy data.(c) 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 289-307, 2015
All Author(s) ListChow YT, Zou J
Journal nameNumerical Methods for Partial Differential Equations
Volume Number31
Issue Number1
Pages289 - 307
LanguagesEnglish-United Kingdom
Keywordsreconstruction; single measurement; wave equation
Web of Science Subject CategoriesMathematics; Mathematics, Applied

Last updated on 2021-22-01 at 01:12