Abstract
We construct, analyze and implement an approximately globally convergent finite element scheme for a hyperbolic coefficient inverse problem in the case of backscattering data. This extends the computational aspects introduced in Asadzadeh and Beilina (Inv. Probl. 26, 115007, 2010), where using Laplace transformation, the continuous problem is reduced to a nonlinear elliptic equation with a gradient dependent nonlinearity. We investigate the behavior of the nonlinear term and discuss the stability issues as well as optimal a posteriori error bounds, based on an adaptive procedure and due to the maximal available regularity of the exact solution. Numerical implementations justify the efficiency of adaptive a posteriori approach in the globally convergent setting.
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References
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Tables of dielectric constants at http://www.asiinstr.com/technical/DielectricConstants.htm
Software package WavES at http://www.waves24.com/
Acknowledgements
The research of the authors was supported by the Swedish Research Council, the Swedish Foundation for Strategic Research (SSF) through the Gothenburg Mathematical Modelling Centre (GMMC), and by the Swedish Institute, Visby Program.
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Asadzadeh, M., Beilina, L. (2013). Adaptive Approximate Globally Convergent Algorithm with Backscattered Data. In: Beilina, L., Shestopalov, Y. (eds) Inverse Problems and Large-Scale Computations. Springer Proceedings in Mathematics & Statistics, vol 52. Springer, Cham. https://doi.org/10.1007/978-3-319-00660-4_1
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DOI: https://doi.org/10.1007/978-3-319-00660-4_1
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