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An optimal perturbation regularization algorithm for function reconstruction and its application. (English) Zbl 1317.65196

Wang, Yanfei (ed.) et al., Computational methods for applied inverse problems. Selected papers based on the presentations at the international workshop, Beijing, China, July 12–16, 2010. Berlin: de Gruyter (ISBN 978-3-11-025904-9/hbk; 978-3-11-025905-6/ebook). Inverse and Ill-Posed Problems Series 56, 143-167 (2012).
Summary: This chapter deals with several inverse problems of determining coefficient functions in advection-diffusion equation by an optimal perturbation regularization algorithm. The inversion algorithm is implemented successfully with numerical simulations for reconstruction problems of time-dependent, and space-dependent linear function, and state-dependent nonlinear source term, and space-dependent diffusion coefficient, respectively. Furthermore, the inversion algorithm is applied to determine key parameters in two real inverse problems, and reconstructed data basically coincide with the measured data.
For the entire collection see [Zbl 1255.65010].

MSC:

65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
65D15 Algorithms for approximation of functions
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