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Numerical methods for parameter identification in stationary radiative transfer. (English) Zbl 1333.49050
Summary: We investigate the identification of scattering and absorption rates in the stationary radiative transfer equation. For a stable solution of this parameter identification problem, we consider Tikhonov regularization in Banach spaces. A regularized solution is then defined via an optimal control problem constrained by an integro-partial differential equation. By establishing the weak continuity of the parameter-to-solution map, we are able to ensure the existence of minimizers and thus the well-posedness of the regularization method. In addition, we prove certain differentiability properties, which allow us to construct numerical algorithms for finding the minimizers and to analyze their convergence. Numerical results are presented to support the theoretical findings and illustrate the necessity of the assumptions made in the analysis.

MSC:
49N45 Inverse problems in optimal control
49M30 Other numerical methods in calculus of variations (MSC2010)
49J20 Existence theories for optimal control problems involving partial differential equations
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
35R09 Integral partial differential equations
35Q93 PDEs in connection with control and optimization
Software:
TIGRA
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References:
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