Optimization and Inverse Problems in Radiative Heat Transfer
We discuss the derivation and investigation of efficient mathematical methods for the solution of optimization and identification problems for radiation dominant processes, which are described by a nonlinear integrodifferential system or diffusive type approximations. These processes are for example relevant in glass production or in the layout of gas turbine combustion chambers. The main focus is on the investigation of optimization algorithms based on the adjoint variables, which are applied to the full radiative heat transfer system as well as to diffusive type approximations. In addition to the optimization we also study new approaches to the reconstruction of the initial temperature from boundary measurements, since its precise knowledge is mandatory for any satisfactory simulation. In particular, we develop a fast, derivative-free method for the solution of the inverse problem, such that we can use many different models for the simulation of the radiative process.
KeywordsRadiative heat transfer SPnapproximation optimal boundary control inverse problem optimality conditions analysis numerics adjoints integro-differential equations reduced order modeling.
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- 1.M.K. Choudhary and N.T. Huff. Mathematical modeling in the glass industry: An overview of status and needs. Glastech. Ber. Glass Sci. Technol., 70:363–370, 1997.Google Scholar
- 6.M. Hinze, R. Pinnau, M. Ulbrich and S. Ulbrich. Optimization with Partial Differential Equations. Mathematical Modelling: Theory and Applications, Volume 23, Springer, 2009.Google Scholar
- 12.M.F. Modest, Radiative Heat Transfer. McGraw-Hill, 1993.Google Scholar
- 14.S. Pereverzyev. Method of Regularized Fixed-Point and its Application. PhD Thesis, TU Kaiserslautern, 2006.Google Scholar
- 15.S. Pereverzyev, R. Pinnau and N. Siedow. Initial Temperature Reconstruction for a Nonlinear Heat Equation: Application to Radiative Heat Transfer. D. Lesnic (ed.), Proceedings of the 5th International Conference on Inverse Problems in Engineering: Theory and Practice, Cambridge. Vol. III, ch. P02, pp. 1–8, 2005.Google Scholar
- 19.R. Pinnau. Model Reduction via Proper Orthogonal Decomposition. In W.H.A. Schilder, H. van der Vorst: Model Order Reduction: Theory, Research Aspects and Applications, pp. 96–109, Springer, 2008.Google Scholar
- 25.A. Schulze. Minimizing thermal stresses in glass cooling processes. PhD thesis, TU Kaiserslautern, 2006.Google Scholar
- 27.G. Thömmes, Radiative Heat Transfer Equations for Glass Cooling Problems: Analysis and Numerics, PhD Thesis, TU Darmstadt, 2002.Google Scholar