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.

[1]  H. Engl,et al.  Regularization of Inverse Problems , 1996 .

[2]  C. Kelley.  Existence and uniqueness of solutions of nonlinear systems of conductive-radiative heat transfer equations , 1996 .

[3]  M. Laitinen,et al.  Integro-differential equation modelling heat transfer in conducting, radiating and semitransparent materials , 1998 .

[4]  René Pinnau,et al.  A HIERARCHY OF APPROXIMATIONS TO THE RADIATIVE HEAT TRANSFER EQUATIONS: MODELLING, ANALYSIS AND SIMULATION , 2005 .

[5]  R. Pinnau,et al.  Newton's method for optimal temperature-tracking of glass cooling processes , 2007 .

[6]  R. Pinnau,et al.  Initial temperature reconstruction for nonlinear heat equation: application to a coupled radiative–conductive heat transfer problem , 2008 .

[7]  Asymptotic and discrete concepts for optimal control in radiative transfer , 2007 .

[8]  M. Modest.  Radiative heat transfer , 1993 .

[9]  J. Lang.  Adaptive computation for boundary control of radiative heat transfer in glass , 2005 .

[10]  Axel Klar,et al.  New Frequency-Averaged Approximations to the Equations of Radiative Heat Transfer , 2004, SIAM J. Appl. Math..

[11]  René Pinnau,et al.  Analysis of optimal boundary control for radiative heat transfer modeled by the $SP_{n}$-system , 2007 .

[12]  R. Pinnau.  Model Reduction via Proper Orthogonal Decomposition , 2008 .

[13]  Initial Temperature Reconstruction for a Nonlinear Heat Equation: Application to Radiative Heat Transfer , 2005 .

[14]  G. Thömmes,et al.  Optimal boundary control of glass cooling processes , 2004 .

[15]  Axel Klar,et al.  Numerical Solvers for Radiation and Conduction in High Temperature Gas Flows , 2005 .

[16]  Guido Thömmes.  Radiative Heat Transfer Equations for Glass Cooling Problems: Analysis and Numerics , 2002 .

[17]  M. K. Choudhary,et al.  Mathematical modeling in the glass industry : An overview of status and needs , 1997 .

[18]  Axel Klar,et al.  Half-moment closure for radiative transfer equations , 2002 .

[19]  Axel Klar,et al.  Simplified P N approximations to the equations of radiative heat transfer and applications , 2002 .

[20]  René Pinnau,et al.  Radiation, Frequency Averaging and Proper Orthogonal Decomposition , 2006 .

[21]  Mohammed Seaïd,et al.  Optimal control in radiative transfer , 2007, Optim. Methods Softw..

[22]  R. Pinnau,et al.  Regularized fixed-point iterations for nonlinear inverse problems , 2006 .

[23]  Alexander Schulze,et al.  Model reduction techniques for frequency averaging in radiative heat transfer , 2007, J. Comput. Phys..

[24]  O. S. Narayanaswamy.  A Model of Structural Relaxation in Glass , 1971 .